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Condition assessment of shield tunnel using a new indicator: The tunnel serviceability index
Tunnelling and Underground Space Technology 67 (2017) 98–106
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Condition assessment of shield tunnel using a new indicator: The tunnel serviceability index
MARK
⁎
Xiaojun Lia,b, , Xiaodong Lina, Hehua Zhua,b, Xiuzhi Wangc, Zhaoming Liuc a b c
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China Shanghai Shentong Metro Group, 909 Guilin Road, Shanghai 201103, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Shield tunnel Tunnel serviceability index (TSI) Partial least squares regression Expert rating
The condition assessment of shield tunnels is one of the key issues in the structural maintenance during the service life of the tunnel. Traditionally, the shield tunnel condition has been graded based on certain types of tunnel distresses, such as convergence deformation, differential settlement, cracks, and water leakage. However, the overall condition of the tunnel cannot be so easily assessed, as it often depends on experts’ decisions and evaluations. This paper proposes a comprehensive tunnel serviceability index (TSI) to evaluate the overall condition of a shield tunnel in soft ground. The TSI is a mathematical combination of measurable tunnel distresses that can be obtained by employing the following steps: (1) select the types of tunnel distresses to be included in the TSI, (2) prepare the tunnel samples with distresses, (3) have experts rate the tunnel serviceability, and (4) regress the TSI formula using the partial least squares (PLS) method. The TSI formula can then be applied to evaluate the serviceability of tunnels that are similar to the tunnel samples in step (2). Metro shield tunnels in Shanghai’s soft ground are selected for a case study. Six common distresses, namely, relative settlement, differential settlement, convergence deformation, water leakage, cracking, and spalling, are selected for inclusion in the TSI. Tunnel serviceability ratings of 40 samples were conducted to regress the TSI formula. The TSI formula reveals that relative settlement, differential settlement, convergence deformation and water leakage are the four significant variables that impact the serviceability of Shanghai’s metro shield tunnel with loading factors of −0.62, −0.13, −0.25 and −0.19, respectively. Cracking and spalling are two weak indicators with loading factors of −0.06 and −0.03, respectively. These conclusions, in general, are consistent with the maintenance experiences of the Shanghai metro group.
1. Introduction The maintenance and repair of shield tunnels has become an increasingly important topic in the field of tunneling (e.g., Richards, 1998; Asakura and Kojima, 2003; Yuan et al., 2013). A significant issue when making decisions regarding the maintenance and rehabilitation of shield tunnels is the condition assessment of such facilities (Yuan et al., 2012). Usually, the condition of a shield tunnel can be graded according to the severity of certain types of distresses. For instance, the Federal Highway Administration released a manual that specifies the inspection and rating methodologies for transportation tunnels (FHWA, 2005), whereas Park et al. (2006) developed guidelines for assessing the condition of old railway tunnels. Furthermore, the Chinese Metro Design Code (GB50157, 2013) specifies the limit values for distresses such as leakage, spalling, cracking and deformation. However, as
⁎
different grades would be obtained if different types of distresses are specified in the above approaches, the overall condition of the tunnel cannot be easily assessed, and thus, it often depends on the decisions of experts. Alternatively, the condition of a shield tunnel can be assessed using a mathematical model that can take multiple types of distresses into account. Xu et al. (2010) applied a fuzzy-set method to evaluate the health status of shield tunnels based on fault tree analysis. Nývlt et al. (2011) used a probabilistic risk assessment approach for the making of decisions with respect to tunnel construction and operation. Zhang et al. (2014) used a fuzzy analytic hierarchy process to consider different types of health monitoring data in the rating of shield tunnel structures. Although multiple types of distresses are considered and the overall condition of the tunnel can be obtained, these methods sometimes suffer from unreasonable grading results because the correlations between and among the different types of distresses are ignored.
Corresponding author at: Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China. E-mail addresses: [email protected] (X. Li), [email protected] (X. Lin), [email protected] (H. Zhu), [email protected] (X. Wang), [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.tust.2017.05.007 Received 26 November 2016; Accepted 5 May 2017 0886-7798/ © 2017 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 67 (2017) 98–106
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date. (4) Tunnel serviceability rating (TSR): The mean of all experts' ratings of tunnel serviceability. (5) Tunnel serviceability index (TSI): A mathematical combination of measurable variables obtained from shield tunnel samples. The TSI can be used to evaluate the serviceability of tunnels that are similar to the tunnel samples.
In recent years, researchers have used mechanical models to assess tunnel conditions. Yuan et al. (2012) established a framework for a structural assessment procedure using the principle of limit state design, which is performed sequentially with structural components, portions of linings and whole lining structures. Spyridis (2014) presented a reliability life-cycle based methodology to adjust safety factors used in the design of tunnel linings to attain a specified service life. However, building a mechanical model that is close to the real structure is extremely difficult, especially when distresses are considered. Even if the mechanical model can be built, the computations would be tremendously time consuming. In the fields of pavement engineering and bridge engineering, there is a similar demand for the condition assessment of pavement sections and bridge structures, and accordingly, the expert rating approach has been proved to be an operable and effective method to meet this demand. The American Association of State Highway Officials (AASHO) developed a pavement serviceability index (PSI) based on users’ ratings of 72 pavement sections in America (Highway Research Board, 1962). According to the serviceability rating results, many statistical pavement performance models were developed that could be used to improve assessment results and predict structural conditions (Ramaswamy, 1989; Prozzi and Madanat, 2003; Chu and Durango-Cohen, 2007). Saito and Sinha (1991) conducted a study whereby they sought the opinions of bridge inspectors and engineers and established a relationship between the subjective rating and the severity and extent of the distresses. To date, experts’ opinions regarding the condition of shield tunnels have rarely been reported in the literature. This research is motivated by the growing demand for condition assessments of shield tunnel structures and the successful application of the expert rating approach in the condition assessments of pavement sections and bridge structures. This research offers several contributions to the field. (1) A comprehensive tunnel serviceability index (TSI) is proposed to evaluate the overall condition of a shield tunnel in soft ground. (2) The methodology to obtain the TSI formula is presented. (3) The application of the TSI to a Shanghai metro shield tunnel is provided. This paper is organized as follows. The terms and assumptions related to the condition assessment of shield tunnel structures are introduced in Section 2. Inspection data of Shanghai metro shield tunnels, e.g., settlement, convergence and various distresses, are described in Section 3. The methodology to obtain the TSI formula is presented in Section 4. The application of the TSI to a specific case is provided in Section 5. The application of the method is then discussed in Section 6, and conclusions are discussed in Section 7.
2.2. Assumptions (1) Tunnel serviceability is based on the condition at the current time. This means the past condition is excluded in the rating process because the main objective of this research is to build a mathematical relationship between tunnel serviceability and measurable variables. If the past condition is considered, many historical data would be required, a consideration that is sometimes impractical. However, the conditions of the past and the future can be taken into account through the performance deterioration models (Chu and Durango-Cohen, 2008). (2) Tunnel serviceability is only related to measurable variables. The measurable variables reveal the relationship between tunnel distresses and its condition, while the explanatory variables explain the deterioration process (Ramaswamy, 1989). The explanatory variables are not considered because shield tunnel deterioration is a separate topic that is outside the scope of this paper. 3. Inspections of Shanghai metro shield tunnels Shanghai, an area of soft deposit, is located at the alluviation of the Yangtze River Delta where the Huangpu River joins the Yangtze River. It has been more than 20 years since the first metro line was put into operation in the 1990 s. At the end of December 2015, there were 14 metro lines and 366 stations, which accounted for a total length of 617 km in operation. An additional four metro lines are in the planning phase and expected to be built in the next five years. The Code for the Structural Appraisal of Shield Tunnels (DG/TJ082123-2013, 2013) and the Highway and Rail Transit Tunnel Inspection Manual (FHWA, 2005) have identified and defined the tunnel inspection items, such as distresses, structural deformation, concrete and steel corrosion, and levels of CO2 , Cl− and SO42− in the air and water. Although corrosion and ion diffusion impacts tunnel performance (Djerbi et al., 2008; Liu et al., 2013), they were not included in the routine inspections in Shanghai. The common inspection items included in the Shanghai metro shield tunnels include water leakage, spalling, cracking, dislocation, joint opening, longitudinal settlement and circumferential convergence (Ye et al., 2007). These inspection items can be further divided into three categories, namely, longitudinal deformation, circumferential deformation, and distresses on interior lining surfaces. In this research, Shanghai metro lines 1, 2 and 4 are selected as the rating samples because these lines have been in operation for a period long enough to provide stable and sufficient data.
2. Terms and assumptions 2.1. Terms related to the condition assessment of shield tunnel structures To succinctly describe the condition assessment problem, it is necessary to introduce certain terms that refer to the AASHO road test (Highway Research Board, 1962).
3.1. Longitudinal deformation (1) Measurable variable: The observable effects that can be measured, either through visual inspection, total stations, or tunnel section scanning devices, of shield tunnel structure condition changes, such as longitudinal settlement, circumferential convergence and distresses. (2) Explanatory variable: The unobservable fundamental variables that can describe observed phenomena. Structure deterioration is the result of a variety of these variables. For example, age, traffic, environmental erosion, maintenance activities, etc. constitute explanatory variables. (3) Tunnel serviceability: The ability of a specific section of the shield tunnel structure to provide normal and safe use in its existing condition on the date of the rating, not on a past date or a future
According to field monitoring, significant settlement and substantial differential settlement occur after more than ten years of operation (Shen et al., 2014). The main reasons for the long-term settlement of shield tunnels are the sublayer subsidence, the disturbances from posttunneling and nearby construction, the infiltration of the groundwater and the cyclic loading of trains (Chai et al., 2004; Shen et al., 2014). Because the uniform settlement does no harm to the structure’s safety, the inspections of longitudinal deformation focus on relative settlement and differential settlement. The concepts of uniform settlement and relative settlement are presented in Fig. 1. Differential settlement is the settlement difference between two monitoring points divided by their distance and is given by 99
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1800 Ground
Metro Line 1 Metro Line 2 Metro Line 4
1600 1400
Measured settlement
Records number
Initial additional settlement is zero Uniform settlement Highest point Total settlement
Relative settlement
1200 1000 800 600 400 200 0
leakage
cracking
spalling
dislocation opening
Distresses Fig. 2. Distress statistics of Shanghai Metro Lines 1, 2 and 4. Fig. 1. The concept of the relative settlement.
3.3. Distresses
sdiff i =
|sri−sr (i −1) | li
(1)
The common inspected distresses in the Shanghai metro shield tunnels were water leakage, cracking, spalling, dislocation, and joint opening. Fig. 2 displays the number of recorded distresses of the Shanghai Metro Lines 1, 2 and 4 in 2011 and 2012. In general, 73.6% of the observed distresses were water leakage, whereas 14.5% and 11.4% were cracking and spalling distresses, respectively. Dislocation and joint opening accounted for only a small proportion of the distresses. The reason for the small number of recorded dislocation and joint openings was because these distresses are not easy to recognize through routine visual inspections. Total water leakage area dl , total cracking length dc , and total spalling area ds , per 100 rings are chosen as the remaining three measurable variables. Dislocation and joint opening are excluded because the recorded number of dislocation and joint opening are very small and previous studies have found that dislocation and joint openings are correlated with longitudinal and circumferential deformation (Liao et al., 2005; Wang, 2009; Wang and Zhang, 2013; Li et al., 2015b).
where sdiff i is differential settlement at monitoring point i; sri is the measured settlement at monitoring point i; and li is the distance between the i-th and (i−1)-th monitoring points. Average relative settlement and average differential settlement are chosen as two measurable variables and are given by m
∑ save =
sri
i =1
(2)
m m
∑ sdiff ave =
sdiff i
i =2
(3)
m−1
where save is average relative settlement; sdiff ave is the average differential settlement; andm is the number of settlement monitoring points.
3.4. Statistics of the measured variables
3.2. Circumferential deformation
Six measurable variables are selected, namely, average relative settlement save , average differential settlement sdiff ave , average convergence ratio cave , total water leakage area dl , total cracking length dc , and total spalling area ds . Table 1 presents the statistics of the measurable variables.
Circumferential deformation is another major issue that affects the structural performance during operation. Large convergence deformation could result in a reduction of structural safety and could increase maintenance costs (Mahdevari and Torabi, 2012). In the Shanghai metro shield tunnels, the bolt begins to yield when the convergence reaches 7.7‰D (D is the designed external diameter). An increase in bolt stress leads to an increase in the joint opening (Li et al., 2015a). The joint opening then reaches the waterproof control limit when the convergence reaches 9.6‰D, and the concrete at the tunnel waist reaches its characteristic value of strength when the convergence further reaches 13.6‰D (Wang and Zhang, 2013). The average convergence ratio is chosen as the third measurable variable and is defined as m
∑ cave =
4. Methodology to obtain TSI formula 4.1. Tunnel serviceability rating Tunnel serviceability ratings were obtained using rating forms rather than field ratings because it was impractical for an expert to enter the tunnel at midnight and rate a number of tunnels in a short time. Fig. 3 provides a sample rating form that consists of basic information, a distress maps and deformation charts. The rating section includes 200 segmented rings that are 240 m long. The basic information consists of the structure location and inspection date. The distress map illustrates the location, shape and associated value of each recorded distress on the structure unfolded map. The deformation charts provide the longitudinal deformation and circumferential convergence of the section. Yuan et al. (2012) and the Code for the Structural Appraisal of Shield Tunnels (DG/TJ08-2123-2013, 2013) use five service states,
m
∑
|di−D|
i =1
Dm
× 1000 =
|Δi |
i =1
Dm
× 1000
(4)
where cave is the average convergence ratio; m is the number of convergence monitoring points; di is the measured external diameter of the i-th monitoring points; D is the designed external diameter of the segmented linings; and Δi is the difference between the measured diameter and the designed diameter. 100
Tunnelling and Underground Space Technology 67 (2017) 98–106
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Table 1 Statistics of the six measurable variables.
Table 2 Information regarding rating panel members.
Measurable variables
Minimum
First quartile
Median
Third quartile
Maximum
Mean value
save
1.2
8.2
19.6
40.2
130.1
27.8
1.5
4.2
9.5
19.8
58.0
12.5
2.4
6.1
7.3
8.4
12.0
1.5
0.00
0.16
0.42
1.11
5.74
0.86
0.00
0.00
0.00
0.90
5.67
0.76
(mm) sdiff ave (mm/ 100 m) cave (‰D) dl (m2/100 rings) dc (m/100 rings) ds (m2/100 rings)
0.00
0.00
0.00
0.01
1.30
No.
Age
Years of employment
Background/interest
1 2
45 44
14 21
3 4 5 6 7 8 9
60 43 41 36 47 40 46
36 9 10 10 27 10 17
Metro structure design Metro construction and operation management Structure monitoring Structure maintenance Structure maintenance Structure rehabilitation Structure rehabilitation Structure engineering researcher Geotechnical engineering researcher
independent decisions with respect to the ratings. The panel rated 39 sections, 18 of which were rated on January 17, 2015 and 21 of which were rated on May 23, 2015. If there was no excessive deformation or distress in the tunnel section, the tunnel serviceability was rated a 5 (very good, the No. 40 sample). The rating results are given in Table 3. The 2nd column of Table 3 (TSR) presents the mean values of the tunnel serviceability ratings, which range from 4.9 to 2.1, where 5.0 is the ideal status. Standard deviations of the TSR are listed in the 3rd column, and measurable variables of the rated samples are listed in the 4th-through 8th columns. The tunnel serviceability index (TSI) and the differences between the TSI and TSR are listed in the last two columns.
0.08
namely, suitable, degraded, deteriorated, unavailable and unstable, for the structural performance of the tunnel lining. A simpler description, that is, very good (5), good (4), fair (3), poor (2) and very poor (1), is adopted in this research to represent the five service states. The rating panel, which consisted of nine experts, represents a wide variety of interests, including design, construction, administration, maintenance and research (see Table 2). The members of the rating panel were informed of the pertinent definition, and they discussed their opinions before the ratings. They were instructed to make leakage area: 0.7 m 2
D
Information
leakage area: 1.6 m 2
Metro Line: --
B
cracking length: 0.73 m
Start Station: -End Station: -Start Ring: 600
L
End Ring: 800 Date: 2011.11.03
spalling area: 0.01 m 2
F
L
Legend
leakage area: 1.3 m 2
leakage area: 0.50 m 2
Leakage Spalling Dislocation
B
Cracking Joint Opening
D
D) ŝƌĐƵŵĨĞƌĞŶƟĂl convergence(¡ ë
Accum ulated settlement (mm )
0
- 30
- 60 600
700 Ring No.
800
20
10
Status
Rating
Very good
5
Good
4
Fair Poor
3
Very poor
1
Rating result 0 600
700 Ring No.
Fig. 3. Tunnel serviceability rating form.
101
800
2
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Table 3 Tunnel serviceability rating results. No.
TSR
Std. dev. of TSR
save (mm)
sdiff ave (mm/100 m)
cave (‰D)
dl (m2/100 rings)
dc (m/100 rings)
ds (m2/100 rings)
TSI
Diff.TSI & TSR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
3.3 3.7 4.9 4.3 2.6 3.1 3.3 4.1 2.5 3.3 4.3 4.1 3.7 3.9 4.0 3.3 4.8 4.7 4.2 2.7 4.7 3.7 3.7 2.0 2.5 3.5 4.0 4.0 3.7 2.7 4.0 4.5 2.6 3.7 2.9 2.9 2.1 2.9 3.5 5.0
0.7 1.0 0.3 0.5 0.9 0.8 0.7 0.4 1.0 0.9 0.5 0.4 1.1 0.8 1.0 0.5 0.4 0.5 0.7 0.4 0.5 0.7 0.9 0.7 0.7 0.5 0.5 0.3 0.7 1.1 0.6 0.5 0.9 0.7 0.8 0.8 0.8 0.9 0.7 0.0
10.4 10.4 2.4 5.3 88.6 43.6 25.5 10.8 125.3 27.3 25.0 6.9 6.6 15.1 32.4 16.0 5.3 3.6 31.5 69.3 3.2 38.1 15.6 131.4 96.6 22.8 20.3 25.0 9.2 50.3 7.1 12.5 142.0 5.0 33.9 75.6 143.2 43.2 18.8 0.0
26.4 4.2 4.9 8.4 21.6 12.9 12.9 17.3 17.4 8.0 2.5 19.6 23.3 27.2 3.3 23.3 9.0 1.2 3.7 10.7 17.5 8.3 25.6 29.2 40.5 4.9 4.5 20.4 26.4 23.3 26.1 6.0 57.0 6.4 4.3 21.6 54.2 27.1 27.9 0.0
3.9 7.8 2.8 3.8 8.5 6.8 9.2 5.6 9.4 8.0 3.5 4.5 5.1 7.3 7.9 4.1 4.4 3.1 4.1 5.7 5.0 6.5 6.0 6.8 8.1 6.2 7.9 7.2 3.6 7.5 6.4 3.5 9.1 7.3 10.2 7.6 9.2 7.1 5.3 0.0
0.35 5.55 0.00 4.60 0.70 1.95 1.05 0.00 0.20 0.35 0.90 0.00 5.80 0.00 2.05 5.75 0.00 0.00 1.35 0.25 0.95 0.25 2.50 1.95 0.70 0.00 0.35 0.00 5.75 0.00 0.75 0.00 0.00 1.55 1.20 0.70 0.25 0.00 2.75 0.00
0.00 0.00 0.00 0.00 0.00 0.44 1.03 0.00 4.19 0.44 0.00 0.00 0.00 2.33 0.36 0.00 0.00 0.00 0.00 1.14 0.00 0.33 0.00 0.66 0.67 1.35 0.00 0.00 0.00 0.63 0.00 0.00 0.36 1.12 0.00 0.00 2.36 1.13 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.05 0.15 0.00 0.05 0.05 0.00 0.05 0.00 0.00 0.05 0.00 0.05 0.00 0.00 0.05 0.00 0.00 0.00 0.15 0.10 0.00 0.05 0.10 0.00 0.05 0.11 0.00 0.00 0.05 0.00 0.15 0.15 0.10 0.00 0.00
4.1 3.6 4.7 4.1 2.8 3.3 3.3 4.1 2.3 3.6 4.1 4.2 3.7 3.6 3.4 3.6 4.4 4.7 3.9 3.2 4.3 3.6 3.7 2.3 2.5 3.9 3.8 3.6 3.7 3.2 3.9 4.3 2.0 4.0 3.3 2.9 1.8 3.2 3.6 5.2
0.8 0.1 0.2 0.2 0.2 0.2 0.0 0.0 0.2 0.3 0.2 0.1 0.0 0.3 0.6 0.3 0.4 0.0 0.3 0.5 0.4 0.1 0.0 0.3 0.0 0.4 0.2 0.4 0.0 0.5 0.1 0.2 0.6 0.3 0.4 0.0 0.3 0.3 0.1 0.2
found in references such as Tobias (1995) and Wang (1998). Step 1. Denote the measurable variables as X = [x1,x2,⋯,xm] and TSI as y . x1,x2,…,xm and y are n dimensional vectors, m is the number of measurable variables and n is the size of the samples. Both X and y are centered by subtracting their averages and scaled to unite the variances through dividing by their standard deviations. E0 is the normalized matrix of X , and F0 is the normalized variable of y . Step 2. Repeat step 3 to step 6 to obtain the component of E0 until the stop criterion in step 6 is satisfied. Let Ei and Fi denote the residuals of E0 and F0 after the i-th repetition. Step 3. In the i-th repetition, ti is denoted as the i-th component of Ei−1 and wi is denoted as the weights. For ti to carry more data variance information of Ei−1, according to the theory of principal component analysis (Jolliffe, 2002),
4.2. Relationship between the TSR and measurable variables Fig. 4 presents scatter diagrams of the TSR and each measurable variable. The settlement, differential settlement and convergence are fitted using three candidate functions, namely, linear function, logarithmic function and square root function. R2, a statistical measure of how close the data are to the fitted regression line, is used to indicate the goodness-of-fit. The function with a maximum R2 represents the best fitted function. As illustrated in Fig. 4a, the fit line that belongs to the square root curve function has a maximum R2 of 0.75, whereas the linear curve and logarithmic curve have R2 values of 0.67 and 0.74, respectively. Similarly, the linear fit line with an R2 of 0.40 is the best for the differential settlement average (Fig. 4b) and with an R2 of 0.49 is the best for convergence (Fig. 4c). As displayed in Fig. 4d–4f, because there are no obvious relationships between the three distress variables and the TSR, no linear transformation is necessary.
Var (ti ) = Var (Ei −1 wi ) → max
(5)
where Var (·) is the variance operator. Step 4. In the regression model, ti is required to explain the target Fi−1. Referring to the theory of canonical correlation analysis (Thompson, 2005),
4.3. Partial least squares regression A partial least squares (PLS) regression model is adopted to regress the TSR results. Furthermore, PLS has advantages in solving the problem of multicollinearity. Moreover, it combines the basic functions of the regression model, the principal components analysis (PCA) and the canonical correlation analysis (CCA). The algorithm of the PLS is introduced briefly herein; however, details regarding the method can be
r (ti,Fi−1) → max
(6)
where r (·) is the correlation coefficient operator. Step 5. From Eqs. (5) and (6), wi is proved to be the unit eigenvector corresponding to the maximum eigenvalue of matrix EiT−1 Fi −1 FiT−1 Ei −1. Thus, 102
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5
5
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
4
4
Function Adj. R-squar y=ax+b 0.66046 y=alog(x+1)+ 0.74557 y=asqrt(x)+b 0.75125
1 0
0
20
40
60
80
3
TSR
2
2 Function Adj. R-square y=ax+b 0.39983 y=alog(x+1)+ 0.38201 y=asqrt(x)+b 0.39935
1
100 120 140 160
Average relative settlement (mm)
0
0
10
20
30
40
50
2 Function Adj. R-square y=ax+b 0.48674 y=alog(x+1)+ 0.41503 y=asqrt(x)+b 0.43318
1 0
60
0
2
Average differential settlement (mm/m)
(a) Settlement 5
TSR
3
3
TSR
3
TSR
4
2 1
0
0
1
2
3
4
5
Leakage (m2/100 rings)
6
7
0
8
10
5
TSR
4
1
6
12
(c) Convergence
4
2
4
Average conver gence ra tio (‰)
(b) Differential settlement
5
TSR
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
4
3
TSR
TSR
3
5
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
TSR
2 1
0.0
0.3
0.6
0.9
1.2
1.5
0
0.00
Cracking (m/100 rings)
(d) Leakage
(e) Cracking
0.04
0.08
0.12
0.16
0.20
Spalling (m2/100 rings)
(f) Spalling
Fig. 4. The relationship between the TSR and each measurable variable.
ti = Ei −1 wi
(7)
E0 = t1 p1T + t2 p2T + …+tk pkT + Ek
(15)
Ei = Ei −1−ti piT
(8)
F0 = t1 r1T + t2 r2T + …+tk rkT + Fk
(16)
Fi = Fi −1−ti riT
(9) 4.4. TSI formula
where pi denotes the loadings of X and ri denotes the loadings of y .
pi =
ri =
EiT−1 ti ‖ti ‖2
FiT−1 ti ‖ti ‖2
(10)
Measurable variables in the regression model are save , sdiff ave , cave , dl , dc and ds . According to the PLS regression theory and the linear transformation results, let X = [ save ,sdiff ave,cave,dl,dc,ds] and y = TSR . The PLS regression result is in the format
(11)
TSR = A1 save + A2 sdiff ave + B1 cave + C1 dl + C2 dc + C3 ds + C + Fk
(17)
TSI = A1 save + A2 sdiff ave + B1 cave + C1 dl + C2 dc + C3 ds + C
(18)
TSR = TSI + Fk
(19)
Step 6. Cross validation is used as the stop criterion. yi is defined as the i-th actual data; ŷhi is the i-th prediction data using all samples with components t1,t2,…,th ; and ŷh (−i ) denotes the i-th prediction data using all samples except the i-th sample with components t1,t2,…,th . The residual sum of squares (RSS) and the predicted error sum of squares (PRESS) are defined as
where A1, A2 , B1, C1, C2 , C3 and C are coefficients to be estimated and Fk is the residual not explained by the regression function. It is expected that A1, A2 , B1, C1, C2 and C3 will have negative signs. The estimation for normalized measurable variables by the PLS regression is:
n
RSSh =
∑
(yi −yhî )2
i =1
(12)
′ −0.13sdiff ′ ave−0.25cave ′ −0.19dl′−0.06dc′−0.03ds′ TSI′ = −0.62 save
n
PRESSh =
∑
(yi −yĥ (−i ) )2
i =1
where s′ave , s′diff ave , c′ave , d′l , d′c and d′s are the normalized results of save , sdiff ave , cave , dl , dc and ds . After replacing them with the original data, we have
(13)
The stop criterion Q 2 is then defined as
Q 2 = 1−
PRESSh RSSh −1
(20)
TSI = 5.23−0.16 save −0.01sdiff ave−0.09cave−0.08dl−0.05dc−0.50ds (14)
(21)
Fig. 5 reveals the comparison and relationship between the TSR and the TSI. Fig. 5a indicates that the correlation coefficient of Eq. (21) is R = 0.917 and that R square is 0.841. This suggests that the TSI formula accounts for 84.1% of the variation in the TSR. The calculated values for the TSI and the residuals are listed in the last two columns of
In practice, when Q 2 ⩾ (1−0.952 ) = 0.0975 components continue to be extracted, otherwise the iteration stops. Step 7. Through cross validation, suppose k components are selected. Then, E0 and F0 are given as 103
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5.0
and it consists of 1207 segment rings. The external diameter of the tunnel is 6.2 m, and the internal diameter is 5.5 m. The ring width and thickness are 1.2 m and 0.35 m, respectively. The lining ring consists of six segments, specifically, one key segment, two adjacent segments, two standard segments, and one bottom segment. The tunnel was put into operation in 2013. A view of the tunnel is presented Fig. 6. The subsidence of the tunnel was measured along its longitudinal direction using an electronic level, and convergence of the tunnel was measured using a total station. The distresses of the tunnel were based on visual inspections. In the following, we focus only on the upgoing line of the tunnel. Fig. 7a displays the total settlement, which ranged from 0 to 9 mm, whereas Fig. 7b presents the convergence, which ranged from 0 to 10‰D. There were 19 leakages, 23 cracks and 12 spallings found (Fig. 7c). The tunnel was divided into six sections, and the TSI of each section are listed in Fig. 7d. The TSIs range from 3.6 to 4.2, which means the tunnel structure is generally in good serviceability.
TSI-TSR Fitting Line
4.5
TSI
4.0 3.5 Equation Residual Sum of Squares Pearson's r
3.0 2.5
Intercept Slope
2.0 2.0
2.5
3.0
3.5
4.0
y = a + b*x 3.28909 0.91738 Value 0.5214 0.8552
4.5
5.0
TSR (a) Relationship between the TSR and TSI for the rated samples
6. Discussion
5
6.1. Measurable variable of deformation rate
TSR & TSI
4
In Section 2.2, it is assumed that tunnel serviceability represents the existing condition of the tunnel structure. As the rate of deformation is related to the past condition, it is excluded in this paper. However, when selecting the measurable variables, some experts were concerned about the rate of longitudinal settlement and convergence. The TSI at different times can be obtained using the historical data to determine the rate of deformation, and we can further build deterioration models as was in pavement engineering (e.g., Ramaswamy, 1989; Prozzi and Madanat, 2003; Chu and Durango-Cohen, 2007).
3 2
TSR TSI
1 0
0
10
20
30
6.2. Application of TSI in practice
40
The TSI formula is established based on the data from the Shanghai Metro Lines 1, 2 and 4. However, it can be easily modified for other shield tunnels by following the steps presented in Fig. 8. Before calculating the TSI of a specific tunnel, the tunnel should be divided into several sections with a rating length at first, e.g., 200 rings as in this paper. Measurable variables, e.g., save , cave , dl , dc and ds , can then be calculated for each section. The TSI of each tunnel section can be obtained by substituting the measurable variables in the TSI formula. It is recommended that the project managers focus on the tunnel sections with low TSI values.
The sample No. (b) Comparison between the TSR and TSI for the rated samples Fig. 5. Comparisons and relationships between the TSR and TSI. (a) Relationship between the TSR and TSI for the rated samples; (b) Comparison between the TSR and TSI for the rated samples.
Table 3. Fig. 5b indicates that the residuals are less than 0.5, with the exception of the No. 1 and No. 15 samples. The No. 1 and No. 15 samples have large variables of differential settlement and relative settlement, whereas the other variables are small. The reason is that the experts believe that large settlements would lead to lower serviceability, whereas small values of variables for both samples lead to higher TSI values than TSR values, according to the experts.
6.3. Further works The TSI formula reveals the relationship between tunnel serviceability and measurable variables. It does not explain why the serviceability worsens during operation. Further studies that, for example, consider the explainable variables (Ramaswamy, 1989) are needed. In addition, the deterioration process of tunnels is an important issue that should be investigated in future studies (Jiang and Sinha, 1989; Mishalani and Madanat, 2002).
5. Case study The shield tunnel, which is between the International Passenger Terminal Station and the Tiantong Road Station, Shanghai Metro Line 12, is chosen as the case study. The total length of the tunnel is 1.4 km,
Fig. 6. Plan view of the tunnel between the International Passenger Terminal Station and the Tiantong Road Station, Shanghai Metro Line 12.
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(a) Settlement
(b) Convergence
(c) Distresses
(d) TSI results Fig. 7. Settlement, convergence, distresses, and TSI results of the tunnel.
7. Conclusions This paper proposes a comprehensive tunnel serviceability index (TSI) to evaluate the overall condition of shield tunnels in soft ground. The procedure to obtain a TSI formula includes selecting types of tunnel distresses, preparing sample tunnels for rating, rating the sample tunnels by experts, and regressing the TSI formula. The advantages of using a TSI in the condition assessment of shield tunnels are that (1) the TSI is a comprehensive index that represents the overall condition of the shield tunnel structure; (2) the correlations among measurable variables can be taken into account; (3) the application of the TSI formula in engineering practices is relatively easy. The proposed method is demonstrated through its application in the Shanghai metro shield tunnels. Relative settlement, differential settlement, convergence deformation, water leakage, cracking, and spalling were selected as common distresses, and 40 samples were rated to regress the TSI. The TSI result accounts for 84.1% of the variation information in expert rating. The TSI formula reveals that relative settlement, differential settlement, convergence deformation and water leakage are the four significant variables that impact the Shanghai
Fig. 8. The procedure for developing the TSI for other shield tunnels.
105
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metro shield tunnel serviceability with loading factors of −0.62, −0.13, −0.25 and −0.19, respectively. Moreover, cracking and spalling are two weak indicators with loading factors of −0.06 and −0.03.
Technol. 46, 52–63. Liao, S., Hou, X., Peng, F., 2005. Longitudinal shear transfer of tunnel and its 1 D analytical solution. Yanshilixue Yu GongchengXuebao/Chin. J. Rock Mech. Eng. 24 (7), 1110–1116. Liu, W., Liu, X., Wang, S., Du, D., 2013. Influence of stochastic cracks on sulfate diffusion in concrete of underground structure. J. Southwest Jiaotong Univ. 48 (6), 996–1001. Mahdevari, S., Torabi, S.R., 2012. Prediction of tunnel convergence using artificial neural networks. Tunn. Undergr. Space Technol. 28, 218–228. Mishalani, R.G., Madanat, S.M., 2002. Computation of infrastructure transition probabilities using stochastic duration models. J. Infrastruct. Syst. 8 (4), 139–148. Nývlt, O., Prívara, S., Ferkl, L., 2011. Probabilistic risk assessment of highway tunnels. Tunn. Undergr. Space Technol. 26, 71–82. Park, S.W., Shin, Y.S., Oh, Y.S., Ahn, S.R., 2006. A guideline on condition assessment of existing old railway tunnels. Tunn. Undergr. Space Technol. 21, 329–330. Prozzi, J.A., Madanat, S., 2003. Analysis of experimental pavement failure data using duration models. University of California Transportation Center. Ramaswamy, R., 1989. Estimation of latent pavement performance from damage measurements. Massachusetts Institute of Technology. Richards, J.A., 1998. Inspection, maintenance and repair of tunnels: international lessons and practice. Tunn. Undergr. Space Technol. 13 (4), 369–375. Saito, M., Sinha, K.C., 1991. Delphi study on bridge condition rating and effects of improvements. J. Transport. Eng. 117 (3), 320–334. Shen, S., Wu, H., Cui, Y., Yin, Z., 2014. Long-term settlement behaviour of metro tunnels in the soft deposits of Shanghai. Tunn. Undergr. Space Technol. 40, 309–323. Spyridis, P., 2014. Adjustment of tunnel lining service life through appropriate safety factors. Tunn. Undergr. Space Technol. 40, 324–332. Thompson, B., 2005. Canonical correlation analysis. Encyclopedia of statistics in behavioral science. Tobias, R.D., 1995. An introduction to partial least squares regression, Proc. Ann. SAS Users Group Int. Conf., 20th, Orlando, FL. Citeseer, pp. 2–5. Wang, H., 1998. Application of partial least squares regression method. National Defence Industry Press. Wang, R., 2009. Longitudinal deformation analysis for shanghai subway tunnel constructed by shield method. Undergr. Eng. Tunn. 4, 1–6. Wang, R., Zhang, D., 2013. Mechanism of transverse deformation and assessment index for shield tunnels in soft clay under surface surcharge. Chinese J. Geotech. Eng. 35 (6), 1092–1101. Xu, B., Wang, H., Xia, C., 2010. Study on comprehensive evaluation of shield tunnel structural defections. Chinese J. Undergr. Space Eng. 6 (1), 201–207. Ye, Y., Zhu, H., Wang, R., 2007. Analysis on the current status of metro operating tunnel damage in soft ground and its causes. Chinese J. Undergr. Space Eng. 3 (1), 157–160. Yuan, Y., Bai, Y., Liu, J., 2012. Assessment service state of tunnel structure. Tunn. Undergr. Space Technol. 27 (1), 72–85. Yuan, Y., Jiang, X., Liu, X., 2013. Predictive maintenance of shield tunnels. Tunn. Undergr. Space Technol. 38, 69–86. Zhang, W., Sun, K., Lei, C., Zhang, Y., Li, H., Spencer, B.F., 2014. Fuzzy analytic hierarchy process synthetic evaluation models for the health monitoring of shield tunnels. Comput.-Aided Civil Infrastruct. Eng. 29 (9), 676–688.
Acknowledgements The authors gratefully acknowledge the support from the National Natural Science Foundation of China with Grant No. 51478341, the National Basic Research Program of China (973 Program: 2011CB013800), Shanghai Municipal Science and Technology Commission with Grant No. 14231200604, the Research Program of State Key Laboratory for Disaster Reduction in Civil Engineering (SLDRCE14-B-29), and the Fundamental Research Funds for Central Universities. References Asakura, T., Kojima, Y., 2003. Tunnel maintenance in Japan. Tunn. Undergr. Space Technol. 18 (2), 161–169. Chai, J., Shen, S., Zhu, H., 2004. Land subsidence due to groundwater drawdown in Shanghai. Geotechnique 54 (2), 143–147. Chu, C.Y., Durango-Cohen, P.L., 2007. Estimation of infrastructure performance models using state-space specifications of time series models. Transport. Res. Part C: Emerging Technol. 15 (1), 17–32. Chu, C.Y., Durango-Cohen, P.L., 2008. Empirical comparison of statistical pavement performance models. J. Infrastruct. Syst. 14 (2), 138–149. DG/TJ08-2123-2013, 2013. Code for structural appraisal of shield tunnel. Shanghai municipal commission of city development and transport. Djerbi, A., Bonnet, S., Khelidj, A., Baroghel-Bouny, V., 2008. Influence of traversing crack on chloride diffusion into concrete. Cem. Concr. Res. 38 (6), 877–883. FHWA, 2005. Highway and rail transit tunnel inspection manual. GB50157, 2013. Code for Design of Metro. China Architecture and Building Press, Beijing. Highway Research Board, 1962. The AASHO Roads Test: Pavement research. Report 5. National Academy of Sciences-National Research Council. Jiang, Y., Sinha, K.C., 1989. Bridge service life prediction model using the Markov chain. Transp. Res. Rec. 1223, 24–30. Jolliffe, I., 2002. Principal Compon. Anal. John Wiley Sons, Ltd. Li, X., Yan, Z., Wang, Z., Zhu, H., 2015a. A progressive model to simulate the full mechanical behavior of concrete segmental lining longitudinal joints. Eng. Struct. 93, 97–113. Li, X., Yan, Z., Wang, Z., Zhu, H., 2015b. Experimental and analytical study on longitudinal joint opening of concrete segmental lining. Tunn. Undergr. Space
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Condition assessment of shield tunnel using a new indicator: The tunnel serviceability index
MARK
⁎
Xiaojun Lia,b, , Xiaodong Lina, Hehua Zhua,b, Xiuzhi Wangc, Zhaoming Liuc a b c
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China Shanghai Shentong Metro Group, 909 Guilin Road, Shanghai 201103, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Shield tunnel Tunnel serviceability index (TSI) Partial least squares regression Expert rating
The condition assessment of shield tunnels is one of the key issues in the structural maintenance during the service life of the tunnel. Traditionally, the shield tunnel condition has been graded based on certain types of tunnel distresses, such as convergence deformation, differential settlement, cracks, and water leakage. However, the overall condition of the tunnel cannot be so easily assessed, as it often depends on experts’ decisions and evaluations. This paper proposes a comprehensive tunnel serviceability index (TSI) to evaluate the overall condition of a shield tunnel in soft ground. The TSI is a mathematical combination of measurable tunnel distresses that can be obtained by employing the following steps: (1) select the types of tunnel distresses to be included in the TSI, (2) prepare the tunnel samples with distresses, (3) have experts rate the tunnel serviceability, and (4) regress the TSI formula using the partial least squares (PLS) method. The TSI formula can then be applied to evaluate the serviceability of tunnels that are similar to the tunnel samples in step (2). Metro shield tunnels in Shanghai’s soft ground are selected for a case study. Six common distresses, namely, relative settlement, differential settlement, convergence deformation, water leakage, cracking, and spalling, are selected for inclusion in the TSI. Tunnel serviceability ratings of 40 samples were conducted to regress the TSI formula. The TSI formula reveals that relative settlement, differential settlement, convergence deformation and water leakage are the four significant variables that impact the serviceability of Shanghai’s metro shield tunnel with loading factors of −0.62, −0.13, −0.25 and −0.19, respectively. Cracking and spalling are two weak indicators with loading factors of −0.06 and −0.03, respectively. These conclusions, in general, are consistent with the maintenance experiences of the Shanghai metro group.
1. Introduction The maintenance and repair of shield tunnels has become an increasingly important topic in the field of tunneling (e.g., Richards, 1998; Asakura and Kojima, 2003; Yuan et al., 2013). A significant issue when making decisions regarding the maintenance and rehabilitation of shield tunnels is the condition assessment of such facilities (Yuan et al., 2012). Usually, the condition of a shield tunnel can be graded according to the severity of certain types of distresses. For instance, the Federal Highway Administration released a manual that specifies the inspection and rating methodologies for transportation tunnels (FHWA, 2005), whereas Park et al. (2006) developed guidelines for assessing the condition of old railway tunnels. Furthermore, the Chinese Metro Design Code (GB50157, 2013) specifies the limit values for distresses such as leakage, spalling, cracking and deformation. However, as
⁎
different grades would be obtained if different types of distresses are specified in the above approaches, the overall condition of the tunnel cannot be easily assessed, and thus, it often depends on the decisions of experts. Alternatively, the condition of a shield tunnel can be assessed using a mathematical model that can take multiple types of distresses into account. Xu et al. (2010) applied a fuzzy-set method to evaluate the health status of shield tunnels based on fault tree analysis. Nývlt et al. (2011) used a probabilistic risk assessment approach for the making of decisions with respect to tunnel construction and operation. Zhang et al. (2014) used a fuzzy analytic hierarchy process to consider different types of health monitoring data in the rating of shield tunnel structures. Although multiple types of distresses are considered and the overall condition of the tunnel can be obtained, these methods sometimes suffer from unreasonable grading results because the correlations between and among the different types of distresses are ignored.
Corresponding author at: Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China. E-mail addresses: [email protected] (X. Li), [email protected] (X. Lin), [email protected] (H. Zhu), [email protected] (X. Wang), [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.tust.2017.05.007 Received 26 November 2016; Accepted 5 May 2017 0886-7798/ © 2017 Elsevier Ltd. All rights reserved.
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date. (4) Tunnel serviceability rating (TSR): The mean of all experts' ratings of tunnel serviceability. (5) Tunnel serviceability index (TSI): A mathematical combination of measurable variables obtained from shield tunnel samples. The TSI can be used to evaluate the serviceability of tunnels that are similar to the tunnel samples.
In recent years, researchers have used mechanical models to assess tunnel conditions. Yuan et al. (2012) established a framework for a structural assessment procedure using the principle of limit state design, which is performed sequentially with structural components, portions of linings and whole lining structures. Spyridis (2014) presented a reliability life-cycle based methodology to adjust safety factors used in the design of tunnel linings to attain a specified service life. However, building a mechanical model that is close to the real structure is extremely difficult, especially when distresses are considered. Even if the mechanical model can be built, the computations would be tremendously time consuming. In the fields of pavement engineering and bridge engineering, there is a similar demand for the condition assessment of pavement sections and bridge structures, and accordingly, the expert rating approach has been proved to be an operable and effective method to meet this demand. The American Association of State Highway Officials (AASHO) developed a pavement serviceability index (PSI) based on users’ ratings of 72 pavement sections in America (Highway Research Board, 1962). According to the serviceability rating results, many statistical pavement performance models were developed that could be used to improve assessment results and predict structural conditions (Ramaswamy, 1989; Prozzi and Madanat, 2003; Chu and Durango-Cohen, 2007). Saito and Sinha (1991) conducted a study whereby they sought the opinions of bridge inspectors and engineers and established a relationship between the subjective rating and the severity and extent of the distresses. To date, experts’ opinions regarding the condition of shield tunnels have rarely been reported in the literature. This research is motivated by the growing demand for condition assessments of shield tunnel structures and the successful application of the expert rating approach in the condition assessments of pavement sections and bridge structures. This research offers several contributions to the field. (1) A comprehensive tunnel serviceability index (TSI) is proposed to evaluate the overall condition of a shield tunnel in soft ground. (2) The methodology to obtain the TSI formula is presented. (3) The application of the TSI to a Shanghai metro shield tunnel is provided. This paper is organized as follows. The terms and assumptions related to the condition assessment of shield tunnel structures are introduced in Section 2. Inspection data of Shanghai metro shield tunnels, e.g., settlement, convergence and various distresses, are described in Section 3. The methodology to obtain the TSI formula is presented in Section 4. The application of the TSI to a specific case is provided in Section 5. The application of the method is then discussed in Section 6, and conclusions are discussed in Section 7.
2.2. Assumptions (1) Tunnel serviceability is based on the condition at the current time. This means the past condition is excluded in the rating process because the main objective of this research is to build a mathematical relationship between tunnel serviceability and measurable variables. If the past condition is considered, many historical data would be required, a consideration that is sometimes impractical. However, the conditions of the past and the future can be taken into account through the performance deterioration models (Chu and Durango-Cohen, 2008). (2) Tunnel serviceability is only related to measurable variables. The measurable variables reveal the relationship between tunnel distresses and its condition, while the explanatory variables explain the deterioration process (Ramaswamy, 1989). The explanatory variables are not considered because shield tunnel deterioration is a separate topic that is outside the scope of this paper. 3. Inspections of Shanghai metro shield tunnels Shanghai, an area of soft deposit, is located at the alluviation of the Yangtze River Delta where the Huangpu River joins the Yangtze River. It has been more than 20 years since the first metro line was put into operation in the 1990 s. At the end of December 2015, there were 14 metro lines and 366 stations, which accounted for a total length of 617 km in operation. An additional four metro lines are in the planning phase and expected to be built in the next five years. The Code for the Structural Appraisal of Shield Tunnels (DG/TJ082123-2013, 2013) and the Highway and Rail Transit Tunnel Inspection Manual (FHWA, 2005) have identified and defined the tunnel inspection items, such as distresses, structural deformation, concrete and steel corrosion, and levels of CO2 , Cl− and SO42− in the air and water. Although corrosion and ion diffusion impacts tunnel performance (Djerbi et al., 2008; Liu et al., 2013), they were not included in the routine inspections in Shanghai. The common inspection items included in the Shanghai metro shield tunnels include water leakage, spalling, cracking, dislocation, joint opening, longitudinal settlement and circumferential convergence (Ye et al., 2007). These inspection items can be further divided into three categories, namely, longitudinal deformation, circumferential deformation, and distresses on interior lining surfaces. In this research, Shanghai metro lines 1, 2 and 4 are selected as the rating samples because these lines have been in operation for a period long enough to provide stable and sufficient data.
2. Terms and assumptions 2.1. Terms related to the condition assessment of shield tunnel structures To succinctly describe the condition assessment problem, it is necessary to introduce certain terms that refer to the AASHO road test (Highway Research Board, 1962).
3.1. Longitudinal deformation (1) Measurable variable: The observable effects that can be measured, either through visual inspection, total stations, or tunnel section scanning devices, of shield tunnel structure condition changes, such as longitudinal settlement, circumferential convergence and distresses. (2) Explanatory variable: The unobservable fundamental variables that can describe observed phenomena. Structure deterioration is the result of a variety of these variables. For example, age, traffic, environmental erosion, maintenance activities, etc. constitute explanatory variables. (3) Tunnel serviceability: The ability of a specific section of the shield tunnel structure to provide normal and safe use in its existing condition on the date of the rating, not on a past date or a future
According to field monitoring, significant settlement and substantial differential settlement occur after more than ten years of operation (Shen et al., 2014). The main reasons for the long-term settlement of shield tunnels are the sublayer subsidence, the disturbances from posttunneling and nearby construction, the infiltration of the groundwater and the cyclic loading of trains (Chai et al., 2004; Shen et al., 2014). Because the uniform settlement does no harm to the structure’s safety, the inspections of longitudinal deformation focus on relative settlement and differential settlement. The concepts of uniform settlement and relative settlement are presented in Fig. 1. Differential settlement is the settlement difference between two monitoring points divided by their distance and is given by 99
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1800 Ground
Metro Line 1 Metro Line 2 Metro Line 4
1600 1400
Measured settlement
Records number
Initial additional settlement is zero Uniform settlement Highest point Total settlement
Relative settlement
1200 1000 800 600 400 200 0
leakage
cracking
spalling
dislocation opening
Distresses Fig. 2. Distress statistics of Shanghai Metro Lines 1, 2 and 4. Fig. 1. The concept of the relative settlement.
3.3. Distresses
sdiff i =
|sri−sr (i −1) | li
(1)
The common inspected distresses in the Shanghai metro shield tunnels were water leakage, cracking, spalling, dislocation, and joint opening. Fig. 2 displays the number of recorded distresses of the Shanghai Metro Lines 1, 2 and 4 in 2011 and 2012. In general, 73.6% of the observed distresses were water leakage, whereas 14.5% and 11.4% were cracking and spalling distresses, respectively. Dislocation and joint opening accounted for only a small proportion of the distresses. The reason for the small number of recorded dislocation and joint openings was because these distresses are not easy to recognize through routine visual inspections. Total water leakage area dl , total cracking length dc , and total spalling area ds , per 100 rings are chosen as the remaining three measurable variables. Dislocation and joint opening are excluded because the recorded number of dislocation and joint opening are very small and previous studies have found that dislocation and joint openings are correlated with longitudinal and circumferential deformation (Liao et al., 2005; Wang, 2009; Wang and Zhang, 2013; Li et al., 2015b).
where sdiff i is differential settlement at monitoring point i; sri is the measured settlement at monitoring point i; and li is the distance between the i-th and (i−1)-th monitoring points. Average relative settlement and average differential settlement are chosen as two measurable variables and are given by m
∑ save =
sri
i =1
(2)
m m
∑ sdiff ave =
sdiff i
i =2
(3)
m−1
where save is average relative settlement; sdiff ave is the average differential settlement; andm is the number of settlement monitoring points.
3.4. Statistics of the measured variables
3.2. Circumferential deformation
Six measurable variables are selected, namely, average relative settlement save , average differential settlement sdiff ave , average convergence ratio cave , total water leakage area dl , total cracking length dc , and total spalling area ds . Table 1 presents the statistics of the measurable variables.
Circumferential deformation is another major issue that affects the structural performance during operation. Large convergence deformation could result in a reduction of structural safety and could increase maintenance costs (Mahdevari and Torabi, 2012). In the Shanghai metro shield tunnels, the bolt begins to yield when the convergence reaches 7.7‰D (D is the designed external diameter). An increase in bolt stress leads to an increase in the joint opening (Li et al., 2015a). The joint opening then reaches the waterproof control limit when the convergence reaches 9.6‰D, and the concrete at the tunnel waist reaches its characteristic value of strength when the convergence further reaches 13.6‰D (Wang and Zhang, 2013). The average convergence ratio is chosen as the third measurable variable and is defined as m
∑ cave =
4. Methodology to obtain TSI formula 4.1. Tunnel serviceability rating Tunnel serviceability ratings were obtained using rating forms rather than field ratings because it was impractical for an expert to enter the tunnel at midnight and rate a number of tunnels in a short time. Fig. 3 provides a sample rating form that consists of basic information, a distress maps and deformation charts. The rating section includes 200 segmented rings that are 240 m long. The basic information consists of the structure location and inspection date. The distress map illustrates the location, shape and associated value of each recorded distress on the structure unfolded map. The deformation charts provide the longitudinal deformation and circumferential convergence of the section. Yuan et al. (2012) and the Code for the Structural Appraisal of Shield Tunnels (DG/TJ08-2123-2013, 2013) use five service states,
m
∑
|di−D|
i =1
Dm
× 1000 =
|Δi |
i =1
Dm
× 1000
(4)
where cave is the average convergence ratio; m is the number of convergence monitoring points; di is the measured external diameter of the i-th monitoring points; D is the designed external diameter of the segmented linings; and Δi is the difference between the measured diameter and the designed diameter. 100
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Table 1 Statistics of the six measurable variables.
Table 2 Information regarding rating panel members.
Measurable variables
Minimum
First quartile
Median
Third quartile
Maximum
Mean value
save
1.2
8.2
19.6
40.2
130.1
27.8
1.5
4.2
9.5
19.8
58.0
12.5
2.4
6.1
7.3
8.4
12.0
1.5
0.00
0.16
0.42
1.11
5.74
0.86
0.00
0.00
0.00
0.90
5.67
0.76
(mm) sdiff ave (mm/ 100 m) cave (‰D) dl (m2/100 rings) dc (m/100 rings) ds (m2/100 rings)
0.00
0.00
0.00
0.01
1.30
No.
Age
Years of employment
Background/interest
1 2
45 44
14 21
3 4 5 6 7 8 9
60 43 41 36 47 40 46
36 9 10 10 27 10 17
Metro structure design Metro construction and operation management Structure monitoring Structure maintenance Structure maintenance Structure rehabilitation Structure rehabilitation Structure engineering researcher Geotechnical engineering researcher
independent decisions with respect to the ratings. The panel rated 39 sections, 18 of which were rated on January 17, 2015 and 21 of which were rated on May 23, 2015. If there was no excessive deformation or distress in the tunnel section, the tunnel serviceability was rated a 5 (very good, the No. 40 sample). The rating results are given in Table 3. The 2nd column of Table 3 (TSR) presents the mean values of the tunnel serviceability ratings, which range from 4.9 to 2.1, where 5.0 is the ideal status. Standard deviations of the TSR are listed in the 3rd column, and measurable variables of the rated samples are listed in the 4th-through 8th columns. The tunnel serviceability index (TSI) and the differences between the TSI and TSR are listed in the last two columns.
0.08
namely, suitable, degraded, deteriorated, unavailable and unstable, for the structural performance of the tunnel lining. A simpler description, that is, very good (5), good (4), fair (3), poor (2) and very poor (1), is adopted in this research to represent the five service states. The rating panel, which consisted of nine experts, represents a wide variety of interests, including design, construction, administration, maintenance and research (see Table 2). The members of the rating panel were informed of the pertinent definition, and they discussed their opinions before the ratings. They were instructed to make leakage area: 0.7 m 2
D
Information
leakage area: 1.6 m 2
Metro Line: --
B
cracking length: 0.73 m
Start Station: -End Station: -Start Ring: 600
L
End Ring: 800 Date: 2011.11.03
spalling area: 0.01 m 2
F
L
Legend
leakage area: 1.3 m 2
leakage area: 0.50 m 2
Leakage Spalling Dislocation
B
Cracking Joint Opening
D
D) ŝƌĐƵŵĨĞƌĞŶƟĂl convergence(¡ ë
Accum ulated settlement (mm )
0
- 30
- 60 600
700 Ring No.
800
20
10
Status
Rating
Very good
5
Good
4
Fair Poor
3
Very poor
1
Rating result 0 600
700 Ring No.
Fig. 3. Tunnel serviceability rating form.
101
800
2
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Table 3 Tunnel serviceability rating results. No.
TSR
Std. dev. of TSR
save (mm)
sdiff ave (mm/100 m)
cave (‰D)
dl (m2/100 rings)
dc (m/100 rings)
ds (m2/100 rings)
TSI
Diff.TSI & TSR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
3.3 3.7 4.9 4.3 2.6 3.1 3.3 4.1 2.5 3.3 4.3 4.1 3.7 3.9 4.0 3.3 4.8 4.7 4.2 2.7 4.7 3.7 3.7 2.0 2.5 3.5 4.0 4.0 3.7 2.7 4.0 4.5 2.6 3.7 2.9 2.9 2.1 2.9 3.5 5.0
0.7 1.0 0.3 0.5 0.9 0.8 0.7 0.4 1.0 0.9 0.5 0.4 1.1 0.8 1.0 0.5 0.4 0.5 0.7 0.4 0.5 0.7 0.9 0.7 0.7 0.5 0.5 0.3 0.7 1.1 0.6 0.5 0.9 0.7 0.8 0.8 0.8 0.9 0.7 0.0
10.4 10.4 2.4 5.3 88.6 43.6 25.5 10.8 125.3 27.3 25.0 6.9 6.6 15.1 32.4 16.0 5.3 3.6 31.5 69.3 3.2 38.1 15.6 131.4 96.6 22.8 20.3 25.0 9.2 50.3 7.1 12.5 142.0 5.0 33.9 75.6 143.2 43.2 18.8 0.0
26.4 4.2 4.9 8.4 21.6 12.9 12.9 17.3 17.4 8.0 2.5 19.6 23.3 27.2 3.3 23.3 9.0 1.2 3.7 10.7 17.5 8.3 25.6 29.2 40.5 4.9 4.5 20.4 26.4 23.3 26.1 6.0 57.0 6.4 4.3 21.6 54.2 27.1 27.9 0.0
3.9 7.8 2.8 3.8 8.5 6.8 9.2 5.6 9.4 8.0 3.5 4.5 5.1 7.3 7.9 4.1 4.4 3.1 4.1 5.7 5.0 6.5 6.0 6.8 8.1 6.2 7.9 7.2 3.6 7.5 6.4 3.5 9.1 7.3 10.2 7.6 9.2 7.1 5.3 0.0
0.35 5.55 0.00 4.60 0.70 1.95 1.05 0.00 0.20 0.35 0.90 0.00 5.80 0.00 2.05 5.75 0.00 0.00 1.35 0.25 0.95 0.25 2.50 1.95 0.70 0.00 0.35 0.00 5.75 0.00 0.75 0.00 0.00 1.55 1.20 0.70 0.25 0.00 2.75 0.00
0.00 0.00 0.00 0.00 0.00 0.44 1.03 0.00 4.19 0.44 0.00 0.00 0.00 2.33 0.36 0.00 0.00 0.00 0.00 1.14 0.00 0.33 0.00 0.66 0.67 1.35 0.00 0.00 0.00 0.63 0.00 0.00 0.36 1.12 0.00 0.00 2.36 1.13 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.05 0.15 0.00 0.05 0.05 0.00 0.05 0.00 0.00 0.05 0.00 0.05 0.00 0.00 0.05 0.00 0.00 0.00 0.15 0.10 0.00 0.05 0.10 0.00 0.05 0.11 0.00 0.00 0.05 0.00 0.15 0.15 0.10 0.00 0.00
4.1 3.6 4.7 4.1 2.8 3.3 3.3 4.1 2.3 3.6 4.1 4.2 3.7 3.6 3.4 3.6 4.4 4.7 3.9 3.2 4.3 3.6 3.7 2.3 2.5 3.9 3.8 3.6 3.7 3.2 3.9 4.3 2.0 4.0 3.3 2.9 1.8 3.2 3.6 5.2
0.8 0.1 0.2 0.2 0.2 0.2 0.0 0.0 0.2 0.3 0.2 0.1 0.0 0.3 0.6 0.3 0.4 0.0 0.3 0.5 0.4 0.1 0.0 0.3 0.0 0.4 0.2 0.4 0.0 0.5 0.1 0.2 0.6 0.3 0.4 0.0 0.3 0.3 0.1 0.2
found in references such as Tobias (1995) and Wang (1998). Step 1. Denote the measurable variables as X = [x1,x2,⋯,xm] and TSI as y . x1,x2,…,xm and y are n dimensional vectors, m is the number of measurable variables and n is the size of the samples. Both X and y are centered by subtracting their averages and scaled to unite the variances through dividing by their standard deviations. E0 is the normalized matrix of X , and F0 is the normalized variable of y . Step 2. Repeat step 3 to step 6 to obtain the component of E0 until the stop criterion in step 6 is satisfied. Let Ei and Fi denote the residuals of E0 and F0 after the i-th repetition. Step 3. In the i-th repetition, ti is denoted as the i-th component of Ei−1 and wi is denoted as the weights. For ti to carry more data variance information of Ei−1, according to the theory of principal component analysis (Jolliffe, 2002),
4.2. Relationship between the TSR and measurable variables Fig. 4 presents scatter diagrams of the TSR and each measurable variable. The settlement, differential settlement and convergence are fitted using three candidate functions, namely, linear function, logarithmic function and square root function. R2, a statistical measure of how close the data are to the fitted regression line, is used to indicate the goodness-of-fit. The function with a maximum R2 represents the best fitted function. As illustrated in Fig. 4a, the fit line that belongs to the square root curve function has a maximum R2 of 0.75, whereas the linear curve and logarithmic curve have R2 values of 0.67 and 0.74, respectively. Similarly, the linear fit line with an R2 of 0.40 is the best for the differential settlement average (Fig. 4b) and with an R2 of 0.49 is the best for convergence (Fig. 4c). As displayed in Fig. 4d–4f, because there are no obvious relationships between the three distress variables and the TSR, no linear transformation is necessary.
Var (ti ) = Var (Ei −1 wi ) → max
(5)
where Var (·) is the variance operator. Step 4. In the regression model, ti is required to explain the target Fi−1. Referring to the theory of canonical correlation analysis (Thompson, 2005),
4.3. Partial least squares regression A partial least squares (PLS) regression model is adopted to regress the TSR results. Furthermore, PLS has advantages in solving the problem of multicollinearity. Moreover, it combines the basic functions of the regression model, the principal components analysis (PCA) and the canonical correlation analysis (CCA). The algorithm of the PLS is introduced briefly herein; however, details regarding the method can be
r (ti,Fi−1) → max
(6)
where r (·) is the correlation coefficient operator. Step 5. From Eqs. (5) and (6), wi is proved to be the unit eigenvector corresponding to the maximum eigenvalue of matrix EiT−1 Fi −1 FiT−1 Ei −1. Thus, 102
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5
5
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
4
4
Function Adj. R-squar y=ax+b 0.66046 y=alog(x+1)+ 0.74557 y=asqrt(x)+b 0.75125
1 0
0
20
40
60
80
3
TSR
2
2 Function Adj. R-square y=ax+b 0.39983 y=alog(x+1)+ 0.38201 y=asqrt(x)+b 0.39935
1
100 120 140 160
Average relative settlement (mm)
0
0
10
20
30
40
50
2 Function Adj. R-square y=ax+b 0.48674 y=alog(x+1)+ 0.41503 y=asqrt(x)+b 0.43318
1 0
60
0
2
Average differential settlement (mm/m)
(a) Settlement 5
TSR
3
3
TSR
3
TSR
4
2 1
0
0
1
2
3
4
5
Leakage (m2/100 rings)
6
7
0
8
10
5
TSR
4
1
6
12
(c) Convergence
4
2
4
Average conver gence ra tio (‰)
(b) Differential settlement
5
TSR
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
4
3
TSR
TSR
3
5
TSR y=ax+b y=alog(x+1)+b y=asqrt(x)+b
TSR
2 1
0.0
0.3
0.6
0.9
1.2
1.5
0
0.00
Cracking (m/100 rings)
(d) Leakage
(e) Cracking
0.04
0.08
0.12
0.16
0.20
Spalling (m2/100 rings)
(f) Spalling
Fig. 4. The relationship between the TSR and each measurable variable.
ti = Ei −1 wi
(7)
E0 = t1 p1T + t2 p2T + …+tk pkT + Ek
(15)
Ei = Ei −1−ti piT
(8)
F0 = t1 r1T + t2 r2T + …+tk rkT + Fk
(16)
Fi = Fi −1−ti riT
(9) 4.4. TSI formula
where pi denotes the loadings of X and ri denotes the loadings of y .
pi =
ri =
EiT−1 ti ‖ti ‖2
FiT−1 ti ‖ti ‖2
(10)
Measurable variables in the regression model are save , sdiff ave , cave , dl , dc and ds . According to the PLS regression theory and the linear transformation results, let X = [ save ,sdiff ave,cave,dl,dc,ds] and y = TSR . The PLS regression result is in the format
(11)
TSR = A1 save + A2 sdiff ave + B1 cave + C1 dl + C2 dc + C3 ds + C + Fk
(17)
TSI = A1 save + A2 sdiff ave + B1 cave + C1 dl + C2 dc + C3 ds + C
(18)
TSR = TSI + Fk
(19)
Step 6. Cross validation is used as the stop criterion. yi is defined as the i-th actual data; ŷhi is the i-th prediction data using all samples with components t1,t2,…,th ; and ŷh (−i ) denotes the i-th prediction data using all samples except the i-th sample with components t1,t2,…,th . The residual sum of squares (RSS) and the predicted error sum of squares (PRESS) are defined as
where A1, A2 , B1, C1, C2 , C3 and C are coefficients to be estimated and Fk is the residual not explained by the regression function. It is expected that A1, A2 , B1, C1, C2 and C3 will have negative signs. The estimation for normalized measurable variables by the PLS regression is:
n
RSSh =
∑
(yi −yhî )2
i =1
(12)
′ −0.13sdiff ′ ave−0.25cave ′ −0.19dl′−0.06dc′−0.03ds′ TSI′ = −0.62 save
n
PRESSh =
∑
(yi −yĥ (−i ) )2
i =1
where s′ave , s′diff ave , c′ave , d′l , d′c and d′s are the normalized results of save , sdiff ave , cave , dl , dc and ds . After replacing them with the original data, we have
(13)
The stop criterion Q 2 is then defined as
Q 2 = 1−
PRESSh RSSh −1
(20)
TSI = 5.23−0.16 save −0.01sdiff ave−0.09cave−0.08dl−0.05dc−0.50ds (14)
(21)
Fig. 5 reveals the comparison and relationship between the TSR and the TSI. Fig. 5a indicates that the correlation coefficient of Eq. (21) is R = 0.917 and that R square is 0.841. This suggests that the TSI formula accounts for 84.1% of the variation in the TSR. The calculated values for the TSI and the residuals are listed in the last two columns of
In practice, when Q 2 ⩾ (1−0.952 ) = 0.0975 components continue to be extracted, otherwise the iteration stops. Step 7. Through cross validation, suppose k components are selected. Then, E0 and F0 are given as 103
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5.0
and it consists of 1207 segment rings. The external diameter of the tunnel is 6.2 m, and the internal diameter is 5.5 m. The ring width and thickness are 1.2 m and 0.35 m, respectively. The lining ring consists of six segments, specifically, one key segment, two adjacent segments, two standard segments, and one bottom segment. The tunnel was put into operation in 2013. A view of the tunnel is presented Fig. 6. The subsidence of the tunnel was measured along its longitudinal direction using an electronic level, and convergence of the tunnel was measured using a total station. The distresses of the tunnel were based on visual inspections. In the following, we focus only on the upgoing line of the tunnel. Fig. 7a displays the total settlement, which ranged from 0 to 9 mm, whereas Fig. 7b presents the convergence, which ranged from 0 to 10‰D. There were 19 leakages, 23 cracks and 12 spallings found (Fig. 7c). The tunnel was divided into six sections, and the TSI of each section are listed in Fig. 7d. The TSIs range from 3.6 to 4.2, which means the tunnel structure is generally in good serviceability.
TSI-TSR Fitting Line
4.5
TSI
4.0 3.5 Equation Residual Sum of Squares Pearson's r
3.0 2.5
Intercept Slope
2.0 2.0
2.5
3.0
3.5
4.0
y = a + b*x 3.28909 0.91738 Value 0.5214 0.8552
4.5
5.0
TSR (a) Relationship between the TSR and TSI for the rated samples
6. Discussion
5
6.1. Measurable variable of deformation rate
TSR & TSI
4
In Section 2.2, it is assumed that tunnel serviceability represents the existing condition of the tunnel structure. As the rate of deformation is related to the past condition, it is excluded in this paper. However, when selecting the measurable variables, some experts were concerned about the rate of longitudinal settlement and convergence. The TSI at different times can be obtained using the historical data to determine the rate of deformation, and we can further build deterioration models as was in pavement engineering (e.g., Ramaswamy, 1989; Prozzi and Madanat, 2003; Chu and Durango-Cohen, 2007).
3 2
TSR TSI
1 0
0
10
20
30
6.2. Application of TSI in practice
40
The TSI formula is established based on the data from the Shanghai Metro Lines 1, 2 and 4. However, it can be easily modified for other shield tunnels by following the steps presented in Fig. 8. Before calculating the TSI of a specific tunnel, the tunnel should be divided into several sections with a rating length at first, e.g., 200 rings as in this paper. Measurable variables, e.g., save , cave , dl , dc and ds , can then be calculated for each section. The TSI of each tunnel section can be obtained by substituting the measurable variables in the TSI formula. It is recommended that the project managers focus on the tunnel sections with low TSI values.
The sample No. (b) Comparison between the TSR and TSI for the rated samples Fig. 5. Comparisons and relationships between the TSR and TSI. (a) Relationship between the TSR and TSI for the rated samples; (b) Comparison between the TSR and TSI for the rated samples.
Table 3. Fig. 5b indicates that the residuals are less than 0.5, with the exception of the No. 1 and No. 15 samples. The No. 1 and No. 15 samples have large variables of differential settlement and relative settlement, whereas the other variables are small. The reason is that the experts believe that large settlements would lead to lower serviceability, whereas small values of variables for both samples lead to higher TSI values than TSR values, according to the experts.
6.3. Further works The TSI formula reveals the relationship between tunnel serviceability and measurable variables. It does not explain why the serviceability worsens during operation. Further studies that, for example, consider the explainable variables (Ramaswamy, 1989) are needed. In addition, the deterioration process of tunnels is an important issue that should be investigated in future studies (Jiang and Sinha, 1989; Mishalani and Madanat, 2002).
5. Case study The shield tunnel, which is between the International Passenger Terminal Station and the Tiantong Road Station, Shanghai Metro Line 12, is chosen as the case study. The total length of the tunnel is 1.4 km,
Fig. 6. Plan view of the tunnel between the International Passenger Terminal Station and the Tiantong Road Station, Shanghai Metro Line 12.
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(a) Settlement
(b) Convergence
(c) Distresses
(d) TSI results Fig. 7. Settlement, convergence, distresses, and TSI results of the tunnel.
7. Conclusions This paper proposes a comprehensive tunnel serviceability index (TSI) to evaluate the overall condition of shield tunnels in soft ground. The procedure to obtain a TSI formula includes selecting types of tunnel distresses, preparing sample tunnels for rating, rating the sample tunnels by experts, and regressing the TSI formula. The advantages of using a TSI in the condition assessment of shield tunnels are that (1) the TSI is a comprehensive index that represents the overall condition of the shield tunnel structure; (2) the correlations among measurable variables can be taken into account; (3) the application of the TSI formula in engineering practices is relatively easy. The proposed method is demonstrated through its application in the Shanghai metro shield tunnels. Relative settlement, differential settlement, convergence deformation, water leakage, cracking, and spalling were selected as common distresses, and 40 samples were rated to regress the TSI. The TSI result accounts for 84.1% of the variation information in expert rating. The TSI formula reveals that relative settlement, differential settlement, convergence deformation and water leakage are the four significant variables that impact the Shanghai
Fig. 8. The procedure for developing the TSI for other shield tunnels.
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metro shield tunnel serviceability with loading factors of −0.62, −0.13, −0.25 and −0.19, respectively. Moreover, cracking and spalling are two weak indicators with loading factors of −0.06 and −0.03.
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