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Condition evaluation of urban metro shield tunnels in Shanghai through multiple indicators multiple causes model combined with multiple regression method
Tunnelling and Underground Space Technology 85 (2019) 170–181
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Condition evaluation of urban metro shield tunnels in Shanghai through multiple indicators multiple causes model combined with multiple regression method Xueqin Chena, Xiaojun Lib, Hehua Zhub, a b
T
⁎
Department of Civil Engineering, College of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
ARTICLE INFO
ABSTRACT
Keywords: Tunnel Serviceability Index (TSI) MIMIC Multiple regression Condition evaluation Metro shield tunnel Latent variable
Many existing condition evaluations of metro shield tunnels are developed based on the experts’ judgments or single deformation/defect measurements. In addition, the influence of factors such as buried depth and age on the condition of shield tunnels was not quantified in previous research. This study proposed a comprehensive condition index, the Tunnel Serviceability Index (TSI), through the Multiple Indicators Multiple Causes (MIMIC) model combined with a multiple regression method. The contributions of the deformation/defect variables and the influencing factors to the TSI were evaluated. The observed deformation/defect variables included average relative settlement, differential settlement, average convergence ratio, water leakage area, cracking length, and spalling area. The influencing factors included the operation age, burial depth, and so on. The relationship among the TSI, deformation/defect variables, and influence factors was quantified, and an expression for the TSI was obtained. The paired-sample t test demonstrated that there were no significant differences between the experts’ ratings in our group’s previous research and the tunnel condition evaluation used by the MIMIC model in this study at the significance level = 0.05. Among the six observed deformation and defect variables, approximately 95% of the TSI deterioration was caused by the increase of convergence ratio, relative settlement and differential settlement. Finally, the case of Shanghai Metro Line No. 1 was investigated to evaluate its condition.
1. Introduction It has been more than 25 years since the first metro shield tunnel was put into use in Shanghai in the 1990s. Metro tunnels have played a vital role in improving the construction of urban infrastructure systems and facilitating public transportation. Meanwhile, as a type of underground structure, shield tunnels have some unique characteristics, such as uncertainty, nonreversibility, high construction and accident costs and long service periods when compared with superstructures. Since the metro shield tunnels in Shanghai are excavated in soft soils, the uncertainty of shield tunnels results primarily from the uncertainty of geological conditions, such as the uncertainty of the soil characteristics and unexpected presence of water, the uncertainty of the loading conditions including the water pressure, soil pressure and the interaction between the shield tunnels and stratum, and the uncertainty of the analysis model. The nonreversibility refers to the idea that once the shield tunnels are excavated, the strata are disturbed, and it is
⁎
impossible for the geological strata to be restored to their original state. High cost is necessary even if the underground space can be theoretically restored. Therefore, it is of great importance to evaluate and then maintain the condition of shield tunnels above a certain level, predict performance and eventually make cost-effective maintenance and rehabilitation decisions. Ever since beginning operation, the occurrence of defects and deformation has contributed to the deterioration of shield tunnels. Based on experts’ experience and the inspection and monitoring data of shield tunnels in Shanghai, the current major defects include water leakage, segment spalling, cracking, segment faulting, joint opening, material deterioration and forth. The structural deformation includes the circumferential convergence, longitudinal settlement, and longitudinal differential settlement. The extent and severity of defects and deformations can reflect the condition of shield tunnels. Many researchers have made great efforts to evaluate the conditions of shield tunnels based on defect and deformation measurements through various
Corresponding author. E-mail addresses: [email protected] (X. Chen), [email protected] (X. Li), [email protected] (H. Zhu).
https://doi.org/10.1016/j.tust.2018.11.044 Received 13 December 2015; Received in revised form 29 August 2018; Accepted 25 November 2018 0886-7798/ © 2018 Published by Elsevier Ltd.
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analysis methods. Wu et al. (2007) analyzed the influence of cracking width, length, direction and density on the durability of segment structure through fuzzy synthetic discrimination. The health conditions of shield tunnels in Shanghai were classified into five grades through fuzzy synthetic discrimination and an analytic hierarchy process based on water leakage, circumferential deformation, and longitudinal deformation measurements (Ye, 2007; Ye et al., 2007). Xu et al. (2010) evaluated the effect of defects on shield tunnels by using the improved analytic hierarchy process-product scale method. Yuan et al. (2012) categorized the service states of the lining structures of shield tunnels into five grades, namely, Suitable, Degraded, Deteriorated, Unavailable and Unstable, by taking the inspection data of the structural condition and operation condition into consideration. It can be summarized that most existing condition assessments of shield tunnels are based on empirical or qualitative judgments. Meanwhile, the threshold values of some defects and deformations in shield tunnels were regulated by codes to evaluate the condition (Ministry of Construction of the People's Republic of China, 2003, 2008). For instance, the threshold value of convergence suggested by “Code for design of metro” is 4-6‰ D (D is the outer diameter of the shield tunnel), and the threshold value of cracking width suggested by “Technical code for waterproofing of underground works” is 0.2 mm. If the value is greater than the threshold, the corresponding maintenance and rehabilitation actions should be taken. Although a single defect or deformation measurement can provide information on the tunnel condition, the integrated condition index, which can take several defects or deformation measurements into consideration, is more intuitive and comprehensive. In pavement engineering, pavement performance is defined as the serviceability trend of the pavement over a design period of time, where serviceability indicates the ability of the pavement to serve the demand of the traffic in the existing condition (AASHO, 1962). The pavement distresses, such as cracking and rutting are measured and used to evaluate pavement serviceability. Similar to pavement serviceability, the Tunnel Serviceability Index (TSI) was proposed and adopted to assess the comprehensive condition of shield tunnels in this study. It is defined as the ability of shield tunnels to service the demand of the metro operation in the existing condition. The TSI can be quantified through inspected tunnel defects, including cracking, leakage, and spalling, and monitored deformation, including settlement and convergence. There are many factors related to the defects and deformation of shield tunnels: the soft soil deposits in Shanghai, land subsidence, project construction activity in the neighborhood of shield tunnels, design and construction quality and metro train vibration (Wang, 2009; Ye et al., 2007). Shen et al. (2014) summarized that the locations where the tunnel crosses below the river, where the soil conditions are various, between the station and tunnel section, and at the cross passage section are the main sections where differential settlement occurs. They also noted that the great long-term settlement in Shanghai results from sublayer subsidence, postconstruction settlement, nearby construction disturbances, groundwater infiltration and cyclic loading of trains (Shen et al., 2014). All of these factors interact in a complicated way, influencing the condition of shield tunnels. However, the effects of the factors on the condition of shield tunnels were not quantified in previous findings. Therefore, a multiple indicators multiple causes (MIMIC) model, which is a special case of a structural equation model (SEM), was adopted to analyze the complex relationships among variables, including the condition, the defect and deformation measurements, and the influencing factors in this study. An SEM is a statistical method that originates from the field of social science, psychology, economics and so on (Brown, 2014; Khine, 2013; Kline, 2010; Wang and Wang, 2012). It treats the variables that cannot be easily or directly measured as latent variables and the measured variables as observed variables. It can handle the complex relationships between latent and observed variables simultaneously. Although it is rarely used in the tunneling field, there are some applications in other
areas of engineering in recent years. In the traffic engineering field, Lee et al. (2008) proposed a new index named “traffic accident size” that is indicated by the number of deaths, the number of injured, the number of involved vehicles and the number of damaged vehicles. The relationship between traffic accident size and exogenous factors, including road factors, environmental factors, and driver factors, was estimated. Hassan and Abdel-Aty (2011) analyzed drivers’ responses under low visibility conditions and their relationships with visibility, traffic conditions, and roadway types. Jou et al. (2011) investigated freeway drivers’ intention to adopt electronic toll collection service by taking the effects of technology acceptance, planned behavior, impression changes, government attitude and risk into consideration. Cheng and Huang (2013) examined high-speed rail consumers’ willingness to adopt mobile ticketing services by considering both the metal accounting theory and technology acceptance model. In the pavement engineering field, Ben-Akiva and Ramaswamy (1993) estimated the latent pavement performance from the observed pavement damages, pavement characteristics, traffic and environmental factors, and maintenance activities through an SEM. Based on the work of Ben-Akiva and Ramaswamy (1993), Chu and Durango-Cohen (2008) used an SEM to estimate the effect of maintenance on rutting, slope variance and serviceability of pavements. Chen et al. (2016) proposed a combined pavement condition index by investigating the Long-Term Pavement Performance (LTPP) database. In this study, the tunnel condition cannot be measured directly, while the observed defects and deformation can indicate the degree of the tunnel condition. Since SEM has demonstrated great potential for extensive application to evaluate the correlations among latent variables and observed variables, it was used to analyze the shield tunnel condition for the first time in this study. The data, methodology, and results are discussed in the following sections. 2. Common defects and deformation in shield tunnels In Shanghai, most of the metro tunnels are constructed in the silty clay, silty clay and sandy silt layers that have some distinguishing characteristics, such as high underground water level, which is usually 0.5–0.7 m below the ground (Ding et al., 2008), high water content, high void ratio, high compressibility, low strength and low permeability (Ye et al., 2007). Considering the characteristics of soft deposits, the metro tunnels in Shanghai are usually driven by a Tunnel Boring Machine (TBM) in soft soils through methods such as Earth Pressure Balance (EPB) and Slurry Pressure Balance (SPB) rather than the cut and cover methods. The TBM assembles the segments together to form the tunnel lining. Generally, the segment lining of metro shield tunnels in Shanghai is composed of six segments: one capped block F, two adjacent blocks L1 and L2, two standard blocks B1 and B2, and one bottom block D, as shown in Fig. 1. For a whole segment ring, the central angles of the capped block F, adjacent block L1 (L2), standard block B1 (B2) and bottom block D are 16°, 65°, 65° and 84°, respectively. The adjacent segments are connected by circumferential bolts, and the adjacent lining rings are connected through longitudinal bolts. Under this circumstance, the longitudinal and circumferential joints are formed. The hand holes on the segments are prefabricated to install the bolts. Currently, the standard inner radius is 2750 mm, and the outer radius is 3100 mm in Shanghai, as shown in Fig. 1. Yuan et al. (2012) summarized many types of defects that exist in shield tunnels, such as chloride corrosion permeation, bolt rusting and cracking. Many of those defects are immeasurable because of the weak corrosive environment, the short operation age of metro shield tunnels in Shanghai and the insufficient inspection techniques currently. For instance, it is difficult to inspect the deterioration of the connectors between two adjacent segments at present. Based on previous experience and inspection and monitoring results, the common defects of metro shield tunnels in Shanghai include segment spalling, water leakage, cracking, faulting and joint opening, and the structural 171
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1. Joints For the transverse section of tunnel lining shown in Fig. 1, there are approximately six longitudinal joints in one lining ring. For a tunnel interval with a length of 1.2 km, there are approximately 1000 circumferential joints and 6000 longitudinal joints, which are the main water leakage paths, as shown in Fig. 2(a). 2. Grouting holes The prefabricated grouting holes on the segments are used to backfill grouting and then make up the strata loss. After the grouting is completed, the grouting holes become another main water leakage path, as shown in Fig. 2(b). 3. Bolt holes The diameter of the bolt hole is usually greater than that of the bolt to make the bolt installation procedure operable. If the ground water leaks through the opening joints, it can leak through the bolt holes into the tunnel, as shown in Fig. 2(c). 4. Segment cracking
Fig. 1. The segmental tunnel lining of the metro shield tunnel in Shanghai.
Segment cracking on the segment surface is also a leakage path, but it is quite rare, as shown in Fig. 2(d).
deformation includes circumferential convergence and longitudinal settlement (Li et al., 2017; Shanghai Rail Transit Maintenance Support Limited Company, 2010; Wang, 2009). Due to the limitations of visual inspection and manual measurement, the records of faulting and joint opening are much lower in number than for other defects. Therefore, faulting and joint opening were not investigated in this study. As automatic and advanced inspection techniques will be applied and more data will be available in the future, other types of defects can be added to the condition evaluation, and the model proposed in the following part of this study can be updated.
2.1.2. Spalling Spalling is the missing corner of segments, as shown in Fig. 3. The main reasons for spalling include initial construction defects and differential settlement. The initial construction defects include fabrication errors during the construction periods, the collision of segments during transportation, the assembling force acting on the segments during the assembling phase and operation mistakes. The differential settlement would cause extra moment, normal force and shear force on the lining and then cause spalling at the corner (Shanghai Rail Transit Maintenance Support Limited Company, 2010).
2.1. Defects 2.1.1. Water leakage Due to the abundant underground water in Shanghai, water leakage is one of the most severe defects. Generally, there are four main paths for water leakage in shield tunnels, as shown in Fig. 2.
2.1.3. Cracking Segment cracking is the cracking on the segment surface that inspectors can observe with the naked eye, as shown in Fig. 4. Cracking can be observed in the fabrication, construction and operation periods. Cracking is mainly caused by structural deformation and exterior loading (Wu et al., 2007). 2.2. Deformation The deformation in the shield tunnel includes the circumferential convergence in the transverse direction and settlement in the longitudinal direction.
(a). Leakage at the joints
(b). Leakage at the grouting hole
(c). Leakage at the bolt hole
(d). Leakage at the connected cracking
2.2.1. Circumferential convergence The tunnel squeezes under the act of soil pressure, and the squeezing shape in soft soils in Shanghai is usually similar to the
Fig. 2. Water leakage.
Fig. 3. Spalling. 172
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was determined. Therefore, the tunnel section with a length of 200 lining rings was also used in this study (Li et al., 2017). In addition, the results of Li et al. (2017) indicated that the variable square root of average relative settlement Settave , average differential settlement Settdiff _ave , average convergence ratio Covave , total water leakage area per 100 rings dl , total cracking length per 100 rings dc , and total spalling area per 100 rings ds can be used as the deformation and defect measurements. The average relative settlement Settave is the average of relative settlement Settri , and it can be calculated through Eq. (1).
Fig. 4. Cracking.
“transverse duck egg”. According to the Code for design of metro GB 50157-2003 (Ministry of Construction of the People's Republic of China, 2003), the circumferential convergence value should be less than 5‰ of D (D is the outer diameter of the shield tunnel). The statistical result of 46 lining rings of one tunnel interval in Shanghai shows that the convergence values of 85 percent of the monitored lining rings are greater than the regulated value (Ye et al., 2007). Large convergence could lead to longitudinal joint opening at the tunnel crown, cracking, etc. According to the research results (Wang and Zhang, 2013), when the convergence is approximately 7.7‰ of the tunnel outer diameter, the bolt stress would be 640 MPa, and it would yield. When the convergence is 9.6‰ of the tunnel outer diameter, the maximum joint opening value would be 6 mm, which is the waterproofing control standard.
Settave =
n i=1
Settri
(1)
n
where Settri (mm) is the relative settlement of the ith monitoring point. It is the difference of the settlement at the ith monitoring point Settri (mm) and the uniform settlement (minimal settlement) Settu (mm). Settri can be calculated through Eq. (2), where n is the total number of monitoring points, and i ranges from 1 to n.
Settri = Settti
(2)
Settu
Li et al. (2017) found that the goodness of fit of Settave was better than that of Settave . Therefore, Settave was used in the following analysis. The average differential settlement Settdiff _ave can be calculated through Eqs. (3) and (4).
Settdiff _i =
2.2.2. Longitudinal settlement The longitudinal settlement is the difference between the monitored elevation and the designed elevation at certain locations. Considering the soft deposit characteristics, the excessive pumping of groundwater, etc., Shanghai is going through a large land subsidence. The recorded cumulative subsidence has even been 2–3 m in the central area of Shanghai (Chai et al., 2004). Since the metro tunnel is constructed in soil, its deformation is consistent with the land subsidence. In addition to land subsidence, the construction of other engineering projects around the metro tunnel, the crossing tunnels, the cyclic loads above the tunnel and the increase of vertical loads can also cause settlement. According to the inspection and monitoring data, for some tunnel intervals, settlement was the most severe condition measurement that affected the tunnel condition. For instance, the settlement of the tunnel interval between People’s Square Station and South Huangpi Road Station was even greater than 200 mm. The various settlements at different locations form the differential settlement. The differential settlement of metro tunnels in Shanghai mainly occurs at the section where the soil conditions are various, between the station and tunnel section, and at the cross passage section (Shen et al., 2014). Great differential settlement may lead to the distortion of track (Wu et al., 2011) and aggregate water leakage, spalling, cracking and joint opening. According to the Code for design of metro GB 50157-2003 (Ministry of Construction of the People's Republic of China, 2003), the curvature radius in the longitudinal direction should be greater than 15,000 m.
|Settri
Settr (i li
n i=2
Settdiff _ave =
n
1) |
(3)
Settdiff _i
(4)
1
where Settdiff _i (mm/m) is the differential settlement between the ith and (i-1)th points; li (m) is the length between the ith and (i-1)th points; Settri (mm) is the relative settlement at the ith point; Settr (i 1) (mm) is the relative settlement at the (i-1)th point; and Settdiff _ave (mm) is the average differential settlement. The average convergence ratio Covave can be calculated through Eq. (5).
Covave =
m i=1
di
Dm
D
× 1000
(5)
where di (mm) is the monitored outer diameter at the ith point; D (mm) is the designed outer diameter; Covave (‰) is the average convergence ratio; and m is the number of monitoring points among the 200 lining rings. The total water leakage area per 100 rings dl (m2/100 rings) can be calculated through Eq. (6), where lt (m2) is the total leakage area in a tunnel section with 200 rings.
dl =
lt 2
(6)
The total cracking length per 100 rings dc (m/100 rings) can be calculated through Eq. (7), where ct (m) is the total cracking length in a tunnel section with 200 rings.
3. Data preparation
dc =
Currently, data on water leakage, spalling, cracking, circumferential convergence and longitudinal settlement are available for analysis. The data for metro shield tunnels in Shanghai in 2011 were collected by Shanghai Shen Tong Metro Group Co., Ltd. Metro lines 1, 2 and 4, including 182 tunnel sections (including both the upstream and downstream directions) and 36,400 segment lining rings, were investigated. In the previous research of our group, nine experts with abundant experience in the design, construction, administration, maintenance and research of shield tunnels in soft soils in Shanghai rated the serviceability of the tunnels, and the tunnel section with a length of 200 rings
ct 2
(7) 2
The total spalling area per 100 rings ds (m /100 rings) can be calculated through Eq. (8), where st (m2) is the total spalling area in a tunnel section with 200 rings.
ds =
st 2
(8)
Therefore, the six defect and deformation variables above are discussed and used in this study. Their descriptive statistics are shown in Table 1. The influencing factors considered in this study are DEPTH (the 173
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Table 1 Descriptive statistics of the observed variables. Genre
Variable
Description
Min.
Max.
Mean
S.D.
Skewness
Kurtosis
Deformation and Defect
Settave Settdiff _ave
Square root of average relative settlement
1.22
11.73
4.72
2.75
1.10
0.26
Average differential settlement (mm/m)
0.87
10.80 9.05 2.89 0.45
0.19
5.91 0.77 0.21 0.02
0.12
1.88 1.47 0.47 0.05
2.19
0.29 2.67 3.26 5.82
7.38
Covave dl dc ds
Average convergence ratio (‰) Total water leakage area per 100 rings (m2/100 rings) Total cracking length per 100 rings (m/100 rings) Total spalling area per 100 rings (m2/100 rings)
0.02
DEPTH STRATUM
Average burial depth (m) 0: Clay stratum; 1: Both clay and sandy silt stratum; 2: Sandy silt stratum 0: Not underneath a river; 1: Underneath a river 0: Not near the station or cross passage; 1: Near the station or cross passage Years from the opening year to 2011 (year)
6.98 0
21.56 2
13.95
3.31
0.00
-0.20
0
1
0
1
4
18.58
12.60
4.51
-0.51
-1.01
Influencing factor
RIVER STATION AGE
y 11 1 2
3
4
x1 x2
x3
x4
1
11
x11
y 21 y 31
x 21 x 31
1
21
2
12
x 41
y 42
2
y 52
y 62
y1
1
y2
2
y3
3
y4
y5 y6
−0.28 7.80 12.01 40.13
4: Statistical Methodology. Khine (2013) indicated that if the absolute value of skewness is greater than 3 and the absolute value of kurtosis is greater than 7, the variable is not normally distributed. As seen from Table 1, the observed variables Settdiff _ave , dc and ds are nonnormally distributed.
Structural model
1
1.51 0 0 0
4. Statistical methodology An SEM is a statistical approach that handles the assumed linear relationships among the latent and observed variables. The latent variables are the unobserved variables, and they are the linear combination of the observed variables. By estimating the coefficients, it can be concluded which is the major factor that influences the latent variable and which indicator is significant. Generally, an SEM consists of path analysis and confirmatory factor analysis. Compared with other methods, an SEM possesses some advantages, such as taking the latent variables into account, analyzing and estimating the complex relationships among latent and observed variables simultaneously (Hassan and Abdel-Aty, 2011; Lee et al., 2008).
4 5 6
Measurement model Fig. 5. Illustration of SEM.
average burial depth), STRATUM (the stratum that the tunnel section crossed), RIVER (whether the tunnel section crossed a river), STATION (whether the tunnel section was near a station or cross passage), and AGE (the operation age of the tunnel section) as shown in Table 1. The factors STRATUM, RIVER, and STATION are categorical variables. The variable STRATUM with a value of 0 indicates that the stratum the tunnel section crosses is clay, 2 indicates that the tunnel section crosses the sandy silt stratum and 1 indicates that the tunnel section crosses both the clay and sandy silt stratum. The variable RIVER with a value of 0 indicates that the tunnel section is not underneath a river, and 1 indicates that the tunnel section is underneath a river. The variable STATION with a value of 0 indicates that the tunnel section is not near a station or cross passage, and 1 indicates that the tunnel section is near a station or cross passage. The variables DEPTH and AGE are continuous variables. DEPTH is the average overburden soil depth above the top of the shield tunnel section. Note that for a tunnel section underneath a river, DEPTH is not the depth from the river surface to the top of the tunnel section but the depth from the soil surface to the top of the tunnel section. AGE is the service year of the metro tunnels and is calculated from the opening year of each metro tunnel section (Shen et al., 2014) to the year 2011. Table 1 shows the descriptive statistics of the observed variables. The six defect and deformation variables are set to “Y observed variables”, which can reflect the shield tunnel condition in the SEM, and the remaining five variables are “X observed variables”, which are the factors that could influence the condition of shield tunnels. The “Y observed variables” and “X observed variables” are elaborated in Part
4.1. Multiple indicators multiple causes (MIMIC) model An SEM consists of two models, the measurement model and structural model, as shown in Fig. 5. The structural model represents the relationship among the latent variables. It is the equation for the endogenous latent variables and exogenous latent variables . The measurement model can analyze the relationship between the observed variables and latent variables. There are two types of measurement models: one is the equation for the endogenous observed variables Y and endogenous latent variables , and the other is the equation for the exogenous observed variables X and exogenous latent variables . The basic form of an SEM is illustrated in Fig. 5. In Fig. 5, the ellipses with shading represent the unobserved variables ( and ), while the other ellipses without shading are the error variables including , and , which are the error terms of , Y and X , respectively; the rectangles represent the observed variables (X and Y); the single-headed arrows represent the path coefficients ( , B and ); and the double-headed arrows represent that the two variables are correlated with each other. The MIMIC model is a simplified SEM whose exogenous observed variable X is the perfect indicator of exogenous latent variable . Hence, the error term of X is set to zero, and the factor loading between exogenous observed variable X and exogenous latent variable equals 1, as shown in Eq. (11). Fig. 6 and Eqs. (9)–(11) show the illustration and equations of the MIMIC model, respectively. As seen from Fig. 6, the error term of X is 0, and there is one structural model and one measurement model in MIMIC. Eq. (9) is the structural model indicating the relationship between the endogenous latent variables and exogenous 174
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X
ξ
Structural model
4.2. Multiple regression method
Measurement model
1
x1
y 11
11
13
x3
14
22
x4
y 21
1
12
x2
Through the MIMIC model, the correlations among the endogenous latent variables, endogenous observed variables, and exogenous observed variables are investigated, but the value of endogenous latent variables cannot be obtained directly from the model. Thus, it is of great necessity to extract the value of endogenous latent variables from the observed variables based on the correlation results. The procedure for obtaining the endogenous latent variables from the observed endogenous and exogenous variables is elaborated in the Appendix. It can be seen from Eq. (A.8) that the endogenous latent variable is the function of the observed variables X , Y and the coefficients in Table 2. After the MIMIC model was analyzed, the coefficients listed in Table 2 and parameters 0 and 1 in Appendix A can be calculated. For each group of X and Y, the corresponding value of can be obtained through Eq. (A.8). Ben-Akiva and Ramaswamy (1993) indicated that the observed variables X can be treated as fixed variables, such as pavement type, material, weather, environment and traffic factors in pavement engineering. Meanwhile, traditional condition indices of infrastructure, such as pavements and bridges, are the formulas of various defect measurements. Therefore, the multiple regression method is employed to obtain the function of the shield tunnel condition indices on defect variables Y. The formula of the multiple regression model is shown in Eq. (12).
12
2
21
y 42
23
24
y 31
2
y 52
y 62
y1
1
y2
2
y3
3
y4
y5 y6
4 5 6
Fig. 6. Illustration of the MIMIC model. Table 2 Elements of MIMIC. Category
Variable
Variable
Y X
Coefficient
y
B
Definition
Dimension
Endogenous latent variables Endogenous observed variables Exogenous observed variable Error terms of endogenous latent variables Error terms of endogenous observed variables Y
k×1 p×1 q×1 k×1 p×1
Factor loading of Y on Coefficient matrix between and Coefficient matrix between X and Variance matrix of X Variance matrix of error term Variance matrix of error term
p×k k×k k×q q×q k×k p×p
= b0 + b1 y1 + b2 y2 + …+ bp yp + e
where b0 is the intercept; b1, b2 , …, bp are the regression coefficients, which are analogous to the slope in the linear regression equation, and e is the random error term. The statistical program JMP Pro 12 (SAS Institute Inc., 2015) can be used for analysis. When multicollinearity exists, that is, the independent variables are related among themselves, the partial least squares method can be employed for parameter estimation. 5. Discussion of results 5.1. Results of the MIMIC model The 11 observed variables, including 5 exogenous observed variables and 6 endogenous observed variables as listed in Table 1, are used to establish the MIMIC model. The MIMIC model is shown in Fig. 7. The factor loading of variable Settave is set as 1.0 so that the model can be identified as shown in Table 3 and Fig. 7. In Fig. 7, e1, e2, e3, e4, e5, and e6 are the error terms of the endogenous observed variables, and eta1 is the error term of the TSI. The exogenous observed variables X are the factors that could affect the condition of shield tunnels and are DEPTH, STRATUM, RIVER, STATION, and AGE, respectively. The endogenous observed variables Y represent the condition level of shield tunnels, and they are the deformation and defect measurements, as shown in Table 1 and Fig. 7.
latent variables . Eq. (10) is the measurement model indicating the relationship between the endogenous observed variables Y and endogenous latent variables . The elements of MIMIC are listed and explained in Table 2, where k is the number of endogenous latent variables , p is the number of endogenous observed variables Y and q is the number of exogenous observed variables X.
= Y=
X
+ y
+
(12)
(9) (10) (11)
After the model is established, parameter estimation is conducted based on the minimization of the discrepancy between the estimated sample variance/covariance matrix and the estimated model-implied variance/covariance (Ben-Akiva and Ramaswamy, 1993; Khine, 2013; Wang and Wang, 2012). In this study, the factors that influence the condition of shield tunnels are considered to be perfect indicators, and no exogenous latent variables are included. Therefore, the endogenous latent variable is the TSI in this study. The endogenous observed variables are the defect and deformation variables, and the exogenous observed variables are the influencing factor variables in Table 1. In addition, statistical program Mplus (Muthén and Muthén, 2012) with its robust maximum likelihood estimator (MLR), which can deal with the nonnormally distributed variables, is used for estimating the coefficients in Table 2.
sqrt_sett_ave
DEPTH STRATUM RIVER STATION AGE
eta1 1 TSI
1
sett_diff_ave conv_ave d_l d_c d_s
Fig. 7. MIMIC model of the shield tunnel condition. 175
1 1 1 1 1 1
e1 e2 e3 e4 e5 e6
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Table 3 Parameter estimates of the MIMIC model.
Table 5 Model goodness of fit.
Observed variable
Estimate
S.E.
Est./S.E.
P-value
Fit index
Value
Criterion of good fit
Settave Settdiff _ave
1.000
0.000
–
–
0.033
0.15 0.000 0.025 0.003
5.300
4.404 0.000 1.862 2.918
0.000
Covave dl dc ds
0.660 0.100 0.047 0.010
0.006
RMSEA CFI TLI SRMR
0.10 0.823 0.850 0.087
≤0.05 ≥0.90 ≥0.90 ≤0.08
DEPTH STRATUM RIVER STATION AGE
0.199 −0.222 0.100 0.615 0.304
0.061 0.229 0.000 0.285 0.043
3.263 −0.97 0.000 2.158 7.128
0.001 0.332 0.000 0.031 0.000
0.000 0.000 0.063 0.004
that the other indices were used for goodness evaluation. Table 5 shows the goodness of fit of the MIMIC model utilized in this paper. As seen from Table 5, RMSEA with a value greater than 0.05 indicates that the model is mediocre fitted and CFI, TLI and SRMR are close to the criteria of good fit, meaning that the model fit is acceptable. If more data samples are available in the future, the model goodness of fit will be further improved.
Table 4 Standardized parameter estimates of MIMIC model. Observed variable
Estimate
S.E.
Est./S.E.
P-value
Settave Settdiff _ave
0.548
0.076
7.173
0.000
0.406 0.514 0.097 0.147 0.280
0.064
6.321
0.000
Covave dl dc ds DEPTH STRATUM RIVER STATION AGE
0.446 −0.072 0.017 0.207 0.929
0.126 0.075 0.003 0.094 0.117
3.538 −0.960 4.902 2.206 7.934
0.000 0.337 0.000 0.027 0.000
0.101 0.018 0.073 0.041
5.099 5.410 2.017 6.782
5.2. Results of the multiple regression method After the analysis of the MIMIC model is completed, the parameters that are necessary for the calculation of 0 and 1, as shown in Eqs. (A.6) and (A.7) in Appendix A are output. Therefore, the value of the endogenous latent variable can be calculated. Then, is multiplied by -1, and its value range is transferred to 0–5 to be better understood and consistent with existing condition indices such as the present serviceability index (PSI) in pavement engineering (Carey and Irick, 1960) and our previous research based on experts’ ratings on tunnel condition (Li et al., 2017). The worst condition is 0, and 5 is the best condition. The tunnel condition can be rated on the basis of the TSI value as 0–1: very poor; 1–2: poor; 2–3: fair; 3–4: good; 4–5: very good. To remedy the multicollinearity, partial least squares regression is used. In practical engineering, inspected defect data are usually used to evaluate tunnel conditions. Based on the results of the MIMIC model, multiple regression is utilized to obtain the model between the TSI and Settave , Settdiff _ave , Covave , dl , ds and dc . The result is shown in Table 6 and Fig. 8. The parameter estimates of Settave , Settdiff _ave , Covave , dl , ds and dc are −0.108, −1.051, −0.121, −0.030, −0.114 and −0.862, respectively. Fig. 8 shows the Prediction Profiler of multiple regression. The black solid line in the middle of the square of the independent variable is the estimated slope, and the shaded area is the 95% confidence interval for the predicted values. The model goodness of fitness R2 is 0.63, indicating that 63% of the samples can be explained by the model. The ultimate expression of the TSI is shown as Eq. (13), which can be used to calculate the tunnel serviceability.
0.000 0.000 0.044 0.000
The statistical program Mplus with its estimator MLR, which does not assume that the variables are normally distributed, is used for analysis. The estimated parameter results are shown in Table 3. The standardized parameter estimation results of the observed variables can also be obtained by subtracting the mean value from each sample and then dividing by the standard deviation as shown in Table 4. It can be seen from Table 3 that all the endogenous observed variables Settave , Settdiff _ave , Covave , dl , dc , and ds are significant or marginally significant, with their factor loadings being 1.000, 0.033, 0.660, 0.100, 0.047 and 0.010 at the significance level = 0.05. The positive factor loadings indicate that as the deformation and defect measurements increase, the condition of shield tunnels will worsen. For the exogenous observed variables, the factor loadings of DEPTH, RIVER, STATION, and AGE are positive and significant at the significance level = 0.05. The positive factor loading of DEPTH means that the conditions of shield tunnels with greater burial depth are worse than for the conditions of those with smaller depth. The variable RIVER positively affects the condition of shield tunnels, indicating that the conditions of shield tunnels underneath a river are worse than the conditions of those that are not underneath a river. The positive factor loading of variable STATION shows that the condition of a shield tunnel section near a station or cross passage is generally worse than for one far away from a station or cross passage. Similarly, the positive factor loading of AGE demonstrates that the tunnel condition will become poorer with increasing operation age. These findings are consistent with the existing empirical and analytical knowledge because greater depth generally increases the loading on shield tunnels, and deformation and defects accumulate as the tunnel becomes older. The leakage of the tunnel sections underneath a river is usually greater than others. The output of Mplus software provides the model fit indicators, including chi-square, root mean square error of approximation (RMSEA), comparative fit index (CFI), Tucker-Lewis Index (TLI) and the standardized root mean square residual (SRMR), to evaluate how the model fit the data. Chi-square is so sensitive to increasing sample size
TSI = 4.978
0.108 Settave 0.030dl
1.051Settdiff _ave 0.114dc
0.121Covave
0.862ds
(13)
5.3. Results comparison The standard parameter estimations of the MIMIC model with multiple regression and previous experts’ ratings (Li et al., 2017) are listed in Table 7. As seen from Table 7, there is a difference between the Table 6 Parameter estimates of multiple regression. Term
Estimate
Std Error
t ratio
Intercept
4.978 −0.108
0.116 0.011
42.88 −9.43
−1.051
0.253
−4.15
Settave Settdiff _ave
Covave dl dc ds
176
−0.121 −0.030 −0.114 −0.862
0.016 0.034 0.111 0.729
−7.37 −0.89 −1.02 −1.18
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5
Fig. 8. Prediction Profiler of the multiple regression analysis. Table 7 Standardized parameter estimation. Variable
MIMIC model with multiple regression
Settave Settdiff _ave
Nonstandardized parameter
Standardized parameter
Nonstandardized parameter
Standardized parameter
−0.108
−0.508
−0.160
−0.620
−1.051
−0.221
1.000
−0.130
−0.121 −0.030 −0.114 −0.862
Covave dl dc ds
Experts’ ratings
−0.389 −0.046 −0.071 −0.082
−0.090 −0.080 −0.050 −0.500
−0.250 −0.190 −0.060 −0.030
Table 8 Paired-sample t test result.
µMIMIC
µExpert
Mean difference
Std Error
Upper 95%
Lower 95%
t-Ratio
DF
Prob > |t|
−0.095
0.085
0.082
−0.273
−1.127
18
0.275
parameter estimated in this study and the parameter estimated through experts’ ratings. This is because the effects of influencing factors on the TSI are considered in the MIMIC model in this study. Both the standard estimations of this study and experts’ ratings demonstrate that Settave , Covave and Settdiff _ave are the three major observed variables representing tunnel serviceability. To illustrate whether there is a significant difference between the previous experts’ ratings (Li et al., 2017) and the objective condition evaluation in this study, the paired-sample t test is utilized, and the result is shown in Table 8. The null hypothesis H0 is that there are no significant differences between the condition evaluations of the MIMIC model with multiple regression in this study and the experts’ ratings, that is, µ MIMIC = µ Expert . The alternative hypothesis H1 is that there are significant differences between them. If the two-tailed p-value is greater than the significance level , the null hypothesis H0 cannot be rejected. If the two-tailed P-value is smaller than , the null hypothesis H0 should be rejected. In Table 8, the t test result shows that the p-value = 0.275 is greater than the significance level = 0.05, indicating that there is no significant difference between the result of this study and the experts’ ratings. Fig. 9 also shows the paired-sample t test result. The upper and lower dashed lines are the upper and lower limits of the 95% confidence interval, respectively. The solid line is the mean difference of the two models. Since the 95% confidence interval contains 0, there is no significant difference between the results of this study and experts’ ratings. The mean values of the defects/deformation variables in Table 1 and the estimated parameters in Table 6 are used to investigate the average effects of the defect/deformation variables on the TSI deterioration. The results are shown in Fig. 10. It can be seen from Fig. 10 that among the six variables, approximately 48% of the TSI deterioration is caused by the increase of the average convergence ratio, showing
that the convergence ratio plays the greatest role in the serviceability deterioration. It also indicates that more attention should be paid to the convergence during the construction and operation period. Approximately 47% of the TSI deterioration consists of the average relative settlement and differential settlement. The other three defect variables, including the spalling, water leakage and cracking, are only a small portion of the reasons that would lead to TSI deterioration. After
Fig. 9. Paired-sample t test result. 177
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sqrt_sett_ave diff_sett_ave conv_ave 48.03%
1.16%
1.55% 2.77%
13.41%
1.61%
34.24%
dl dc ds
Fig. 10. The average effect of the defect/deformation variables on the TSI deterioration.
12
0.35
sqrt_sett_ave
10
0.25
8
0.2
6
0.15
4
0.1
2
0.05
0
0
Station
Station
(a) The square root of average relative settlement
(b) The average differential settlement Settdiff _ ave of ML1
Settave of ML1
10
conv_ave
8
(‰)
diff_sett_ave
0.3
6
4 2 0
Station
(c) The average convergence ratio Covave of ML1
Fig. 11. The observed deformation of ML1.
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5
Table 10 Condition evaluation of ML1.
4.5 4 TSI
3.5
3 2.5 2 1.5 1
Fig. 12. Condition evaluation of ML1. Table 9 The observed deformation of ML1.
Caobao Road∼Shanghai Indoor Stadium Shanghai Indoor Stadium∼Xujiahui Xujiahui∼Henshan Road Henshan Road∼Changshu Road Changshu Road∼South Shaanxi Road South Shaanxi Road∼South Huangpi Road South Huangpi Road∼People's Square People's Square∼Xinzha Road Xinzha Road∼Hanzhong Road Hanzhong Road∼Shanghai Railway Station
Settdiff _ave (mm/m)
Covave (‰)
4.967
0.278
5.802
2.300 6.028 6.218 3.092 5.514
0.107 0.333 0.256 0.181 0.169
5.389 6.530 8.678 7.214 7.262
9.579
0.247
7.518
6.549 4.721 3.797
0.285 0.241 0.220
4.598 6.590 6.191
Settave
TSI
Caobao Road∼Shanghai Indoor Stadium Shanghai Indoor Stadium∼Xujiahui Xujiahui∼Henshan Road Henshan Road∼Changshu Road Changshu Road∼South Shaanxi Road South Shaanxi Road∼South Huangpi Road South Huangpi Road∼People's Square People's Square∼Xinzha Road Xinzha Road∼Hanzhong Road Hanzhong Road∼Shanghai Railway Station
3.389 3.948 3.178 2.971 3.465 3.070 2.727 3.355 3.308 3.548
obtained. Therefore, the data in Figs. 11 and 12 are the average values of the tunnel sections in the corresponding tunnel interval. The results in Part 5.3 show that the square root of the measured average relative settlement Settave , the average differential settlement Settdiff _ave , and the average convergence ratio Covave are the main variables contributing to the TSI deterioration. Therefore, the detailed data of Settave , Settdiff _ave and Covave are shown in Fig. 11 and Table 9. Fig. 11 indicates that the settlement and convergence vary greatly from interval to interval. For instance, the relative settlement of the interval from Shanghai Indoor Stadium to Xujiahui is as low as approximately 4 mm, while the relative settlement of the interval from South Huangpi Road to People’s Square is as high as approximately 100 mm. The differential settlement of the interval from Shanghai Indoor Stadium to Xujiahui is the lowest, with a value of 0.107 mm/m. The differential settlement of the interval from Xujiahui to Henshan Road is the highest, with a value of 0.333 mm/m. The smallest convergence ratio is 4.598‰ for the interval from People’s Square to Xinzha Road. The highest convergence ratio is approximately 8.678‰ for the interval from Henshan Road to Changshu Road. Since the water leakage area, cracking length and spalling area are only small components of the TSI deterioration, their detailed values are not listed herein. Based on the regression results illustrated in the previous part of this paper, the conditions are evaluated, and the results are shown in Fig. 12 and listed in Table 10. As seen from Fig. 12, the TSI values of those tunnel intervals fluctuate because of the observed deformation, which can be referred to in Fig. 11. The TSI values of the interval from South Huangpi Road to People’s Square are the lowest among these investigated intervals because of its high relative settlement, differential settlement and convergence ratio. The serviceability of the interval from Shanghai Indoor Stadium to Xujiahui is the best, considering its relatively low settlement and convergence.
Station
Tunnel station
Tunnel station
consulting the engineers from Shanghai Shen Tong Metro Group Co., Ltd., it is concluded that the effect of water leakage on tunnel condition is the greatest, followed by convergence and settlement. In this study, convergence and settlement are the two major deformation variables that cause the TSI deterioration, which is consistent with the experts’ opinions. The reason why the effect of water leakage is less than the effects of convergence and settlement is that some leakage was fixed before the inspection. Therefore, the inspected water leakage area is smaller than the actual area.
6. Conclusion This study proposed a shield tunnel condition index TSI to evaluate the condition of metro shield tunnels in operation in Shanghai. The indicators of TSI were deformation and defect measurements, including the square root of average relative settlement Settave , average differential settlement Settdiff _ave , average convergence ratio Covave , total water leakage area per 100 rings dl , total cracking length per 100 rings dc , and total spalling area per 100 rings ds . The factors that could influence the tunnel condition were the variables DEPTH, STRATUM, RIVER, STATION, and AGE1. The MIMIC model was used to analyze the correlation among the latent condition index, deformation/defect measurements and factors that influence the condition of metro shield tunnels. Based on the MIMIC model analysis results, the relationship between the condition index and the measurements was derived through a multiple regression method. A paired-sample t test was conducted to analyze whether there was a significant difference between the condition evaluation in this study and experts’ ratings in previous research. Finally, the case of Shanghai Metro Line No. 1 was investigated to evaluate its condition. The conclusions can be
5.4. Case study Shanghai Metro Line No. 1 (ML1) is the oldest metro line in Shanghai and was first put into operation in 1995. ML1 has been undergoing large settlement since beginning its operation. The average cumulative settlement in 2010 reached 111 mm, and the maximum differential settlement was approximately 295 mm (Shen et al., 2014). Considering the long history, large settlement and relatively complete deformation and defect records of ML1, it is chosen as the case study to evaluate the condition of the shield tunnel. The analyzed case included 10 tunnel intervals from Caobao Road Station to North Zhongshan Road Station. Each tunnel section consisting of 200 rings is calculated, and then, the average of the tunnel sections in the same tunnel interval is 179
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summarized as follows.
based on statistically rational analysis, not on experts’ judgment. TSI can be used to evaluate the conditions of metro shield tunnels.
(1) The MIMIC model combined with multiple regression analysis quantified the effects of deformation/defect measurements and the influencing factors on the tunnel condition. The condition of the tunnel with a deep burial depth was worse than the other tunnels. As the age increased, the tunnel condition deteriorated. (2) There was no significant difference between the experts’ ratings and the tunnel condition evaluation in this study at the significance level = 0.05. (3) Covave , Settave and Settdiff _ave were the three major variables contributing to the TSI deterioration. Approximately 48% of the TSI deterioration resulted from the increase of the average convergence ratio, and approximately 47% was caused by the increase of the average relative settlement and differential settlement. (4) The regression relationship between TSI and its measurements was
Acknowledgements This study was funded by National Key Basic Research and Development Program (973 Program) (2011CB013800): Fundamental theory for the performance evolution and sensing-control of urban metro structures and National Natural Science Foundation of China (51478341). Shanghai Shen Tong Metro Group Co., Ltd was acknowledged for providing the original data. The authors also appreciated the support of China Scholarship Council (CSC) during the research in the United States. Dr. Baoshan Huang in The University of Tennessee, Knoxville was also acknowledged for his assistance and authority of Mplus software.
Appendix A It is stated that if two vectors of random variables have finite second moments and variance/covariance matrix, the possible relationship between the two variables can be linear (Ben-Akiva and Ramaswamy, 1993). For the endogenous latent variable and endogenous observed variables Y of the MIMIC model, their possible linear relationship is shown as Eq. (A.1).
=
0
+
1Y
(A.1)
+
where 0 and 1 are the regression parameters and is the error term with its mean value as zero, that is E ( ) = 0 . As can be derived from Eq. (A.1), can be calculated through Eq. (A.2).
= Cov ( , Y ) Cov (Y , Y )
1
1
(A.2)
1
where Cov ( , Y ) and Cov (Y , Y ) are the corresponding covariance/variance matrices. The variance matrix of the observed variables Y Cov (Y , Y ) is given by Eq. (A.4), and Cov ( , Y ) can be calculated through Eq. (A.5) (Ben-Akiva and Ramaswamy, 1993; Wang and Wang, 2012).
Cov (Y , Y ) = E [(Y
E (Y ))(Y
Cov (Y , Y ) =
T
y(
+
T y
)
(A.3)
E (Y ))T ]
(A.4)
+
T y
Cov ( , Y ) =
(A.5)
Substitute Eqs. (A.4) and (A.5) into Eq. (A.2), and then
=
1
T y[
y(
+
)
T y
+
]
Substitute Eqs. (1), (2) and (3) into Eq. (A.1), and 0
= (1
1
y )(1
1
B)
1
can be obtained as Eq. (A.6).
1
(A.6) 0
can be obtained as shown in Eq. (A.7). (A.7)
X
Finally, substitute Eqs. (A.6) and (A.7) into Eq. (A.1). Then, the latent variable can be calculated as shown in Eq. (A.8).
= (1
1
y )(1
B)
1
X+
1Y
(A.8)
+
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Condition evaluation of urban metro shield tunnels in Shanghai through multiple indicators multiple causes model combined with multiple regression method Xueqin Chena, Xiaojun Lib, Hehua Zhub, a b
T
⁎
Department of Civil Engineering, College of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
ARTICLE INFO
ABSTRACT
Keywords: Tunnel Serviceability Index (TSI) MIMIC Multiple regression Condition evaluation Metro shield tunnel Latent variable
Many existing condition evaluations of metro shield tunnels are developed based on the experts’ judgments or single deformation/defect measurements. In addition, the influence of factors such as buried depth and age on the condition of shield tunnels was not quantified in previous research. This study proposed a comprehensive condition index, the Tunnel Serviceability Index (TSI), through the Multiple Indicators Multiple Causes (MIMIC) model combined with a multiple regression method. The contributions of the deformation/defect variables and the influencing factors to the TSI were evaluated. The observed deformation/defect variables included average relative settlement, differential settlement, average convergence ratio, water leakage area, cracking length, and spalling area. The influencing factors included the operation age, burial depth, and so on. The relationship among the TSI, deformation/defect variables, and influence factors was quantified, and an expression for the TSI was obtained. The paired-sample t test demonstrated that there were no significant differences between the experts’ ratings in our group’s previous research and the tunnel condition evaluation used by the MIMIC model in this study at the significance level = 0.05. Among the six observed deformation and defect variables, approximately 95% of the TSI deterioration was caused by the increase of convergence ratio, relative settlement and differential settlement. Finally, the case of Shanghai Metro Line No. 1 was investigated to evaluate its condition.
1. Introduction It has been more than 25 years since the first metro shield tunnel was put into use in Shanghai in the 1990s. Metro tunnels have played a vital role in improving the construction of urban infrastructure systems and facilitating public transportation. Meanwhile, as a type of underground structure, shield tunnels have some unique characteristics, such as uncertainty, nonreversibility, high construction and accident costs and long service periods when compared with superstructures. Since the metro shield tunnels in Shanghai are excavated in soft soils, the uncertainty of shield tunnels results primarily from the uncertainty of geological conditions, such as the uncertainty of the soil characteristics and unexpected presence of water, the uncertainty of the loading conditions including the water pressure, soil pressure and the interaction between the shield tunnels and stratum, and the uncertainty of the analysis model. The nonreversibility refers to the idea that once the shield tunnels are excavated, the strata are disturbed, and it is
⁎
impossible for the geological strata to be restored to their original state. High cost is necessary even if the underground space can be theoretically restored. Therefore, it is of great importance to evaluate and then maintain the condition of shield tunnels above a certain level, predict performance and eventually make cost-effective maintenance and rehabilitation decisions. Ever since beginning operation, the occurrence of defects and deformation has contributed to the deterioration of shield tunnels. Based on experts’ experience and the inspection and monitoring data of shield tunnels in Shanghai, the current major defects include water leakage, segment spalling, cracking, segment faulting, joint opening, material deterioration and forth. The structural deformation includes the circumferential convergence, longitudinal settlement, and longitudinal differential settlement. The extent and severity of defects and deformations can reflect the condition of shield tunnels. Many researchers have made great efforts to evaluate the conditions of shield tunnels based on defect and deformation measurements through various
Corresponding author. E-mail addresses: [email protected] (X. Chen), [email protected] (X. Li), [email protected] (H. Zhu).
https://doi.org/10.1016/j.tust.2018.11.044 Received 13 December 2015; Received in revised form 29 August 2018; Accepted 25 November 2018 0886-7798/ © 2018 Published by Elsevier Ltd.
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analysis methods. Wu et al. (2007) analyzed the influence of cracking width, length, direction and density on the durability of segment structure through fuzzy synthetic discrimination. The health conditions of shield tunnels in Shanghai were classified into five grades through fuzzy synthetic discrimination and an analytic hierarchy process based on water leakage, circumferential deformation, and longitudinal deformation measurements (Ye, 2007; Ye et al., 2007). Xu et al. (2010) evaluated the effect of defects on shield tunnels by using the improved analytic hierarchy process-product scale method. Yuan et al. (2012) categorized the service states of the lining structures of shield tunnels into five grades, namely, Suitable, Degraded, Deteriorated, Unavailable and Unstable, by taking the inspection data of the structural condition and operation condition into consideration. It can be summarized that most existing condition assessments of shield tunnels are based on empirical or qualitative judgments. Meanwhile, the threshold values of some defects and deformations in shield tunnels were regulated by codes to evaluate the condition (Ministry of Construction of the People's Republic of China, 2003, 2008). For instance, the threshold value of convergence suggested by “Code for design of metro” is 4-6‰ D (D is the outer diameter of the shield tunnel), and the threshold value of cracking width suggested by “Technical code for waterproofing of underground works” is 0.2 mm. If the value is greater than the threshold, the corresponding maintenance and rehabilitation actions should be taken. Although a single defect or deformation measurement can provide information on the tunnel condition, the integrated condition index, which can take several defects or deformation measurements into consideration, is more intuitive and comprehensive. In pavement engineering, pavement performance is defined as the serviceability trend of the pavement over a design period of time, where serviceability indicates the ability of the pavement to serve the demand of the traffic in the existing condition (AASHO, 1962). The pavement distresses, such as cracking and rutting are measured and used to evaluate pavement serviceability. Similar to pavement serviceability, the Tunnel Serviceability Index (TSI) was proposed and adopted to assess the comprehensive condition of shield tunnels in this study. It is defined as the ability of shield tunnels to service the demand of the metro operation in the existing condition. The TSI can be quantified through inspected tunnel defects, including cracking, leakage, and spalling, and monitored deformation, including settlement and convergence. There are many factors related to the defects and deformation of shield tunnels: the soft soil deposits in Shanghai, land subsidence, project construction activity in the neighborhood of shield tunnels, design and construction quality and metro train vibration (Wang, 2009; Ye et al., 2007). Shen et al. (2014) summarized that the locations where the tunnel crosses below the river, where the soil conditions are various, between the station and tunnel section, and at the cross passage section are the main sections where differential settlement occurs. They also noted that the great long-term settlement in Shanghai results from sublayer subsidence, postconstruction settlement, nearby construction disturbances, groundwater infiltration and cyclic loading of trains (Shen et al., 2014). All of these factors interact in a complicated way, influencing the condition of shield tunnels. However, the effects of the factors on the condition of shield tunnels were not quantified in previous findings. Therefore, a multiple indicators multiple causes (MIMIC) model, which is a special case of a structural equation model (SEM), was adopted to analyze the complex relationships among variables, including the condition, the defect and deformation measurements, and the influencing factors in this study. An SEM is a statistical method that originates from the field of social science, psychology, economics and so on (Brown, 2014; Khine, 2013; Kline, 2010; Wang and Wang, 2012). It treats the variables that cannot be easily or directly measured as latent variables and the measured variables as observed variables. It can handle the complex relationships between latent and observed variables simultaneously. Although it is rarely used in the tunneling field, there are some applications in other
areas of engineering in recent years. In the traffic engineering field, Lee et al. (2008) proposed a new index named “traffic accident size” that is indicated by the number of deaths, the number of injured, the number of involved vehicles and the number of damaged vehicles. The relationship between traffic accident size and exogenous factors, including road factors, environmental factors, and driver factors, was estimated. Hassan and Abdel-Aty (2011) analyzed drivers’ responses under low visibility conditions and their relationships with visibility, traffic conditions, and roadway types. Jou et al. (2011) investigated freeway drivers’ intention to adopt electronic toll collection service by taking the effects of technology acceptance, planned behavior, impression changes, government attitude and risk into consideration. Cheng and Huang (2013) examined high-speed rail consumers’ willingness to adopt mobile ticketing services by considering both the metal accounting theory and technology acceptance model. In the pavement engineering field, Ben-Akiva and Ramaswamy (1993) estimated the latent pavement performance from the observed pavement damages, pavement characteristics, traffic and environmental factors, and maintenance activities through an SEM. Based on the work of Ben-Akiva and Ramaswamy (1993), Chu and Durango-Cohen (2008) used an SEM to estimate the effect of maintenance on rutting, slope variance and serviceability of pavements. Chen et al. (2016) proposed a combined pavement condition index by investigating the Long-Term Pavement Performance (LTPP) database. In this study, the tunnel condition cannot be measured directly, while the observed defects and deformation can indicate the degree of the tunnel condition. Since SEM has demonstrated great potential for extensive application to evaluate the correlations among latent variables and observed variables, it was used to analyze the shield tunnel condition for the first time in this study. The data, methodology, and results are discussed in the following sections. 2. Common defects and deformation in shield tunnels In Shanghai, most of the metro tunnels are constructed in the silty clay, silty clay and sandy silt layers that have some distinguishing characteristics, such as high underground water level, which is usually 0.5–0.7 m below the ground (Ding et al., 2008), high water content, high void ratio, high compressibility, low strength and low permeability (Ye et al., 2007). Considering the characteristics of soft deposits, the metro tunnels in Shanghai are usually driven by a Tunnel Boring Machine (TBM) in soft soils through methods such as Earth Pressure Balance (EPB) and Slurry Pressure Balance (SPB) rather than the cut and cover methods. The TBM assembles the segments together to form the tunnel lining. Generally, the segment lining of metro shield tunnels in Shanghai is composed of six segments: one capped block F, two adjacent blocks L1 and L2, two standard blocks B1 and B2, and one bottom block D, as shown in Fig. 1. For a whole segment ring, the central angles of the capped block F, adjacent block L1 (L2), standard block B1 (B2) and bottom block D are 16°, 65°, 65° and 84°, respectively. The adjacent segments are connected by circumferential bolts, and the adjacent lining rings are connected through longitudinal bolts. Under this circumstance, the longitudinal and circumferential joints are formed. The hand holes on the segments are prefabricated to install the bolts. Currently, the standard inner radius is 2750 mm, and the outer radius is 3100 mm in Shanghai, as shown in Fig. 1. Yuan et al. (2012) summarized many types of defects that exist in shield tunnels, such as chloride corrosion permeation, bolt rusting and cracking. Many of those defects are immeasurable because of the weak corrosive environment, the short operation age of metro shield tunnels in Shanghai and the insufficient inspection techniques currently. For instance, it is difficult to inspect the deterioration of the connectors between two adjacent segments at present. Based on previous experience and inspection and monitoring results, the common defects of metro shield tunnels in Shanghai include segment spalling, water leakage, cracking, faulting and joint opening, and the structural 171
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1. Joints For the transverse section of tunnel lining shown in Fig. 1, there are approximately six longitudinal joints in one lining ring. For a tunnel interval with a length of 1.2 km, there are approximately 1000 circumferential joints and 6000 longitudinal joints, which are the main water leakage paths, as shown in Fig. 2(a). 2. Grouting holes The prefabricated grouting holes on the segments are used to backfill grouting and then make up the strata loss. After the grouting is completed, the grouting holes become another main water leakage path, as shown in Fig. 2(b). 3. Bolt holes The diameter of the bolt hole is usually greater than that of the bolt to make the bolt installation procedure operable. If the ground water leaks through the opening joints, it can leak through the bolt holes into the tunnel, as shown in Fig. 2(c). 4. Segment cracking
Fig. 1. The segmental tunnel lining of the metro shield tunnel in Shanghai.
Segment cracking on the segment surface is also a leakage path, but it is quite rare, as shown in Fig. 2(d).
deformation includes circumferential convergence and longitudinal settlement (Li et al., 2017; Shanghai Rail Transit Maintenance Support Limited Company, 2010; Wang, 2009). Due to the limitations of visual inspection and manual measurement, the records of faulting and joint opening are much lower in number than for other defects. Therefore, faulting and joint opening were not investigated in this study. As automatic and advanced inspection techniques will be applied and more data will be available in the future, other types of defects can be added to the condition evaluation, and the model proposed in the following part of this study can be updated.
2.1.2. Spalling Spalling is the missing corner of segments, as shown in Fig. 3. The main reasons for spalling include initial construction defects and differential settlement. The initial construction defects include fabrication errors during the construction periods, the collision of segments during transportation, the assembling force acting on the segments during the assembling phase and operation mistakes. The differential settlement would cause extra moment, normal force and shear force on the lining and then cause spalling at the corner (Shanghai Rail Transit Maintenance Support Limited Company, 2010).
2.1. Defects 2.1.1. Water leakage Due to the abundant underground water in Shanghai, water leakage is one of the most severe defects. Generally, there are four main paths for water leakage in shield tunnels, as shown in Fig. 2.
2.1.3. Cracking Segment cracking is the cracking on the segment surface that inspectors can observe with the naked eye, as shown in Fig. 4. Cracking can be observed in the fabrication, construction and operation periods. Cracking is mainly caused by structural deformation and exterior loading (Wu et al., 2007). 2.2. Deformation The deformation in the shield tunnel includes the circumferential convergence in the transverse direction and settlement in the longitudinal direction.
(a). Leakage at the joints
(b). Leakage at the grouting hole
(c). Leakage at the bolt hole
(d). Leakage at the connected cracking
2.2.1. Circumferential convergence The tunnel squeezes under the act of soil pressure, and the squeezing shape in soft soils in Shanghai is usually similar to the
Fig. 2. Water leakage.
Fig. 3. Spalling. 172
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was determined. Therefore, the tunnel section with a length of 200 lining rings was also used in this study (Li et al., 2017). In addition, the results of Li et al. (2017) indicated that the variable square root of average relative settlement Settave , average differential settlement Settdiff _ave , average convergence ratio Covave , total water leakage area per 100 rings dl , total cracking length per 100 rings dc , and total spalling area per 100 rings ds can be used as the deformation and defect measurements. The average relative settlement Settave is the average of relative settlement Settri , and it can be calculated through Eq. (1).
Fig. 4. Cracking.
“transverse duck egg”. According to the Code for design of metro GB 50157-2003 (Ministry of Construction of the People's Republic of China, 2003), the circumferential convergence value should be less than 5‰ of D (D is the outer diameter of the shield tunnel). The statistical result of 46 lining rings of one tunnel interval in Shanghai shows that the convergence values of 85 percent of the monitored lining rings are greater than the regulated value (Ye et al., 2007). Large convergence could lead to longitudinal joint opening at the tunnel crown, cracking, etc. According to the research results (Wang and Zhang, 2013), when the convergence is approximately 7.7‰ of the tunnel outer diameter, the bolt stress would be 640 MPa, and it would yield. When the convergence is 9.6‰ of the tunnel outer diameter, the maximum joint opening value would be 6 mm, which is the waterproofing control standard.
Settave =
n i=1
Settri
(1)
n
where Settri (mm) is the relative settlement of the ith monitoring point. It is the difference of the settlement at the ith monitoring point Settri (mm) and the uniform settlement (minimal settlement) Settu (mm). Settri can be calculated through Eq. (2), where n is the total number of monitoring points, and i ranges from 1 to n.
Settri = Settti
(2)
Settu
Li et al. (2017) found that the goodness of fit of Settave was better than that of Settave . Therefore, Settave was used in the following analysis. The average differential settlement Settdiff _ave can be calculated through Eqs. (3) and (4).
Settdiff _i =
2.2.2. Longitudinal settlement The longitudinal settlement is the difference between the monitored elevation and the designed elevation at certain locations. Considering the soft deposit characteristics, the excessive pumping of groundwater, etc., Shanghai is going through a large land subsidence. The recorded cumulative subsidence has even been 2–3 m in the central area of Shanghai (Chai et al., 2004). Since the metro tunnel is constructed in soil, its deformation is consistent with the land subsidence. In addition to land subsidence, the construction of other engineering projects around the metro tunnel, the crossing tunnels, the cyclic loads above the tunnel and the increase of vertical loads can also cause settlement. According to the inspection and monitoring data, for some tunnel intervals, settlement was the most severe condition measurement that affected the tunnel condition. For instance, the settlement of the tunnel interval between People’s Square Station and South Huangpi Road Station was even greater than 200 mm. The various settlements at different locations form the differential settlement. The differential settlement of metro tunnels in Shanghai mainly occurs at the section where the soil conditions are various, between the station and tunnel section, and at the cross passage section (Shen et al., 2014). Great differential settlement may lead to the distortion of track (Wu et al., 2011) and aggregate water leakage, spalling, cracking and joint opening. According to the Code for design of metro GB 50157-2003 (Ministry of Construction of the People's Republic of China, 2003), the curvature radius in the longitudinal direction should be greater than 15,000 m.
|Settri
Settr (i li
n i=2
Settdiff _ave =
n
1) |
(3)
Settdiff _i
(4)
1
where Settdiff _i (mm/m) is the differential settlement between the ith and (i-1)th points; li (m) is the length between the ith and (i-1)th points; Settri (mm) is the relative settlement at the ith point; Settr (i 1) (mm) is the relative settlement at the (i-1)th point; and Settdiff _ave (mm) is the average differential settlement. The average convergence ratio Covave can be calculated through Eq. (5).
Covave =
m i=1
di
Dm
D
× 1000
(5)
where di (mm) is the monitored outer diameter at the ith point; D (mm) is the designed outer diameter; Covave (‰) is the average convergence ratio; and m is the number of monitoring points among the 200 lining rings. The total water leakage area per 100 rings dl (m2/100 rings) can be calculated through Eq. (6), where lt (m2) is the total leakage area in a tunnel section with 200 rings.
dl =
lt 2
(6)
The total cracking length per 100 rings dc (m/100 rings) can be calculated through Eq. (7), where ct (m) is the total cracking length in a tunnel section with 200 rings.
3. Data preparation
dc =
Currently, data on water leakage, spalling, cracking, circumferential convergence and longitudinal settlement are available for analysis. The data for metro shield tunnels in Shanghai in 2011 were collected by Shanghai Shen Tong Metro Group Co., Ltd. Metro lines 1, 2 and 4, including 182 tunnel sections (including both the upstream and downstream directions) and 36,400 segment lining rings, were investigated. In the previous research of our group, nine experts with abundant experience in the design, construction, administration, maintenance and research of shield tunnels in soft soils in Shanghai rated the serviceability of the tunnels, and the tunnel section with a length of 200 rings
ct 2
(7) 2
The total spalling area per 100 rings ds (m /100 rings) can be calculated through Eq. (8), where st (m2) is the total spalling area in a tunnel section with 200 rings.
ds =
st 2
(8)
Therefore, the six defect and deformation variables above are discussed and used in this study. Their descriptive statistics are shown in Table 1. The influencing factors considered in this study are DEPTH (the 173
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Table 1 Descriptive statistics of the observed variables. Genre
Variable
Description
Min.
Max.
Mean
S.D.
Skewness
Kurtosis
Deformation and Defect
Settave Settdiff _ave
Square root of average relative settlement
1.22
11.73
4.72
2.75
1.10
0.26
Average differential settlement (mm/m)
0.87
10.80 9.05 2.89 0.45
0.19
5.91 0.77 0.21 0.02
0.12
1.88 1.47 0.47 0.05
2.19
0.29 2.67 3.26 5.82
7.38
Covave dl dc ds
Average convergence ratio (‰) Total water leakage area per 100 rings (m2/100 rings) Total cracking length per 100 rings (m/100 rings) Total spalling area per 100 rings (m2/100 rings)
0.02
DEPTH STRATUM
Average burial depth (m) 0: Clay stratum; 1: Both clay and sandy silt stratum; 2: Sandy silt stratum 0: Not underneath a river; 1: Underneath a river 0: Not near the station or cross passage; 1: Near the station or cross passage Years from the opening year to 2011 (year)
6.98 0
21.56 2
13.95
3.31
0.00
-0.20
0
1
0
1
4
18.58
12.60
4.51
-0.51
-1.01
Influencing factor
RIVER STATION AGE
y 11 1 2
3
4
x1 x2
x3
x4
1
11
x11
y 21 y 31
x 21 x 31
1
21
2
12
x 41
y 42
2
y 52
y 62
y1
1
y2
2
y3
3
y4
y5 y6
−0.28 7.80 12.01 40.13
4: Statistical Methodology. Khine (2013) indicated that if the absolute value of skewness is greater than 3 and the absolute value of kurtosis is greater than 7, the variable is not normally distributed. As seen from Table 1, the observed variables Settdiff _ave , dc and ds are nonnormally distributed.
Structural model
1
1.51 0 0 0
4. Statistical methodology An SEM is a statistical approach that handles the assumed linear relationships among the latent and observed variables. The latent variables are the unobserved variables, and they are the linear combination of the observed variables. By estimating the coefficients, it can be concluded which is the major factor that influences the latent variable and which indicator is significant. Generally, an SEM consists of path analysis and confirmatory factor analysis. Compared with other methods, an SEM possesses some advantages, such as taking the latent variables into account, analyzing and estimating the complex relationships among latent and observed variables simultaneously (Hassan and Abdel-Aty, 2011; Lee et al., 2008).
4 5 6
Measurement model Fig. 5. Illustration of SEM.
average burial depth), STRATUM (the stratum that the tunnel section crossed), RIVER (whether the tunnel section crossed a river), STATION (whether the tunnel section was near a station or cross passage), and AGE (the operation age of the tunnel section) as shown in Table 1. The factors STRATUM, RIVER, and STATION are categorical variables. The variable STRATUM with a value of 0 indicates that the stratum the tunnel section crosses is clay, 2 indicates that the tunnel section crosses the sandy silt stratum and 1 indicates that the tunnel section crosses both the clay and sandy silt stratum. The variable RIVER with a value of 0 indicates that the tunnel section is not underneath a river, and 1 indicates that the tunnel section is underneath a river. The variable STATION with a value of 0 indicates that the tunnel section is not near a station or cross passage, and 1 indicates that the tunnel section is near a station or cross passage. The variables DEPTH and AGE are continuous variables. DEPTH is the average overburden soil depth above the top of the shield tunnel section. Note that for a tunnel section underneath a river, DEPTH is not the depth from the river surface to the top of the tunnel section but the depth from the soil surface to the top of the tunnel section. AGE is the service year of the metro tunnels and is calculated from the opening year of each metro tunnel section (Shen et al., 2014) to the year 2011. Table 1 shows the descriptive statistics of the observed variables. The six defect and deformation variables are set to “Y observed variables”, which can reflect the shield tunnel condition in the SEM, and the remaining five variables are “X observed variables”, which are the factors that could influence the condition of shield tunnels. The “Y observed variables” and “X observed variables” are elaborated in Part
4.1. Multiple indicators multiple causes (MIMIC) model An SEM consists of two models, the measurement model and structural model, as shown in Fig. 5. The structural model represents the relationship among the latent variables. It is the equation for the endogenous latent variables and exogenous latent variables . The measurement model can analyze the relationship between the observed variables and latent variables. There are two types of measurement models: one is the equation for the endogenous observed variables Y and endogenous latent variables , and the other is the equation for the exogenous observed variables X and exogenous latent variables . The basic form of an SEM is illustrated in Fig. 5. In Fig. 5, the ellipses with shading represent the unobserved variables ( and ), while the other ellipses without shading are the error variables including , and , which are the error terms of , Y and X , respectively; the rectangles represent the observed variables (X and Y); the single-headed arrows represent the path coefficients ( , B and ); and the double-headed arrows represent that the two variables are correlated with each other. The MIMIC model is a simplified SEM whose exogenous observed variable X is the perfect indicator of exogenous latent variable . Hence, the error term of X is set to zero, and the factor loading between exogenous observed variable X and exogenous latent variable equals 1, as shown in Eq. (11). Fig. 6 and Eqs. (9)–(11) show the illustration and equations of the MIMIC model, respectively. As seen from Fig. 6, the error term of X is 0, and there is one structural model and one measurement model in MIMIC. Eq. (9) is the structural model indicating the relationship between the endogenous latent variables and exogenous 174
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X
ξ
Structural model
4.2. Multiple regression method
Measurement model
1
x1
y 11
11
13
x3
14
22
x4
y 21
1
12
x2
Through the MIMIC model, the correlations among the endogenous latent variables, endogenous observed variables, and exogenous observed variables are investigated, but the value of endogenous latent variables cannot be obtained directly from the model. Thus, it is of great necessity to extract the value of endogenous latent variables from the observed variables based on the correlation results. The procedure for obtaining the endogenous latent variables from the observed endogenous and exogenous variables is elaborated in the Appendix. It can be seen from Eq. (A.8) that the endogenous latent variable is the function of the observed variables X , Y and the coefficients in Table 2. After the MIMIC model was analyzed, the coefficients listed in Table 2 and parameters 0 and 1 in Appendix A can be calculated. For each group of X and Y, the corresponding value of can be obtained through Eq. (A.8). Ben-Akiva and Ramaswamy (1993) indicated that the observed variables X can be treated as fixed variables, such as pavement type, material, weather, environment and traffic factors in pavement engineering. Meanwhile, traditional condition indices of infrastructure, such as pavements and bridges, are the formulas of various defect measurements. Therefore, the multiple regression method is employed to obtain the function of the shield tunnel condition indices on defect variables Y. The formula of the multiple regression model is shown in Eq. (12).
12
2
21
y 42
23
24
y 31
2
y 52
y 62
y1
1
y2
2
y3
3
y4
y5 y6
4 5 6
Fig. 6. Illustration of the MIMIC model. Table 2 Elements of MIMIC. Category
Variable
Variable
Y X
Coefficient
y
B
Definition
Dimension
Endogenous latent variables Endogenous observed variables Exogenous observed variable Error terms of endogenous latent variables Error terms of endogenous observed variables Y
k×1 p×1 q×1 k×1 p×1
Factor loading of Y on Coefficient matrix between and Coefficient matrix between X and Variance matrix of X Variance matrix of error term Variance matrix of error term
p×k k×k k×q q×q k×k p×p
= b0 + b1 y1 + b2 y2 + …+ bp yp + e
where b0 is the intercept; b1, b2 , …, bp are the regression coefficients, which are analogous to the slope in the linear regression equation, and e is the random error term. The statistical program JMP Pro 12 (SAS Institute Inc., 2015) can be used for analysis. When multicollinearity exists, that is, the independent variables are related among themselves, the partial least squares method can be employed for parameter estimation. 5. Discussion of results 5.1. Results of the MIMIC model The 11 observed variables, including 5 exogenous observed variables and 6 endogenous observed variables as listed in Table 1, are used to establish the MIMIC model. The MIMIC model is shown in Fig. 7. The factor loading of variable Settave is set as 1.0 so that the model can be identified as shown in Table 3 and Fig. 7. In Fig. 7, e1, e2, e3, e4, e5, and e6 are the error terms of the endogenous observed variables, and eta1 is the error term of the TSI. The exogenous observed variables X are the factors that could affect the condition of shield tunnels and are DEPTH, STRATUM, RIVER, STATION, and AGE, respectively. The endogenous observed variables Y represent the condition level of shield tunnels, and they are the deformation and defect measurements, as shown in Table 1 and Fig. 7.
latent variables . Eq. (10) is the measurement model indicating the relationship between the endogenous observed variables Y and endogenous latent variables . The elements of MIMIC are listed and explained in Table 2, where k is the number of endogenous latent variables , p is the number of endogenous observed variables Y and q is the number of exogenous observed variables X.
= Y=
X
+ y
+
(12)
(9) (10) (11)
After the model is established, parameter estimation is conducted based on the minimization of the discrepancy between the estimated sample variance/covariance matrix and the estimated model-implied variance/covariance (Ben-Akiva and Ramaswamy, 1993; Khine, 2013; Wang and Wang, 2012). In this study, the factors that influence the condition of shield tunnels are considered to be perfect indicators, and no exogenous latent variables are included. Therefore, the endogenous latent variable is the TSI in this study. The endogenous observed variables are the defect and deformation variables, and the exogenous observed variables are the influencing factor variables in Table 1. In addition, statistical program Mplus (Muthén and Muthén, 2012) with its robust maximum likelihood estimator (MLR), which can deal with the nonnormally distributed variables, is used for estimating the coefficients in Table 2.
sqrt_sett_ave
DEPTH STRATUM RIVER STATION AGE
eta1 1 TSI
1
sett_diff_ave conv_ave d_l d_c d_s
Fig. 7. MIMIC model of the shield tunnel condition. 175
1 1 1 1 1 1
e1 e2 e3 e4 e5 e6
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Table 3 Parameter estimates of the MIMIC model.
Table 5 Model goodness of fit.
Observed variable
Estimate
S.E.
Est./S.E.
P-value
Fit index
Value
Criterion of good fit
Settave Settdiff _ave
1.000
0.000
–
–
0.033
0.15 0.000 0.025 0.003
5.300
4.404 0.000 1.862 2.918
0.000
Covave dl dc ds
0.660 0.100 0.047 0.010
0.006
RMSEA CFI TLI SRMR
0.10 0.823 0.850 0.087
≤0.05 ≥0.90 ≥0.90 ≤0.08
DEPTH STRATUM RIVER STATION AGE
0.199 −0.222 0.100 0.615 0.304
0.061 0.229 0.000 0.285 0.043
3.263 −0.97 0.000 2.158 7.128
0.001 0.332 0.000 0.031 0.000
0.000 0.000 0.063 0.004
that the other indices were used for goodness evaluation. Table 5 shows the goodness of fit of the MIMIC model utilized in this paper. As seen from Table 5, RMSEA with a value greater than 0.05 indicates that the model is mediocre fitted and CFI, TLI and SRMR are close to the criteria of good fit, meaning that the model fit is acceptable. If more data samples are available in the future, the model goodness of fit will be further improved.
Table 4 Standardized parameter estimates of MIMIC model. Observed variable
Estimate
S.E.
Est./S.E.
P-value
Settave Settdiff _ave
0.548
0.076
7.173
0.000
0.406 0.514 0.097 0.147 0.280
0.064
6.321
0.000
Covave dl dc ds DEPTH STRATUM RIVER STATION AGE
0.446 −0.072 0.017 0.207 0.929
0.126 0.075 0.003 0.094 0.117
3.538 −0.960 4.902 2.206 7.934
0.000 0.337 0.000 0.027 0.000
0.101 0.018 0.073 0.041
5.099 5.410 2.017 6.782
5.2. Results of the multiple regression method After the analysis of the MIMIC model is completed, the parameters that are necessary for the calculation of 0 and 1, as shown in Eqs. (A.6) and (A.7) in Appendix A are output. Therefore, the value of the endogenous latent variable can be calculated. Then, is multiplied by -1, and its value range is transferred to 0–5 to be better understood and consistent with existing condition indices such as the present serviceability index (PSI) in pavement engineering (Carey and Irick, 1960) and our previous research based on experts’ ratings on tunnel condition (Li et al., 2017). The worst condition is 0, and 5 is the best condition. The tunnel condition can be rated on the basis of the TSI value as 0–1: very poor; 1–2: poor; 2–3: fair; 3–4: good; 4–5: very good. To remedy the multicollinearity, partial least squares regression is used. In practical engineering, inspected defect data are usually used to evaluate tunnel conditions. Based on the results of the MIMIC model, multiple regression is utilized to obtain the model between the TSI and Settave , Settdiff _ave , Covave , dl , ds and dc . The result is shown in Table 6 and Fig. 8. The parameter estimates of Settave , Settdiff _ave , Covave , dl , ds and dc are −0.108, −1.051, −0.121, −0.030, −0.114 and −0.862, respectively. Fig. 8 shows the Prediction Profiler of multiple regression. The black solid line in the middle of the square of the independent variable is the estimated slope, and the shaded area is the 95% confidence interval for the predicted values. The model goodness of fitness R2 is 0.63, indicating that 63% of the samples can be explained by the model. The ultimate expression of the TSI is shown as Eq. (13), which can be used to calculate the tunnel serviceability.
0.000 0.000 0.044 0.000
The statistical program Mplus with its estimator MLR, which does not assume that the variables are normally distributed, is used for analysis. The estimated parameter results are shown in Table 3. The standardized parameter estimation results of the observed variables can also be obtained by subtracting the mean value from each sample and then dividing by the standard deviation as shown in Table 4. It can be seen from Table 3 that all the endogenous observed variables Settave , Settdiff _ave , Covave , dl , dc , and ds are significant or marginally significant, with their factor loadings being 1.000, 0.033, 0.660, 0.100, 0.047 and 0.010 at the significance level = 0.05. The positive factor loadings indicate that as the deformation and defect measurements increase, the condition of shield tunnels will worsen. For the exogenous observed variables, the factor loadings of DEPTH, RIVER, STATION, and AGE are positive and significant at the significance level = 0.05. The positive factor loading of DEPTH means that the conditions of shield tunnels with greater burial depth are worse than for the conditions of those with smaller depth. The variable RIVER positively affects the condition of shield tunnels, indicating that the conditions of shield tunnels underneath a river are worse than the conditions of those that are not underneath a river. The positive factor loading of variable STATION shows that the condition of a shield tunnel section near a station or cross passage is generally worse than for one far away from a station or cross passage. Similarly, the positive factor loading of AGE demonstrates that the tunnel condition will become poorer with increasing operation age. These findings are consistent with the existing empirical and analytical knowledge because greater depth generally increases the loading on shield tunnels, and deformation and defects accumulate as the tunnel becomes older. The leakage of the tunnel sections underneath a river is usually greater than others. The output of Mplus software provides the model fit indicators, including chi-square, root mean square error of approximation (RMSEA), comparative fit index (CFI), Tucker-Lewis Index (TLI) and the standardized root mean square residual (SRMR), to evaluate how the model fit the data. Chi-square is so sensitive to increasing sample size
TSI = 4.978
0.108 Settave 0.030dl
1.051Settdiff _ave 0.114dc
0.121Covave
0.862ds
(13)
5.3. Results comparison The standard parameter estimations of the MIMIC model with multiple regression and previous experts’ ratings (Li et al., 2017) are listed in Table 7. As seen from Table 7, there is a difference between the Table 6 Parameter estimates of multiple regression. Term
Estimate
Std Error
t ratio
Intercept
4.978 −0.108
0.116 0.011
42.88 −9.43
−1.051
0.253
−4.15
Settave Settdiff _ave
Covave dl dc ds
176
−0.121 −0.030 −0.114 −0.862
0.016 0.034 0.111 0.729
−7.37 −0.89 −1.02 −1.18
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5
Fig. 8. Prediction Profiler of the multiple regression analysis. Table 7 Standardized parameter estimation. Variable
MIMIC model with multiple regression
Settave Settdiff _ave
Nonstandardized parameter
Standardized parameter
Nonstandardized parameter
Standardized parameter
−0.108
−0.508
−0.160
−0.620
−1.051
−0.221
1.000
−0.130
−0.121 −0.030 −0.114 −0.862
Covave dl dc ds
Experts’ ratings
−0.389 −0.046 −0.071 −0.082
−0.090 −0.080 −0.050 −0.500
−0.250 −0.190 −0.060 −0.030
Table 8 Paired-sample t test result.
µMIMIC
µExpert
Mean difference
Std Error
Upper 95%
Lower 95%
t-Ratio
DF
Prob > |t|
−0.095
0.085
0.082
−0.273
−1.127
18
0.275
parameter estimated in this study and the parameter estimated through experts’ ratings. This is because the effects of influencing factors on the TSI are considered in the MIMIC model in this study. Both the standard estimations of this study and experts’ ratings demonstrate that Settave , Covave and Settdiff _ave are the three major observed variables representing tunnel serviceability. To illustrate whether there is a significant difference between the previous experts’ ratings (Li et al., 2017) and the objective condition evaluation in this study, the paired-sample t test is utilized, and the result is shown in Table 8. The null hypothesis H0 is that there are no significant differences between the condition evaluations of the MIMIC model with multiple regression in this study and the experts’ ratings, that is, µ MIMIC = µ Expert . The alternative hypothesis H1 is that there are significant differences between them. If the two-tailed p-value is greater than the significance level , the null hypothesis H0 cannot be rejected. If the two-tailed P-value is smaller than , the null hypothesis H0 should be rejected. In Table 8, the t test result shows that the p-value = 0.275 is greater than the significance level = 0.05, indicating that there is no significant difference between the result of this study and the experts’ ratings. Fig. 9 also shows the paired-sample t test result. The upper and lower dashed lines are the upper and lower limits of the 95% confidence interval, respectively. The solid line is the mean difference of the two models. Since the 95% confidence interval contains 0, there is no significant difference between the results of this study and experts’ ratings. The mean values of the defects/deformation variables in Table 1 and the estimated parameters in Table 6 are used to investigate the average effects of the defect/deformation variables on the TSI deterioration. The results are shown in Fig. 10. It can be seen from Fig. 10 that among the six variables, approximately 48% of the TSI deterioration is caused by the increase of the average convergence ratio, showing
that the convergence ratio plays the greatest role in the serviceability deterioration. It also indicates that more attention should be paid to the convergence during the construction and operation period. Approximately 47% of the TSI deterioration consists of the average relative settlement and differential settlement. The other three defect variables, including the spalling, water leakage and cracking, are only a small portion of the reasons that would lead to TSI deterioration. After
Fig. 9. Paired-sample t test result. 177
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sqrt_sett_ave diff_sett_ave conv_ave 48.03%
1.16%
1.55% 2.77%
13.41%
1.61%
34.24%
dl dc ds
Fig. 10. The average effect of the defect/deformation variables on the TSI deterioration.
12
0.35
sqrt_sett_ave
10
0.25
8
0.2
6
0.15
4
0.1
2
0.05
0
0
Station
Station
(a) The square root of average relative settlement
(b) The average differential settlement Settdiff _ ave of ML1
Settave of ML1
10
conv_ave
8
(‰)
diff_sett_ave
0.3
6
4 2 0
Station
(c) The average convergence ratio Covave of ML1
Fig. 11. The observed deformation of ML1.
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Table 10 Condition evaluation of ML1.
4.5 4 TSI
3.5
3 2.5 2 1.5 1
Fig. 12. Condition evaluation of ML1. Table 9 The observed deformation of ML1.
Caobao Road∼Shanghai Indoor Stadium Shanghai Indoor Stadium∼Xujiahui Xujiahui∼Henshan Road Henshan Road∼Changshu Road Changshu Road∼South Shaanxi Road South Shaanxi Road∼South Huangpi Road South Huangpi Road∼People's Square People's Square∼Xinzha Road Xinzha Road∼Hanzhong Road Hanzhong Road∼Shanghai Railway Station
Settdiff _ave (mm/m)
Covave (‰)
4.967
0.278
5.802
2.300 6.028 6.218 3.092 5.514
0.107 0.333 0.256 0.181 0.169
5.389 6.530 8.678 7.214 7.262
9.579
0.247
7.518
6.549 4.721 3.797
0.285 0.241 0.220
4.598 6.590 6.191
Settave
TSI
Caobao Road∼Shanghai Indoor Stadium Shanghai Indoor Stadium∼Xujiahui Xujiahui∼Henshan Road Henshan Road∼Changshu Road Changshu Road∼South Shaanxi Road South Shaanxi Road∼South Huangpi Road South Huangpi Road∼People's Square People's Square∼Xinzha Road Xinzha Road∼Hanzhong Road Hanzhong Road∼Shanghai Railway Station
3.389 3.948 3.178 2.971 3.465 3.070 2.727 3.355 3.308 3.548
obtained. Therefore, the data in Figs. 11 and 12 are the average values of the tunnel sections in the corresponding tunnel interval. The results in Part 5.3 show that the square root of the measured average relative settlement Settave , the average differential settlement Settdiff _ave , and the average convergence ratio Covave are the main variables contributing to the TSI deterioration. Therefore, the detailed data of Settave , Settdiff _ave and Covave are shown in Fig. 11 and Table 9. Fig. 11 indicates that the settlement and convergence vary greatly from interval to interval. For instance, the relative settlement of the interval from Shanghai Indoor Stadium to Xujiahui is as low as approximately 4 mm, while the relative settlement of the interval from South Huangpi Road to People’s Square is as high as approximately 100 mm. The differential settlement of the interval from Shanghai Indoor Stadium to Xujiahui is the lowest, with a value of 0.107 mm/m. The differential settlement of the interval from Xujiahui to Henshan Road is the highest, with a value of 0.333 mm/m. The smallest convergence ratio is 4.598‰ for the interval from People’s Square to Xinzha Road. The highest convergence ratio is approximately 8.678‰ for the interval from Henshan Road to Changshu Road. Since the water leakage area, cracking length and spalling area are only small components of the TSI deterioration, their detailed values are not listed herein. Based on the regression results illustrated in the previous part of this paper, the conditions are evaluated, and the results are shown in Fig. 12 and listed in Table 10. As seen from Fig. 12, the TSI values of those tunnel intervals fluctuate because of the observed deformation, which can be referred to in Fig. 11. The TSI values of the interval from South Huangpi Road to People’s Square are the lowest among these investigated intervals because of its high relative settlement, differential settlement and convergence ratio. The serviceability of the interval from Shanghai Indoor Stadium to Xujiahui is the best, considering its relatively low settlement and convergence.
Station
Tunnel station
Tunnel station
consulting the engineers from Shanghai Shen Tong Metro Group Co., Ltd., it is concluded that the effect of water leakage on tunnel condition is the greatest, followed by convergence and settlement. In this study, convergence and settlement are the two major deformation variables that cause the TSI deterioration, which is consistent with the experts’ opinions. The reason why the effect of water leakage is less than the effects of convergence and settlement is that some leakage was fixed before the inspection. Therefore, the inspected water leakage area is smaller than the actual area.
6. Conclusion This study proposed a shield tunnel condition index TSI to evaluate the condition of metro shield tunnels in operation in Shanghai. The indicators of TSI were deformation and defect measurements, including the square root of average relative settlement Settave , average differential settlement Settdiff _ave , average convergence ratio Covave , total water leakage area per 100 rings dl , total cracking length per 100 rings dc , and total spalling area per 100 rings ds . The factors that could influence the tunnel condition were the variables DEPTH, STRATUM, RIVER, STATION, and AGE1. The MIMIC model was used to analyze the correlation among the latent condition index, deformation/defect measurements and factors that influence the condition of metro shield tunnels. Based on the MIMIC model analysis results, the relationship between the condition index and the measurements was derived through a multiple regression method. A paired-sample t test was conducted to analyze whether there was a significant difference between the condition evaluation in this study and experts’ ratings in previous research. Finally, the case of Shanghai Metro Line No. 1 was investigated to evaluate its condition. The conclusions can be
5.4. Case study Shanghai Metro Line No. 1 (ML1) is the oldest metro line in Shanghai and was first put into operation in 1995. ML1 has been undergoing large settlement since beginning its operation. The average cumulative settlement in 2010 reached 111 mm, and the maximum differential settlement was approximately 295 mm (Shen et al., 2014). Considering the long history, large settlement and relatively complete deformation and defect records of ML1, it is chosen as the case study to evaluate the condition of the shield tunnel. The analyzed case included 10 tunnel intervals from Caobao Road Station to North Zhongshan Road Station. Each tunnel section consisting of 200 rings is calculated, and then, the average of the tunnel sections in the same tunnel interval is 179
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summarized as follows.
based on statistically rational analysis, not on experts’ judgment. TSI can be used to evaluate the conditions of metro shield tunnels.
(1) The MIMIC model combined with multiple regression analysis quantified the effects of deformation/defect measurements and the influencing factors on the tunnel condition. The condition of the tunnel with a deep burial depth was worse than the other tunnels. As the age increased, the tunnel condition deteriorated. (2) There was no significant difference between the experts’ ratings and the tunnel condition evaluation in this study at the significance level = 0.05. (3) Covave , Settave and Settdiff _ave were the three major variables contributing to the TSI deterioration. Approximately 48% of the TSI deterioration resulted from the increase of the average convergence ratio, and approximately 47% was caused by the increase of the average relative settlement and differential settlement. (4) The regression relationship between TSI and its measurements was
Acknowledgements This study was funded by National Key Basic Research and Development Program (973 Program) (2011CB013800): Fundamental theory for the performance evolution and sensing-control of urban metro structures and National Natural Science Foundation of China (51478341). Shanghai Shen Tong Metro Group Co., Ltd was acknowledged for providing the original data. The authors also appreciated the support of China Scholarship Council (CSC) during the research in the United States. Dr. Baoshan Huang in The University of Tennessee, Knoxville was also acknowledged for his assistance and authority of Mplus software.
Appendix A It is stated that if two vectors of random variables have finite second moments and variance/covariance matrix, the possible relationship between the two variables can be linear (Ben-Akiva and Ramaswamy, 1993). For the endogenous latent variable and endogenous observed variables Y of the MIMIC model, their possible linear relationship is shown as Eq. (A.1).
=
0
+
1Y
(A.1)
+
where 0 and 1 are the regression parameters and is the error term with its mean value as zero, that is E ( ) = 0 . As can be derived from Eq. (A.1), can be calculated through Eq. (A.2).
= Cov ( , Y ) Cov (Y , Y )
1
1
(A.2)
1
where Cov ( , Y ) and Cov (Y , Y ) are the corresponding covariance/variance matrices. The variance matrix of the observed variables Y Cov (Y , Y ) is given by Eq. (A.4), and Cov ( , Y ) can be calculated through Eq. (A.5) (Ben-Akiva and Ramaswamy, 1993; Wang and Wang, 2012).
Cov (Y , Y ) = E [(Y
E (Y ))(Y
Cov (Y , Y ) =
T
y(
+
T y
)
(A.3)
E (Y ))T ]
(A.4)
+
T y
Cov ( , Y ) =
(A.5)
Substitute Eqs. (A.4) and (A.5) into Eq. (A.2), and then
=
1
T y[
y(
+
)
T y
+
]
Substitute Eqs. (1), (2) and (3) into Eq. (A.1), and 0
= (1
1
y )(1
1
B)
1
can be obtained as Eq. (A.6).
1
(A.6) 0
can be obtained as shown in Eq. (A.7). (A.7)
X
Finally, substitute Eqs. (A.6) and (A.7) into Eq. (A.1). Then, the latent variable can be calculated as shown in Eq. (A.8).
= (1
1
y )(1
B)
1
X+
1Y
(A.8)
+
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