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Evaluation model for immersed tunnel health state: A case study of Honggu Tunnel, Jiangxi Province, China
Tunnelling and Underground Space Technology 90 (2019) 239–248
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Evaluation model for immersed tunnel health state: A case study of Honggu Tunnel, Jiangxi Province, China ⁎
T
⁎
Xiangchun Xua, Liyuan Tonga, , Songyu Liua, , Hongjiang Lib,c a
Institute of Geotechnical Engineering, Institute of Future Underground Space, Jiangsu Key Laboratory of Urban Underground Engineering & Environmental Safety, Southeast University, Nanjing 210096, China b Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, China c Centre for Offshore Foundation Systems, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Fuzzy-AHP Immersed tunnel Health monitoring Fusion weight
The evaluation of the health state of an immersed tunnel is inevitably affected by the variety of influencing factors, the complex relationship between influencing factors and fuzzy characteristics of health evaluation criteria. A targeted method for analysis of the health conditions of an immersed tunnel in operation period is immature. As a case study of the health monitoring of the largest inland river immersed tunnel-Nanchang Honggu Tunnel, a fuzzy analytic hierarchy process (Fuzzy-AHP) method was carried out in this study, which merged different types of data from multiple sensors to map them into comprehensive evaluation value of the immersed tunnel. The hierarchical structure of the health evaluation index was established, and the layout scheme of monitoring sensors was designed through a comprehensive analysis of influencing factors. Additionally, the entropy weight method was introduced to modify the subjective characteristic of index weight in the fuzzy analytic hierarchy model, and then a Fuzzy-AHP evaluation procedure was built. Finally, the proposed evaluation model and evaluation procedure of immersed tunnel health states were verified by the field monitoring data of the Nanchang Honggu Tunnel. The comprehensive evaluation value VF was compared with the rating scales and countermeasures proposed in this study to determine the tunnel health state and corresponding countermeasures. The results indicate that the evaluation health of the whole tunnel sections of Nanchang Honggu Tunnel in December 2018 was in grade A, and further monitoring was needed. The VF values of sections located at the middle of the river and the final joint were slightly smaller than other sections. The proposed Fuzzy-AHP method can give a feasible and effective evaluation for immersed tunnel health states.
1. Introduction Immersed tunnels have received more and more attention (Han, 2016) in China in recent years due to their fast construction speed, shallow buried depth, no influence on navigation and less length of the tunnel approach ramps at the shorelines compared to a bridge or bore tunnel. Under the dual effects of long-term natural environment and operation environment, immersed tunnels inevitably suffer different degrees of leakage, structural uneven settlement, cracks, and other deteriorations. Those have a great impact on the operation safety of the tunnel. Moreover, the difficulty and cost of tunnel maintenance will also increase sharply with the development of the deterioration. Therefore, it is of great significance to track the development of tunnel deterioration in real time and analyze the health state of the tunnel for formulating maintenance countermeasures in time. In the maintenance of the infrastructure, the health monitoring ⁎
technique plays an important role, especially in constructions of bridges and tunnels (Aktan et al., 2000; Sohn et al., 2000; Liu et al., 2009). The method aims at employing in situ, continuous, or regular measurements and analyzing key structural and environmental parameters under the operating conditions to provide warning of impending abnormal states or structural failures, and then avoids casualties as well as informing maintenance and rehabilitation decisions. Since the 1990s, the health monitoring system has attracted the attention of scholars and engineers. In the field of civil engineering, health monitoring system was first applied to bridges (Inaudi and Glisic, 2002; Liu, 2001; Ko et al., 2002), and then buildings, structures and shield tunnels (Metje et al., 2006; Ledesma and Alonso, 2017; Li et al., 2017; Kumar and Hossain, 2018; Song et al., 2006; Su et al., 2007). Application cases of health monitoring system in immersed tunnels were not much extensive yet in China. Compared with shield tunnels and mined tunnels, tubes of
Corresponding authors. E-mail addresses: [email protected] (L. Tong), [email protected] (S. Liu).
https://doi.org/10.1016/j.tust.2019.05.005 Received 25 October 2018; Received in revised form 28 January 2019; Accepted 10 May 2019 Available online 15 May 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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length, and other 3 are 90 m, 90 m, 108 m separately. The construction clearance is 11.5 m × 4.5 m, and the size of the cross sections is 30 m × 8.3 m. Because of the runoff of Ganjiang River concentrated in April to June, accounted for 49.6% of the year, it is easy to induce a highly fluctuating water level from rainy season to dry season, the maximum water level difference at the tunnel location in the past decade reaches 14.18 m. According to the geological investigations, the concentration of Cl−, SO42− and Mg2+ in the water is 22.4 mg/L, 16 mg/L, and 5.75 mg/L, respectively, those much less than the critical value of minor corrosive in the technical standards. Therefore, environmental corrosion effect can be ignored and not involved in this study.
immersed tunnels are prefabricated in a dry dock or factory type facility. Rubber gaskets are generally used to maintain the water tightness of tube joints, which results in that the joint of tubes is more sensitive to water level fluctuation and siltation above the tunnel as well as uneven settlement than the concrete structures. And it should be noted that, the stress conditions of immersed tunnel compared with bridge and mined tunnel seem relatively static. However, in some cases, the high water level fluctuation will impose cyclic loading on the tunnel foundation and tunnel joint, and this will raise the safety risk. Grantz (2001a,b) provided a series of cases of uneven settlement of immersed tunnels. In some of those cases, immersed tunnels have suffered different degrees of water leakage, cracks and tube inclination. Parwani (2014) reported the Kil-tunnel in Netherlands, in which, water leakage and displacements as well as rotations were found in the segment joints. As the health monitoring of immersed tunnel structure is very important for long-term safety and economic operation, it is helpful to merge the various monitoring data into the tunnel structure health state and put forward a reasonable evaluation method. The factors affecting the health state of immersed tunnels are complex, and there is still no clear corresponding relationship between the various factors and the health state. In order to fully understand the health state of immersed tunnels, it is necessary to establish a scientific and reasonable evaluation model. Radu (2009) and Sun et al. (2014) summarized the traditional methods of health evaluation including the qualitative method, quantitative method and semi-quantitative method. To date, the quantitative methods have been widely used in shield tunnel projects and other civil engineering projects. Jin et al. (2016) used MATLAB program to evaluate the health state of mining method tunnel quantitatively. Zhang et al. (2014) adopted the fuzzy theory and analytic hierarchy process (AHP) method in shield tunnel health state evaluation. Chen et al. (2014) employed AHP method by comparing the health indicator to the criteria to evaluate the durability of harbor engineering. There were few evaluation cases of immersed tunnel operation health state, and most of them were focused on qualitative or semi- quantitative method. Liu and Huang (2009) employed the mean stress and contact stress of the GINA in immersed tunnels to calculate the minimum GINA compression for ensuring the waterproofing effect, and proposed a joint waterproof performance evaluation method based on the GINA current compression. Tang et al. (2013) evaluated the corrosion risk of the immersed tunnel of the Hongkong-Zhuhai-Macao Bridge by comparing the environment index with the durability index. In view of the complexity of the evaluation object in immersed tunnel engineering, the AHP method was employed to induce and analyze the influencing factors of the immersed tunnel health state. An objective weight assignment method-entropy weight method was introduced to modify the subjective characteristic of index weight in the AHP model. Meanwhile, a fuzzy mathematics theory considering the fuzziness of the relationship between health state and influencing factors was introduced into AHP to establish the combined Fuzzy-AHP evaluation method subjected to immersed tunnel health state. Then, the evaluation method was verified with the engineering case of Nanchang Honggu Tunnel.
3. Health monitoring configuration The tubes of immersed tunnel are prefabricated in dry docks or factory type facility and then connected in the field. In order to make the immersion joints watertight, the rubber gaskets are used. Also the shear keys are set to resist the shear force. As immersed tunnels are located in rivers or oceans, generally with shallow buried depth, the fluctuation of water level and silting above the tunnel can affect the safety of the tunnel. Some main damages such as: joint damage caused by uneven settlement, failure of rubber gaskets and cracks in tubes should be prevented. In addition, vehicle loads, traffic accidents, earthquakes, shipwrecks and water corrosion are all threatening factors to tunnel structure safety. In this project, five main aspects are summarized in the health monitoring of Nanchang Honggu Tunnel: environmental effects, structural stress, structural deformation, structural cracks and leakage (structure cracks and tunnel joint). These five aspects include water level, thickness of siltation layer, rebar stress, concrete stress, PC cable tensile force, uneven settlement, joint opening, joint compression, tube inclination, crack length, crack width, leakage rate, leakage area, and leakage water pH, etc. Fig. 3 presents the detailed tunnel joint, and the health monitoring sensors layout is shown in Fig. 4. Water level and thickness of siltation layer are measured periodically by water level gauges and acoustic wave detectors; rebar stress and concrete stress are monitored in real-time by vibrating wire rebar and concrete stress meters; PC cable tensile force is monitored in real-time by magnetic flux cable stress meters; tunnel uneven settlement is monitored in real-time by differential pressure meters; joint opening and compression is monitored in real-time by two vibrating wire crack meters assembled at a certain angle; tube inclination is monitored in real-time by vibrating wire inclinometers. Structural crack and leakage are inspected periodic, countermeasures should be taken after defects detected and switched into real-time monitoring if possible. As shown in Fig. 4, there are three typical health monitoring sensors layout sections in this project. Section 1 is located at the joint of the tunnel, and the health state of the tunnel joint is mainly monitored. Section 2 is located at 3.5 m distance from the tunnel joint, and the health state of tunnel structure near the joint is mainly monitored. Section 3 is located at the middle of the tube, and the health state of tube structure is mainly monitored.
2. Background and location of Nanchang Honggu tunnel 4. Development of Fuzzy–AHP evaluation model Nanchang Honggu Tunnel is the largest inland river immersed tunnel in China which was began construction in January 2014 and opened to traffic in July 2017 with complex geological and fracture condition. The typical geological profile is shown in Fig. 1. The tunnel connects the old town in the east bank and the new town in the west bank, with a measured average daily traffic of 26.2 thousands vehicles. The geographical position of the tunnel is shown in Fig. 2. In total, the length of Nanchang Honggu Tunnel is approximately 2650 m, of which the 1329 m-length is the section of the reinforced concrete rectangular immersed tube (including the closure joint). Among 12 immersed tube tunnel elements, there are 9 separate elements with a total 115 m in
4.1. Factor sets As mentioned above, there are four types of monitoring factors contributed to the health state evaluation of the tunnel element, namely structural stress, structural deformation, structural crack and leakage, considering the principal of independence and representativeness. These four factors are constructed as a factor layer, and each factor includes its sub-factors, namely indexes, which form the index layer. In the tunnel health state evaluation process, a sequence from the index layer to the factor layer and then to the target layer is complied. The 240
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Fig. 1. Typical geological profile in the test site.
hierarchical model of Honggu Tunnel health monitoring and evaluation is shown in Fig. 5. The above monitoring indexes were realized through a real-time monitoring and regular inspection. The structural stress and deformation indexes were monitored and transmitted to the system database in real-time; structural crack and leakage indexes were then put into the system database manually after regular inspection. 4.2. Evaluation grade sets The health conditions subjected to tunnel damages can be classified into several grades, as shown in Table 1. In this study, four grades from A to D were counted. The corresponding rating scales and countermeasures were also proposed and shown in Table 1. In addition, factors and indexes in Fig. 1 were all classified into four grades. The grading criterion for each index in the index layer was technically identified by referring to Chinese technical standards and specifications (GB 501532008, GB 50108-2008, SL 191-2008, JTG H12, 2015), Richard and Baber (2013) as well as designer’s advices. Especially for structural stress and structural deformation, among the four grades, grade D is the worst condition, indicating that the structure has been destroyed, with a critical value equals to the design limit value of the index. Grade C indicates that the structure has a tendency to be destroyed. Considering the structural reliability, its critical value is 85% of the design limit
Fig. 3. Detail of tunnel joint.
value of the index, which is believed to be the threshold of unacceptable state for the operation and maintenance of immersed tunnel. Grade B and A indicate that the structure is in normal function. The critical value of grade B is 75% of the design limit value of the index, and grade A is less than 75%.
Fig. 2. The location of the Honggu immersed tunnel. 241
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Fig. 4. The layout of various health monitoring sensors.
Fig. 5. Honggu Tunnel health monitoring and evaluation hierarchical model.
4.3. Weight assignment
The grade vector to characterize the rating scales was introduced, which can be expressed as
G = [3.5
2.5
1.5
0.5]
In the evaluation model, as the importance and distribution between factors and indexes was different, various factors and indexes should be assigned different weights based on their relative importance to the upper layer. Weight assignment method can be divided into two
(1)
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Table 1 Comprehensive evaluation criteria and countermeasure. Grade
Health state
Comprehensive rating scale
Countermeasure
A B C D
Not damaged or slightly damaged Damaged Relatively serious damage Seriously damaged
3 < VF ≤ 4 2 < VF ≤ 3 1 < VF ≤ 2 VF ≤ 1
Monitoring Ready to take countermeasure Take countermeasure as soon as possible Take countermeasure instantly
4.3.2. Objective weight assignment Under the assumption of the index weight is determined according to the amount of information contained in each index (Wang et al., 2015), entropy weight assignment method is deemed to be a reasonable objective method. The specific steps of entropy weight assignment method are shown in Appendix A.
categories according to the origin of the source information: one is the subjective weighting method, in which the source information comes from expert consultation, such as expert consultation method, analytic hierarchy process method; the other is the objective weighting method, in which the source information comes from statistical data, such as principal component analysis method, entropy method. The two categories have their own characteristics. As the subjective weighting method can make full use of expert’s knowledge and experience, and the objective weighting method can make full use of statistical data. The objective weighting method was combined into the AHP to assign the weights of index layer in this study.
4.3.3. Fusion weight The subjective weight and objective weight represent the subjective judgment and the objective data information, respectively. By a combination of them, the comprehensive judgment of the index weight can be made. The conventional approaches of fusion weight calculation are weighted arithmetic mean, weighted square root, weighted square sum, etc. In this study, the weighted arithmetic mean method was used due to its easily understood by field engineers as one of the fusion methods, and the subjective weight was considered a little more important than the objective weight. The fusion weight calculation formula is as follows.
4.3.1. Subjective weight assignment AHP weighting method is one of the commonly used methods in subjective weighting. The key step of AHP weighting method is to obtain the relative importance of indexes to the corresponding factors in the factor layer by comparing them in couple. Then, the importance is transformed into the digital description and the respective weights are obtained according to the digital scale. Commonly used digital scales were 1–9 scale, 9/9–9/1 scale, 10/10–18/2 scale, exponential scale, multiplication scale, etc. As an updated method of AHP, the multiplication scale method generally replaces the 1–9 scale by 1–1.354 scale, by means of same and slightly larger. When importance of index A is the same as index B, the judgment scale is 1, weights of index A and index B are 0.5 and 0.5. Similarly, when index A is slightly larger than index B, the judgment scale is 1.354, weights of index A and index B are 0.575 and 0.425. This method has better judgment transitivity and rational scale value compared to the traditional AHP method. In this project, multiplication scale method was introduced to determine the subjective weight. Judgment matrix was developed by expert comparison and grading, then, the weight vector W(ω1,ω2,…ωn) can be obtained by solving the judgment matrix equation. In addition, the W(ω1,ω2,…ωn) satisfies the normalization function which is given by:
ωi = 0.575ω1i + 0.425ω2i where ω1i is subjective weight, ω2i is objective weight. 4.4. Membership functions
The membership function was employed to assign to each factor the membership grade ranging from zero to one. The membership degree at the middle of the section corresponding to each grade in the evaluation grade was 1 to its fuzzy phase and 0 to its adjacent fuzzy phase. In this study, the normal distribution curve was chosen as the piecewise fuzzy distribution for the membership function. The schematic diagram of the membership function is shown in Fig. 6, and normal distribution function is given by
u (x ) = e−[(x − x 0)/ d]2
n
∑ ωi = 1 i=1
(3)
(4)
Membership functions corresponding to relevant evaluation grades are given by
(2)
In this project, expert scoring method was conducted to determine the important relations comparison of each evaluation index. Then, following steps described above, the subjective weight sets for all the indexes in each level can be identified. The final result is an average data from every expert.
x < b0 /2 ⎧1 ⎪ −( x − b0 /2 )2 d 1 b0 /2 ⩽ x < b0 uA (x ) = e ⎨ x − (b + b )/2 ⎪1 − e−( 0d2 1 )2 b ⩽ x < (b + b )/2 0 0 1 ⎩
Fig. 6. Schematic diagram of the membership function, where a0 = b0/2, and ai is the midpoint of bi to bi+1 section, i was 0, 1, 2pn. 243
(5)
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Fig. 7. Flowchart of the Fuzzy-AHP evaluation procedure.
x < b0 /2, x > (b1 + b2)/2 ⎧0 x − b0 /2 2 ⎪ ) −( d3 b0 /2 ⩽ x < b0 ⎪1 − e uB (x ) = x − (b0 + b1)/2 2 ( ) − ⎨e d4 b0 ⩽ x < b1 ⎪ ⎪1 − e−( x − (b1d+5 b2)/2 )2 b1 ⩽ x < (b1 + b2)/2 ⎩
x < (b0 + b1)/2, x > 3b2 /2 ⎧0 x − (b0 + b1)/2 2 ⎪ −( ) d6 (b0 + b1)/2 ⩽ x < b1 ⎪1 − e uC (x ) = x − (b1+ b2)/2 2 ( ) − ⎨e d6 b1 ⩽ x < b2 ⎪ ⎪1 − e−( x − 3db72 /2 )2 b2 ⩽ x < 3b2 /2 ⎩
x < (b1 + b2)/2 ⎧0 x − (b1+ b2)/2 2 ⎪ −( ) ⎪1 − e d8 (b1 + b2)/2 ⩽ x < b2 uD (x ) = ⎨ −( x − 3b2 /2 )2 d9 b2 ⩽ x < 3b2 /2 ⎪e ⎪1 x ⩾ 3b2 /2 ⎩
in which
rik = uik (mi )
where uik is the membership function for the k grade of Mi, and k = A, B, C, D. Additionally, there existed (6)
D
∑ rik = 1
After the membership grade vectors R of index layer were determined, membership grade vectors Z of factor layer can be obtained by fuzzy operation. (7)
Mx
ωi ∘RT → (z A , zB , z C , zD ) = Z
(13)
The upper formula represents fuzzy operation on ωi and R , and Mx is the fuzzy operator. The weighted algorithm mean was adopted in this model, which can reflect both the role of weights and the role of membership grade vectors. Similarly, the membership grade vector of target layer was obtained through fuzzy operation of ωf and ZT, and ωf was the weight vector of factor layer. Z was the membership grade vector of factor layer. T
(8)
Mx
ωf ∘Z T → (FA, FB , FC , FD ) = F
(14)
G (FA, FB , FC , FD )T = VF
(15)
4.6. Evaluation procedure A computational program was developed based on the model proposed above, and the procedure is depicted by the flowchart. As shown in Fig. 7, the measurement data was input into the corresponding membership functions to obtain the membership grade vectors R. Meanwhile, measurement data was analyzed by objective weight method to obtain the entropy weight, accompanying the subjective weight method, and then the fusion weight sets were determined. The membership grade vectors R and the fusion weight sets were both substituted into the fuzzy operator Mx to obtain the membership grade vectors Z for the factor layer. Then, the membership grade vectors Z and the fusion weight sets were both substituted into the fuzzy operator Mx to obtain the membership grade vector F for the target layer. Finally,
(9)
4.5. Fuzzy operator A monitoring value mi for factor Mi (M could be A, B, C, D, E) in the index layer was substituted into its membership functions and normalized to obtain the corresponding membership grade vector Ri, given by
Ri = [riA riB riC riD]T
(12)
k=A
where x denotes the factor argument, b0, b1, b2 is the junction point of A, B, C, D grade according to the evaluation criteria of each index. d1, d2, … d9 satisfy the following functions
⎧When x = b0 x − (b0 + b1)/2 2 ⎪ −( x − b0 /2 )2 ) d2 d1 = 1 − e−( = 0.5 ⎪e /2 x − b ( )/2 x b b − + 2 2 0 1 0 ⎪ −( ) −( ) d3 d4 =e = 0.5 ⎪1 − e When x = b1 ⎨ x − (b + b )/2 x − (b + b )/2 x − (b + b )/2 ⎪1 − e−( 1d5 2 )2 = 1 − e−( 0d6 1 )2 = e−( 1d6 2 )2 = 0.5 ⎪ ⎪When x = b2 x − (b1+ b2)/2 2 x − 3b2 /2 2 x − 3b2 /2 2 ⎪ ) −( ) d8 d7 = 1 − e−( = e−( d9 ) = 0.5 ⎩1 − e
(11)
(10) 244
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5.2. Fusion weight
the grade vector G, combining with the membership grade vector F were substituted into the fuzzy operator Mx to obtain the evaluation value VF. The evaluation model proposed above was included in the management system developed by the tunnel management department, and then maintenance suggestions and maintenance cases of similar projects were given automatically according to evaluation grade. Once the comprehensive evaluation grade reaches C, system will send prewarning prompts to managers through mobile APP and text messages automatically. Furthermore, once the monitoring index value or evaluation grade was in a bad state, the system will remind managers the necessity of expert consultation.
The subjective weights of indexes and factors in the model were given by multiplication scale method, and the objective weights of indexes were determined by entropy weight method. Subjective weight method was adopted assigning the weights of factor layer. However, for convenience of expression, the weights of factor layer were described in Fig. 9 together with them of index layer. Finally, the weight assignment of Nanchang Honggu Tunnel health evaluation model was compared and shown in Fig. 9.
5. Model validation
The evaluation criteria of index layer were derived according to the relative technical standards and specifications as well as designer’s advices. Details were described in Section 4.2 and shown in Table 3.
5.3. Fuzzy synthetic evaluation
5.1. Monitoring data collection 5.4. Evaluation results and discussion
In this section, the proposed model and procedure were applied to the operating Nanchang Honggu Tunnel, in which health monitoring system was put into operation since September 2017. The tunnel has been in service for 17 months, with a typical monitoring data of Section 3 element 10 shown in Fig. 8. The data include uneven settlement, joint horizontal displacement, PC cable tensile force and shear key stress. The statistical average monitoring data of Section 3 element 10 in December 2018 was chosen for this case study, as shown in Table 2.
5.4.1. Determination of the membership grade vector R In this study, the membership grade vectors R of index layer were determined combined with membership function and shown in Table 4. 5.4.2. Comprehensive evaluation of the tunnel section Comprehensive evaluation of the tunnel Section 3 element 10 was processed according to the evaluation procedure proposed in 4.6. The detailed calculation process is shown in Table 5.
Fig. 8. Typical monitoring data of Section 3 element 10 in the period from September 2017 to December 2018: (a) uneven settlement; (b) joint horizontal displacement; (c) PC cable tensile force; (d) shear key stress. 245
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Table 2 Monitoring data of Section 3 element 10. Index
Value
Index
Value
A1 Rebar stress (MPa) A2 Concrete stress (MPa) A3 Horizontal shear key stress (MPa) A4 Vertical shear key stress (MPa) A5 PC cable tensile force (kN) B1 Uneven settlement (mm) B2 Joint opening (mm) B3 Joint compression (mm)
30.55 5.064 0.27 0.8 300.41 19.2 12 0
B4 Joint horizontal displacement (mm) C1 Crack length (m) C2 Crack width (mm) D1 Leakage rate (L/(Joint·d) D2 Leakage rate* (L/(m2·d) D3 Leakage area (Seepage area/Waterproofing area) D4 Leakage PH
4.7 0 0 0 0 0 –
Table 4 Membership vector R of index layer. Factors
Evaluation grade A
B
C
D
Structural stress
A1 A2 A3 A4 A5
1 1 1 0.997 1
0 0 0 0.003 0
0 0 0 0 0
0 0 0 0 0
Structural deformation
B1 B2 B3 B4
0.947 0.992 1 1
0.053 0.008 0 0
0 0 0 0
0 0 0 0
Structural crack
C1 C2
1 1
0 0
0 0
0 0
Leakage
D1 D2 D3 D4
1 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0
Fig. 9. Weights assignment of index layer and factor layer.
The comprehensive evaluation result showed that the health state of the section was A and the tunnel structure was in good health. 5.4.3. Comprehensive evaluation of the tunnel structure As calculated using equations from Table 5, the comprehensive evaluation values VF of the 36 sections from 12 tubes of the tunnel were calculated and shown in Fig. 10. It can be found that the health state of all the sections in the tunnel structure were A, indicating the structure was in good health overall. As shown in Fig. 10, the VF values of sections located at the middle of the river and near the closure joint were slightly smaller than other sections. Sections in the middle of the river are located at the edge of the central bar, which is immersed in the river in rainy season, and bared in the dry season. This has a great influence on the upper hydraulic pressure and stratum mechanical properties of the tunnel. And sections near the closure joint are located at the channel on the east side of the central bar. Because the tunnel has been opened to traffic for only
Indexes
17 months, further monitoring and analysis is still needed. 6. Conclusions A Fuzzy-AHP synthetic evaluation model was proposed to analyze the uncertainties in immersed tunnel health evaluation. Moreover, a fusion weight method using health monitoring data to modify the subjective weight was developed. Case study of the Nanchang Honggu Tunnel was examined and used as a basis for verifying the proposed model. The following conclusions can be drawn: (1) Based on the analysis of influencing factors of immersed tunnel
Table 3 Classification criteria for evaluation indexes of Honggu Tunnel. Index
A
B
C
D
Rebar stress (MPa) Concrete stress (MPa) Horizontal shear key stress (MPa) Vertical shear key stress (MPa) PC cable tensile force (KN) Joint opening (mm) Joint compression (mm) Joint horizontal displacement (mm) Uneven settlement (mm) Crack length (m) Crack width (mm) Leakage rate (L/(Joint·d)) Leakage rate* (L/(m2·d)) Leakage area (Seepage area/Waterproofing area) Leakage pH
≤270 ≤14.33 ≤0.62 ≤1.5 ≤1334 ≤21.6 ≤20.5 ≤25 ≤30 ≤2 ≤0.15 < 0.0001 < 0.001 < 0.01/1000 6.5–7
270–306 14.33–16.24 0.62–0.7 1.5–1.7 1334–1570 21.6–25 20.5–23.3 25–30 30–40 2–5 0.15–0.2 0.0001–0.0005 0.001–0.01 0.01/1000–0.1/1000 6–6.5
306–360 16.24–19.1 0.7–0.82 1.7–2 1570–1847 25–28.3 23.3–33.3 30–35.3 40–50 5–10 0.2–0.25 0.0005–0.001 0.01–0.05 0.1/1000–1/1000 5.5–6
≥360 ≥19.1 ≥0.82 ≥2 ≥1847 ≥28.3 ≥33.3 ≥35.3 ≥50 > 10 > 0.25 > 0.001 > 0.05 > 1/1000 < 5.5
Notes: All the membership functions were identified using Eqs. (5)–(9). Leakage rate* was corresponding to the concrete structure, and Leakage rate (L/(Joint·d)) was corresponding to the joint. 246
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Table 5 Calculation process detail.
the health state of immersed tunnels comprehensively. The proposed membership function that describes the fuzzy relationship between the evaluation index and the evaluation grade scientifically can reduce the arbitrariness of the supervisor in the evaluation process and realize the quantitative evaluation of the tunnel health state. (3) In order to modify the subjective characteristic of index weight in the health evaluation model, the subjective- objective fusion weight method was put forward, which was verified better to reflect the role of the actual condition according to the field monitoring data. (4) The proposed health rating scales and countermeasures are validated to be reasonable and feasible in the case study of Nanchang Honggu Tunnel. The calculated VF values were compared with health rating scales, from which the tunnel was revealed in a good condition. Both VF values of E6, E7 element located in the middle of the river and E10 element located near the closure joint part were slightly smaller than other segments. Such evaluation results will enhance the maintenance pertinence of tunnel managers. The method proposed in this study will be a reasonable support for further monitoring and evaluation of the Honggu Tunnel.
Fig. 10. Overall health evaluation value of the tunnel structure.
operation health state, the monitoring of immersed tunnel operation health was realized by setting the monitoring indexes and the arrangement of sensors applicable and economic. (2) A Fuzzy-AHP evaluation model was proposed, and its establishment process was described in detail. The proposed model can give a reasonable evaluation of the health state of immersed tunnels comprehensively by establishing an evaluation index system. The Fuzzy-AHP model can easily consider the various factors affecting
Acknowledgements This work was financially supported by the National Key Research and Development Program of China (Grant No. 2016YFC0800201), China and National Natural Science Foundation of China (Grant No. 41572273, 51878157), China.
Appendix A The specific steps of entropy weight assignment method are shown below. ①Establishment of judgment matrix of tunnel health state
x . . . x1n ⎤ ⎡ 11 R= ⎢ ⋮ ⋱ ⋮ ⎥ x x ⋯ nn ⎦ ⎣ n1
(A1)
②Normalized judgment matrix
bij =
x ij − x min (A2)
x max − x min
where x max and x min are the most satisfied and least satisfied index of each health level, respectively. ③Entropy of assessment index
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Determining the entropy of assessment index
Hi = −
fij =
1 ln m
m
∑ fij ln fij
(A3)
j=1
1 + bij m ∑ j=1
(1 + bij )
(A4)
where fij is the specific weight of ith assessment object. ④Entropy weight calculation
ωi =
1 − Hi n n − ∑i = 1 Hi
(A5)
Through these steps, the analysis of measured data can be converted to the weight information of evaluation indexes.
effects. J. Bridge Eng. 14 (4), 257–269. Liu, Xila, 2001. Fundamental research on safety and durability of major structures in civil and hydraulic engineering. China Civil Eng. J. 34 (6), 1–7. Liu, Z.G., Huang, H.W., 2009. Performance evaluation and safety pre-warning of GINA in immersed tube tunnel. Chinese J. Undergr. Space Eng. 5 (2), 347–353. Metje, N., Chapman, D.N., Rogers, C.D.F., et al., 2006. Optical fibre sensors for remote monitoring of tunnel displacements - Prototype tests in the laboratory. Tunnell. Undergr. Space Technol. Incorporat. Trenchless Technol. Res. 21 (3) 417–417. Parwani, K., 2014. Quantifying the impact of loads on connections between segments of an immersed tunnel. Master thesis. TU Delft, Nertherlands. Radu, L.D., 2009. Qualitative, semi-quantitative and quantitative methods for risk assessment: Case of the financial audit. Sci. Ann. Alexandru Ioan Cuza Univ. Iasi : Econ. Sci. Ser. 56, 643–657. Richard, Lunniss, Baber, Jonathan, 2013. Immersed Tunnels. CRC Press, US, pp. 288–289. SL 191-2008, 2008.. Design Code for Hydraulic Concrete Structures. China Water and Power Press, Beijing. Sohn, H., Czarnecki, J.A., Farrar, C.R., 2000. Structural health monitoring using statistical process control. J. Struct. Eng. 126 (11), 1356–1363. Song, G., Mo, Y.L., Otero, K., et al., 2006. Health monitoring and rehabilitation of a concrete structure using intelligent materials. Smart Mater. Struct. 15 (15), 309. Su, Jie, Zhang, D., Niu, X., et al., 2007. Research on design of subsea tunnel structural health monitoring. Chinese J. Rock Mech. Eng. 26 (S2), 3785–3792. Sun, Wei, Zhang, Dongmei, Jiang, Xianghong, 2014. Theory and practice on influence and protection of open excavation on existing large diameter shield tunnel. Tongji Univ. Exp., Shanghai, China. Tang, Y.B., Chen, L., Wang, S.N., et al., 2013. Evaluation of the corrosion risk on the immersed tunnel of the Hongkong-Zhuhai-Macao Bridge. Appl. Mech. Mater. 256–259, 1075–1081. Wang, Yaqiong, Zhou, Shaowen, Sun, Tiejun, et al., 2015. A diagnosis method for lining structure conditions of operated tunnels based on asymmetric closeness degree. Chinese Modern Tunnel. Technol. 52 (2), 52–58. Zhang, W., Sun, K., Lei, C., et al., 2014. Fuzzy analytic hierarchy process synthetic evaluation models for the health monitoring of shield tunnels. Comput.-Aided Civ. Infrastruct. Eng. 29 (9), 676–688.
References Aktan, A.E., Catbas, F.N., Grimmelsman, K.A., et al., 2000. Issues in infrastructure health monitoring for management. J. Eng. Mech. 126 (7), 711–724. Chen, Z., Li, X., Chen, J.Y., et al., 2014. Health evaluation for durability of harbor engineering in south China based on AHP. Adv. Mater. Res. 842, 489–493. GB 50153-2008, 2008. Unified Standard for Reliability Design of Engineering Structures. China Architecture and Building Press, Beijing. GB 50108-2008, 2008. Technical Code for Waterproofing of Underground Works. China Architecture and Building Press, Beijing. Grantz, W.C., 2001a. Immersed tunnel settlements. Part 1: nature of settlements. Tunnell. Underg. Space Technol. Incorporat. Trenchless Technol. Res. 16 (3), 195–201. Grantz, W.C., 2001b. Immersed tunnel settlements : Part 2: case histories. Tunnell. Underg. Space Technol. Incorporat. Trenchless Technol. Res. 16 (3), 203–210. Han, Jiankun, 2016. Study of selection of hydrological conditions of floating transportation and sinking of Honggu Immersed Tunnel in Nanchang. Chinese Tunnel Construct. 36 (9), 1037–1044. Inaudi, D., Glisic, B., 2002. Monitoring of a concrete arch bridge during construction. Proc. SPIE – Int. Soc. Opt. Eng. 4696, 146–153. Jin, Y., Wang, G., Zhao, J., et al., 2016. Research on health evaluation of tunnel in the operation period and its application by MATLAB. Chinese J. Seismol. Res. 39 (1), 120–125. JTG H12-2015, 2015. Technical Specifications of Maintenance for Highway Tunnel. China Communications Press, Beijing. Ko, J.M., Sun, Z.G., Ni, Y.Q., 2002. Multi-stage identification scheme for detecting damage in cable-stayed Kap Shui Mun Bridge. Eng. Struct. 24 (7), 857–868. Kumar, R., Hossain, A., 2018. Experimental performance and study of low power strain gauge based wireless sensor node for structure health monitoring. Wireless Pers. Commun. 101 (1), 1–13. Ledesma, A., Alonso, E.E., 2017. Protecting sensitive constructions from tunnelling: the case of World Heritage buildings in Barcelona. Géotechnique. 67 (10), 914–925. Li, X., Hong, B., Yang, Z., 2017. Design of a structure health monitoring system for shield tunnels and some key issues. Chinese Modern Tunnell. Technol. 54 (1), 17–23. Liu, M., Dan, M.F., Kim, S., 2009. Bridge safety evaluation based on monitored live load
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Evaluation model for immersed tunnel health state: A case study of Honggu Tunnel, Jiangxi Province, China ⁎
T
⁎
Xiangchun Xua, Liyuan Tonga, , Songyu Liua, , Hongjiang Lib,c a
Institute of Geotechnical Engineering, Institute of Future Underground Space, Jiangsu Key Laboratory of Urban Underground Engineering & Environmental Safety, Southeast University, Nanjing 210096, China b Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, China c Centre for Offshore Foundation Systems, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Fuzzy-AHP Immersed tunnel Health monitoring Fusion weight
The evaluation of the health state of an immersed tunnel is inevitably affected by the variety of influencing factors, the complex relationship between influencing factors and fuzzy characteristics of health evaluation criteria. A targeted method for analysis of the health conditions of an immersed tunnel in operation period is immature. As a case study of the health monitoring of the largest inland river immersed tunnel-Nanchang Honggu Tunnel, a fuzzy analytic hierarchy process (Fuzzy-AHP) method was carried out in this study, which merged different types of data from multiple sensors to map them into comprehensive evaluation value of the immersed tunnel. The hierarchical structure of the health evaluation index was established, and the layout scheme of monitoring sensors was designed through a comprehensive analysis of influencing factors. Additionally, the entropy weight method was introduced to modify the subjective characteristic of index weight in the fuzzy analytic hierarchy model, and then a Fuzzy-AHP evaluation procedure was built. Finally, the proposed evaluation model and evaluation procedure of immersed tunnel health states were verified by the field monitoring data of the Nanchang Honggu Tunnel. The comprehensive evaluation value VF was compared with the rating scales and countermeasures proposed in this study to determine the tunnel health state and corresponding countermeasures. The results indicate that the evaluation health of the whole tunnel sections of Nanchang Honggu Tunnel in December 2018 was in grade A, and further monitoring was needed. The VF values of sections located at the middle of the river and the final joint were slightly smaller than other sections. The proposed Fuzzy-AHP method can give a feasible and effective evaluation for immersed tunnel health states.
1. Introduction Immersed tunnels have received more and more attention (Han, 2016) in China in recent years due to their fast construction speed, shallow buried depth, no influence on navigation and less length of the tunnel approach ramps at the shorelines compared to a bridge or bore tunnel. Under the dual effects of long-term natural environment and operation environment, immersed tunnels inevitably suffer different degrees of leakage, structural uneven settlement, cracks, and other deteriorations. Those have a great impact on the operation safety of the tunnel. Moreover, the difficulty and cost of tunnel maintenance will also increase sharply with the development of the deterioration. Therefore, it is of great significance to track the development of tunnel deterioration in real time and analyze the health state of the tunnel for formulating maintenance countermeasures in time. In the maintenance of the infrastructure, the health monitoring ⁎
technique plays an important role, especially in constructions of bridges and tunnels (Aktan et al., 2000; Sohn et al., 2000; Liu et al., 2009). The method aims at employing in situ, continuous, or regular measurements and analyzing key structural and environmental parameters under the operating conditions to provide warning of impending abnormal states or structural failures, and then avoids casualties as well as informing maintenance and rehabilitation decisions. Since the 1990s, the health monitoring system has attracted the attention of scholars and engineers. In the field of civil engineering, health monitoring system was first applied to bridges (Inaudi and Glisic, 2002; Liu, 2001; Ko et al., 2002), and then buildings, structures and shield tunnels (Metje et al., 2006; Ledesma and Alonso, 2017; Li et al., 2017; Kumar and Hossain, 2018; Song et al., 2006; Su et al., 2007). Application cases of health monitoring system in immersed tunnels were not much extensive yet in China. Compared with shield tunnels and mined tunnels, tubes of
Corresponding authors. E-mail addresses: [email protected] (L. Tong), [email protected] (S. Liu).
https://doi.org/10.1016/j.tust.2019.05.005 Received 25 October 2018; Received in revised form 28 January 2019; Accepted 10 May 2019 Available online 15 May 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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length, and other 3 are 90 m, 90 m, 108 m separately. The construction clearance is 11.5 m × 4.5 m, and the size of the cross sections is 30 m × 8.3 m. Because of the runoff of Ganjiang River concentrated in April to June, accounted for 49.6% of the year, it is easy to induce a highly fluctuating water level from rainy season to dry season, the maximum water level difference at the tunnel location in the past decade reaches 14.18 m. According to the geological investigations, the concentration of Cl−, SO42− and Mg2+ in the water is 22.4 mg/L, 16 mg/L, and 5.75 mg/L, respectively, those much less than the critical value of minor corrosive in the technical standards. Therefore, environmental corrosion effect can be ignored and not involved in this study.
immersed tunnels are prefabricated in a dry dock or factory type facility. Rubber gaskets are generally used to maintain the water tightness of tube joints, which results in that the joint of tubes is more sensitive to water level fluctuation and siltation above the tunnel as well as uneven settlement than the concrete structures. And it should be noted that, the stress conditions of immersed tunnel compared with bridge and mined tunnel seem relatively static. However, in some cases, the high water level fluctuation will impose cyclic loading on the tunnel foundation and tunnel joint, and this will raise the safety risk. Grantz (2001a,b) provided a series of cases of uneven settlement of immersed tunnels. In some of those cases, immersed tunnels have suffered different degrees of water leakage, cracks and tube inclination. Parwani (2014) reported the Kil-tunnel in Netherlands, in which, water leakage and displacements as well as rotations were found in the segment joints. As the health monitoring of immersed tunnel structure is very important for long-term safety and economic operation, it is helpful to merge the various monitoring data into the tunnel structure health state and put forward a reasonable evaluation method. The factors affecting the health state of immersed tunnels are complex, and there is still no clear corresponding relationship between the various factors and the health state. In order to fully understand the health state of immersed tunnels, it is necessary to establish a scientific and reasonable evaluation model. Radu (2009) and Sun et al. (2014) summarized the traditional methods of health evaluation including the qualitative method, quantitative method and semi-quantitative method. To date, the quantitative methods have been widely used in shield tunnel projects and other civil engineering projects. Jin et al. (2016) used MATLAB program to evaluate the health state of mining method tunnel quantitatively. Zhang et al. (2014) adopted the fuzzy theory and analytic hierarchy process (AHP) method in shield tunnel health state evaluation. Chen et al. (2014) employed AHP method by comparing the health indicator to the criteria to evaluate the durability of harbor engineering. There were few evaluation cases of immersed tunnel operation health state, and most of them were focused on qualitative or semi- quantitative method. Liu and Huang (2009) employed the mean stress and contact stress of the GINA in immersed tunnels to calculate the minimum GINA compression for ensuring the waterproofing effect, and proposed a joint waterproof performance evaluation method based on the GINA current compression. Tang et al. (2013) evaluated the corrosion risk of the immersed tunnel of the Hongkong-Zhuhai-Macao Bridge by comparing the environment index with the durability index. In view of the complexity of the evaluation object in immersed tunnel engineering, the AHP method was employed to induce and analyze the influencing factors of the immersed tunnel health state. An objective weight assignment method-entropy weight method was introduced to modify the subjective characteristic of index weight in the AHP model. Meanwhile, a fuzzy mathematics theory considering the fuzziness of the relationship between health state and influencing factors was introduced into AHP to establish the combined Fuzzy-AHP evaluation method subjected to immersed tunnel health state. Then, the evaluation method was verified with the engineering case of Nanchang Honggu Tunnel.
3. Health monitoring configuration The tubes of immersed tunnel are prefabricated in dry docks or factory type facility and then connected in the field. In order to make the immersion joints watertight, the rubber gaskets are used. Also the shear keys are set to resist the shear force. As immersed tunnels are located in rivers or oceans, generally with shallow buried depth, the fluctuation of water level and silting above the tunnel can affect the safety of the tunnel. Some main damages such as: joint damage caused by uneven settlement, failure of rubber gaskets and cracks in tubes should be prevented. In addition, vehicle loads, traffic accidents, earthquakes, shipwrecks and water corrosion are all threatening factors to tunnel structure safety. In this project, five main aspects are summarized in the health monitoring of Nanchang Honggu Tunnel: environmental effects, structural stress, structural deformation, structural cracks and leakage (structure cracks and tunnel joint). These five aspects include water level, thickness of siltation layer, rebar stress, concrete stress, PC cable tensile force, uneven settlement, joint opening, joint compression, tube inclination, crack length, crack width, leakage rate, leakage area, and leakage water pH, etc. Fig. 3 presents the detailed tunnel joint, and the health monitoring sensors layout is shown in Fig. 4. Water level and thickness of siltation layer are measured periodically by water level gauges and acoustic wave detectors; rebar stress and concrete stress are monitored in real-time by vibrating wire rebar and concrete stress meters; PC cable tensile force is monitored in real-time by magnetic flux cable stress meters; tunnel uneven settlement is monitored in real-time by differential pressure meters; joint opening and compression is monitored in real-time by two vibrating wire crack meters assembled at a certain angle; tube inclination is monitored in real-time by vibrating wire inclinometers. Structural crack and leakage are inspected periodic, countermeasures should be taken after defects detected and switched into real-time monitoring if possible. As shown in Fig. 4, there are three typical health monitoring sensors layout sections in this project. Section 1 is located at the joint of the tunnel, and the health state of the tunnel joint is mainly monitored. Section 2 is located at 3.5 m distance from the tunnel joint, and the health state of tunnel structure near the joint is mainly monitored. Section 3 is located at the middle of the tube, and the health state of tube structure is mainly monitored.
2. Background and location of Nanchang Honggu tunnel 4. Development of Fuzzy–AHP evaluation model Nanchang Honggu Tunnel is the largest inland river immersed tunnel in China which was began construction in January 2014 and opened to traffic in July 2017 with complex geological and fracture condition. The typical geological profile is shown in Fig. 1. The tunnel connects the old town in the east bank and the new town in the west bank, with a measured average daily traffic of 26.2 thousands vehicles. The geographical position of the tunnel is shown in Fig. 2. In total, the length of Nanchang Honggu Tunnel is approximately 2650 m, of which the 1329 m-length is the section of the reinforced concrete rectangular immersed tube (including the closure joint). Among 12 immersed tube tunnel elements, there are 9 separate elements with a total 115 m in
4.1. Factor sets As mentioned above, there are four types of monitoring factors contributed to the health state evaluation of the tunnel element, namely structural stress, structural deformation, structural crack and leakage, considering the principal of independence and representativeness. These four factors are constructed as a factor layer, and each factor includes its sub-factors, namely indexes, which form the index layer. In the tunnel health state evaluation process, a sequence from the index layer to the factor layer and then to the target layer is complied. The 240
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Fig. 1. Typical geological profile in the test site.
hierarchical model of Honggu Tunnel health monitoring and evaluation is shown in Fig. 5. The above monitoring indexes were realized through a real-time monitoring and regular inspection. The structural stress and deformation indexes were monitored and transmitted to the system database in real-time; structural crack and leakage indexes were then put into the system database manually after regular inspection. 4.2. Evaluation grade sets The health conditions subjected to tunnel damages can be classified into several grades, as shown in Table 1. In this study, four grades from A to D were counted. The corresponding rating scales and countermeasures were also proposed and shown in Table 1. In addition, factors and indexes in Fig. 1 were all classified into four grades. The grading criterion for each index in the index layer was technically identified by referring to Chinese technical standards and specifications (GB 501532008, GB 50108-2008, SL 191-2008, JTG H12, 2015), Richard and Baber (2013) as well as designer’s advices. Especially for structural stress and structural deformation, among the four grades, grade D is the worst condition, indicating that the structure has been destroyed, with a critical value equals to the design limit value of the index. Grade C indicates that the structure has a tendency to be destroyed. Considering the structural reliability, its critical value is 85% of the design limit
Fig. 3. Detail of tunnel joint.
value of the index, which is believed to be the threshold of unacceptable state for the operation and maintenance of immersed tunnel. Grade B and A indicate that the structure is in normal function. The critical value of grade B is 75% of the design limit value of the index, and grade A is less than 75%.
Fig. 2. The location of the Honggu immersed tunnel. 241
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Fig. 4. The layout of various health monitoring sensors.
Fig. 5. Honggu Tunnel health monitoring and evaluation hierarchical model.
4.3. Weight assignment
The grade vector to characterize the rating scales was introduced, which can be expressed as
G = [3.5
2.5
1.5
0.5]
In the evaluation model, as the importance and distribution between factors and indexes was different, various factors and indexes should be assigned different weights based on their relative importance to the upper layer. Weight assignment method can be divided into two
(1)
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Table 1 Comprehensive evaluation criteria and countermeasure. Grade
Health state
Comprehensive rating scale
Countermeasure
A B C D
Not damaged or slightly damaged Damaged Relatively serious damage Seriously damaged
3 < VF ≤ 4 2 < VF ≤ 3 1 < VF ≤ 2 VF ≤ 1
Monitoring Ready to take countermeasure Take countermeasure as soon as possible Take countermeasure instantly
4.3.2. Objective weight assignment Under the assumption of the index weight is determined according to the amount of information contained in each index (Wang et al., 2015), entropy weight assignment method is deemed to be a reasonable objective method. The specific steps of entropy weight assignment method are shown in Appendix A.
categories according to the origin of the source information: one is the subjective weighting method, in which the source information comes from expert consultation, such as expert consultation method, analytic hierarchy process method; the other is the objective weighting method, in which the source information comes from statistical data, such as principal component analysis method, entropy method. The two categories have their own characteristics. As the subjective weighting method can make full use of expert’s knowledge and experience, and the objective weighting method can make full use of statistical data. The objective weighting method was combined into the AHP to assign the weights of index layer in this study.
4.3.3. Fusion weight The subjective weight and objective weight represent the subjective judgment and the objective data information, respectively. By a combination of them, the comprehensive judgment of the index weight can be made. The conventional approaches of fusion weight calculation are weighted arithmetic mean, weighted square root, weighted square sum, etc. In this study, the weighted arithmetic mean method was used due to its easily understood by field engineers as one of the fusion methods, and the subjective weight was considered a little more important than the objective weight. The fusion weight calculation formula is as follows.
4.3.1. Subjective weight assignment AHP weighting method is one of the commonly used methods in subjective weighting. The key step of AHP weighting method is to obtain the relative importance of indexes to the corresponding factors in the factor layer by comparing them in couple. Then, the importance is transformed into the digital description and the respective weights are obtained according to the digital scale. Commonly used digital scales were 1–9 scale, 9/9–9/1 scale, 10/10–18/2 scale, exponential scale, multiplication scale, etc. As an updated method of AHP, the multiplication scale method generally replaces the 1–9 scale by 1–1.354 scale, by means of same and slightly larger. When importance of index A is the same as index B, the judgment scale is 1, weights of index A and index B are 0.5 and 0.5. Similarly, when index A is slightly larger than index B, the judgment scale is 1.354, weights of index A and index B are 0.575 and 0.425. This method has better judgment transitivity and rational scale value compared to the traditional AHP method. In this project, multiplication scale method was introduced to determine the subjective weight. Judgment matrix was developed by expert comparison and grading, then, the weight vector W(ω1,ω2,…ωn) can be obtained by solving the judgment matrix equation. In addition, the W(ω1,ω2,…ωn) satisfies the normalization function which is given by:
ωi = 0.575ω1i + 0.425ω2i where ω1i is subjective weight, ω2i is objective weight. 4.4. Membership functions
The membership function was employed to assign to each factor the membership grade ranging from zero to one. The membership degree at the middle of the section corresponding to each grade in the evaluation grade was 1 to its fuzzy phase and 0 to its adjacent fuzzy phase. In this study, the normal distribution curve was chosen as the piecewise fuzzy distribution for the membership function. The schematic diagram of the membership function is shown in Fig. 6, and normal distribution function is given by
u (x ) = e−[(x − x 0)/ d]2
n
∑ ωi = 1 i=1
(3)
(4)
Membership functions corresponding to relevant evaluation grades are given by
(2)
In this project, expert scoring method was conducted to determine the important relations comparison of each evaluation index. Then, following steps described above, the subjective weight sets for all the indexes in each level can be identified. The final result is an average data from every expert.
x < b0 /2 ⎧1 ⎪ −( x − b0 /2 )2 d 1 b0 /2 ⩽ x < b0 uA (x ) = e ⎨ x − (b + b )/2 ⎪1 − e−( 0d2 1 )2 b ⩽ x < (b + b )/2 0 0 1 ⎩
Fig. 6. Schematic diagram of the membership function, where a0 = b0/2, and ai is the midpoint of bi to bi+1 section, i was 0, 1, 2pn. 243
(5)
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Fig. 7. Flowchart of the Fuzzy-AHP evaluation procedure.
x < b0 /2, x > (b1 + b2)/2 ⎧0 x − b0 /2 2 ⎪ ) −( d3 b0 /2 ⩽ x < b0 ⎪1 − e uB (x ) = x − (b0 + b1)/2 2 ( ) − ⎨e d4 b0 ⩽ x < b1 ⎪ ⎪1 − e−( x − (b1d+5 b2)/2 )2 b1 ⩽ x < (b1 + b2)/2 ⎩
x < (b0 + b1)/2, x > 3b2 /2 ⎧0 x − (b0 + b1)/2 2 ⎪ −( ) d6 (b0 + b1)/2 ⩽ x < b1 ⎪1 − e uC (x ) = x − (b1+ b2)/2 2 ( ) − ⎨e d6 b1 ⩽ x < b2 ⎪ ⎪1 − e−( x − 3db72 /2 )2 b2 ⩽ x < 3b2 /2 ⎩
x < (b1 + b2)/2 ⎧0 x − (b1+ b2)/2 2 ⎪ −( ) ⎪1 − e d8 (b1 + b2)/2 ⩽ x < b2 uD (x ) = ⎨ −( x − 3b2 /2 )2 d9 b2 ⩽ x < 3b2 /2 ⎪e ⎪1 x ⩾ 3b2 /2 ⎩
in which
rik = uik (mi )
where uik is the membership function for the k grade of Mi, and k = A, B, C, D. Additionally, there existed (6)
D
∑ rik = 1
After the membership grade vectors R of index layer were determined, membership grade vectors Z of factor layer can be obtained by fuzzy operation. (7)
Mx
ωi ∘RT → (z A , zB , z C , zD ) = Z
(13)
The upper formula represents fuzzy operation on ωi and R , and Mx is the fuzzy operator. The weighted algorithm mean was adopted in this model, which can reflect both the role of weights and the role of membership grade vectors. Similarly, the membership grade vector of target layer was obtained through fuzzy operation of ωf and ZT, and ωf was the weight vector of factor layer. Z was the membership grade vector of factor layer. T
(8)
Mx
ωf ∘Z T → (FA, FB , FC , FD ) = F
(14)
G (FA, FB , FC , FD )T = VF
(15)
4.6. Evaluation procedure A computational program was developed based on the model proposed above, and the procedure is depicted by the flowchart. As shown in Fig. 7, the measurement data was input into the corresponding membership functions to obtain the membership grade vectors R. Meanwhile, measurement data was analyzed by objective weight method to obtain the entropy weight, accompanying the subjective weight method, and then the fusion weight sets were determined. The membership grade vectors R and the fusion weight sets were both substituted into the fuzzy operator Mx to obtain the membership grade vectors Z for the factor layer. Then, the membership grade vectors Z and the fusion weight sets were both substituted into the fuzzy operator Mx to obtain the membership grade vector F for the target layer. Finally,
(9)
4.5. Fuzzy operator A monitoring value mi for factor Mi (M could be A, B, C, D, E) in the index layer was substituted into its membership functions and normalized to obtain the corresponding membership grade vector Ri, given by
Ri = [riA riB riC riD]T
(12)
k=A
where x denotes the factor argument, b0, b1, b2 is the junction point of A, B, C, D grade according to the evaluation criteria of each index. d1, d2, … d9 satisfy the following functions
⎧When x = b0 x − (b0 + b1)/2 2 ⎪ −( x − b0 /2 )2 ) d2 d1 = 1 − e−( = 0.5 ⎪e /2 x − b ( )/2 x b b − + 2 2 0 1 0 ⎪ −( ) −( ) d3 d4 =e = 0.5 ⎪1 − e When x = b1 ⎨ x − (b + b )/2 x − (b + b )/2 x − (b + b )/2 ⎪1 − e−( 1d5 2 )2 = 1 − e−( 0d6 1 )2 = e−( 1d6 2 )2 = 0.5 ⎪ ⎪When x = b2 x − (b1+ b2)/2 2 x − 3b2 /2 2 x − 3b2 /2 2 ⎪ ) −( ) d8 d7 = 1 − e−( = e−( d9 ) = 0.5 ⎩1 − e
(11)
(10) 244
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5.2. Fusion weight
the grade vector G, combining with the membership grade vector F were substituted into the fuzzy operator Mx to obtain the evaluation value VF. The evaluation model proposed above was included in the management system developed by the tunnel management department, and then maintenance suggestions and maintenance cases of similar projects were given automatically according to evaluation grade. Once the comprehensive evaluation grade reaches C, system will send prewarning prompts to managers through mobile APP and text messages automatically. Furthermore, once the monitoring index value or evaluation grade was in a bad state, the system will remind managers the necessity of expert consultation.
The subjective weights of indexes and factors in the model were given by multiplication scale method, and the objective weights of indexes were determined by entropy weight method. Subjective weight method was adopted assigning the weights of factor layer. However, for convenience of expression, the weights of factor layer were described in Fig. 9 together with them of index layer. Finally, the weight assignment of Nanchang Honggu Tunnel health evaluation model was compared and shown in Fig. 9.
5. Model validation
The evaluation criteria of index layer were derived according to the relative technical standards and specifications as well as designer’s advices. Details were described in Section 4.2 and shown in Table 3.
5.3. Fuzzy synthetic evaluation
5.1. Monitoring data collection 5.4. Evaluation results and discussion
In this section, the proposed model and procedure were applied to the operating Nanchang Honggu Tunnel, in which health monitoring system was put into operation since September 2017. The tunnel has been in service for 17 months, with a typical monitoring data of Section 3 element 10 shown in Fig. 8. The data include uneven settlement, joint horizontal displacement, PC cable tensile force and shear key stress. The statistical average monitoring data of Section 3 element 10 in December 2018 was chosen for this case study, as shown in Table 2.
5.4.1. Determination of the membership grade vector R In this study, the membership grade vectors R of index layer were determined combined with membership function and shown in Table 4. 5.4.2. Comprehensive evaluation of the tunnel section Comprehensive evaluation of the tunnel Section 3 element 10 was processed according to the evaluation procedure proposed in 4.6. The detailed calculation process is shown in Table 5.
Fig. 8. Typical monitoring data of Section 3 element 10 in the period from September 2017 to December 2018: (a) uneven settlement; (b) joint horizontal displacement; (c) PC cable tensile force; (d) shear key stress. 245
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Table 2 Monitoring data of Section 3 element 10. Index
Value
Index
Value
A1 Rebar stress (MPa) A2 Concrete stress (MPa) A3 Horizontal shear key stress (MPa) A4 Vertical shear key stress (MPa) A5 PC cable tensile force (kN) B1 Uneven settlement (mm) B2 Joint opening (mm) B3 Joint compression (mm)
30.55 5.064 0.27 0.8 300.41 19.2 12 0
B4 Joint horizontal displacement (mm) C1 Crack length (m) C2 Crack width (mm) D1 Leakage rate (L/(Joint·d) D2 Leakage rate* (L/(m2·d) D3 Leakage area (Seepage area/Waterproofing area) D4 Leakage PH
4.7 0 0 0 0 0 –
Table 4 Membership vector R of index layer. Factors
Evaluation grade A
B
C
D
Structural stress
A1 A2 A3 A4 A5
1 1 1 0.997 1
0 0 0 0.003 0
0 0 0 0 0
0 0 0 0 0
Structural deformation
B1 B2 B3 B4
0.947 0.992 1 1
0.053 0.008 0 0
0 0 0 0
0 0 0 0
Structural crack
C1 C2
1 1
0 0
0 0
0 0
Leakage
D1 D2 D3 D4
1 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0
Fig. 9. Weights assignment of index layer and factor layer.
The comprehensive evaluation result showed that the health state of the section was A and the tunnel structure was in good health. 5.4.3. Comprehensive evaluation of the tunnel structure As calculated using equations from Table 5, the comprehensive evaluation values VF of the 36 sections from 12 tubes of the tunnel were calculated and shown in Fig. 10. It can be found that the health state of all the sections in the tunnel structure were A, indicating the structure was in good health overall. As shown in Fig. 10, the VF values of sections located at the middle of the river and near the closure joint were slightly smaller than other sections. Sections in the middle of the river are located at the edge of the central bar, which is immersed in the river in rainy season, and bared in the dry season. This has a great influence on the upper hydraulic pressure and stratum mechanical properties of the tunnel. And sections near the closure joint are located at the channel on the east side of the central bar. Because the tunnel has been opened to traffic for only
Indexes
17 months, further monitoring and analysis is still needed. 6. Conclusions A Fuzzy-AHP synthetic evaluation model was proposed to analyze the uncertainties in immersed tunnel health evaluation. Moreover, a fusion weight method using health monitoring data to modify the subjective weight was developed. Case study of the Nanchang Honggu Tunnel was examined and used as a basis for verifying the proposed model. The following conclusions can be drawn: (1) Based on the analysis of influencing factors of immersed tunnel
Table 3 Classification criteria for evaluation indexes of Honggu Tunnel. Index
A
B
C
D
Rebar stress (MPa) Concrete stress (MPa) Horizontal shear key stress (MPa) Vertical shear key stress (MPa) PC cable tensile force (KN) Joint opening (mm) Joint compression (mm) Joint horizontal displacement (mm) Uneven settlement (mm) Crack length (m) Crack width (mm) Leakage rate (L/(Joint·d)) Leakage rate* (L/(m2·d)) Leakage area (Seepage area/Waterproofing area) Leakage pH
≤270 ≤14.33 ≤0.62 ≤1.5 ≤1334 ≤21.6 ≤20.5 ≤25 ≤30 ≤2 ≤0.15 < 0.0001 < 0.001 < 0.01/1000 6.5–7
270–306 14.33–16.24 0.62–0.7 1.5–1.7 1334–1570 21.6–25 20.5–23.3 25–30 30–40 2–5 0.15–0.2 0.0001–0.0005 0.001–0.01 0.01/1000–0.1/1000 6–6.5
306–360 16.24–19.1 0.7–0.82 1.7–2 1570–1847 25–28.3 23.3–33.3 30–35.3 40–50 5–10 0.2–0.25 0.0005–0.001 0.01–0.05 0.1/1000–1/1000 5.5–6
≥360 ≥19.1 ≥0.82 ≥2 ≥1847 ≥28.3 ≥33.3 ≥35.3 ≥50 > 10 > 0.25 > 0.001 > 0.05 > 1/1000 < 5.5
Notes: All the membership functions were identified using Eqs. (5)–(9). Leakage rate* was corresponding to the concrete structure, and Leakage rate (L/(Joint·d)) was corresponding to the joint. 246
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Table 5 Calculation process detail.
the health state of immersed tunnels comprehensively. The proposed membership function that describes the fuzzy relationship between the evaluation index and the evaluation grade scientifically can reduce the arbitrariness of the supervisor in the evaluation process and realize the quantitative evaluation of the tunnel health state. (3) In order to modify the subjective characteristic of index weight in the health evaluation model, the subjective- objective fusion weight method was put forward, which was verified better to reflect the role of the actual condition according to the field monitoring data. (4) The proposed health rating scales and countermeasures are validated to be reasonable and feasible in the case study of Nanchang Honggu Tunnel. The calculated VF values were compared with health rating scales, from which the tunnel was revealed in a good condition. Both VF values of E6, E7 element located in the middle of the river and E10 element located near the closure joint part were slightly smaller than other segments. Such evaluation results will enhance the maintenance pertinence of tunnel managers. The method proposed in this study will be a reasonable support for further monitoring and evaluation of the Honggu Tunnel.
Fig. 10. Overall health evaluation value of the tunnel structure.
operation health state, the monitoring of immersed tunnel operation health was realized by setting the monitoring indexes and the arrangement of sensors applicable and economic. (2) A Fuzzy-AHP evaluation model was proposed, and its establishment process was described in detail. The proposed model can give a reasonable evaluation of the health state of immersed tunnels comprehensively by establishing an evaluation index system. The Fuzzy-AHP model can easily consider the various factors affecting
Acknowledgements This work was financially supported by the National Key Research and Development Program of China (Grant No. 2016YFC0800201), China and National Natural Science Foundation of China (Grant No. 41572273, 51878157), China.
Appendix A The specific steps of entropy weight assignment method are shown below. ①Establishment of judgment matrix of tunnel health state
x . . . x1n ⎤ ⎡ 11 R= ⎢ ⋮ ⋱ ⋮ ⎥ x x ⋯ nn ⎦ ⎣ n1
(A1)
②Normalized judgment matrix
bij =
x ij − x min (A2)
x max − x min
where x max and x min are the most satisfied and least satisfied index of each health level, respectively. ③Entropy of assessment index
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Determining the entropy of assessment index
Hi = −
fij =
1 ln m
m
∑ fij ln fij
(A3)
j=1
1 + bij m ∑ j=1
(1 + bij )
(A4)
where fij is the specific weight of ith assessment object. ④Entropy weight calculation
ωi =
1 − Hi n n − ∑i = 1 Hi
(A5)
Through these steps, the analysis of measured data can be converted to the weight information of evaluation indexes.
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