Long-term condition evaluation for stay cable systems using dead load

Abstract

To ensure the safety of cable-stayed bridges, a long-term condition evaluation method has been proposed based on dead load–induced cable forces. To extract dead load–induced cable forces under random vehicle loadings, a novel approach is first developed by integrating influence lines with monitoring data. Then, based on the extracted dead load–induced cable forces, the evaluation algorithm for stay cable systems is presented. In the assessment algorithm, uniform and non-uniform characteristics are taken into account. Finally, the Third Nanjing Yangtze River Bridge, a typical large span cable-stayed bridge, is used to illustrate the effectiveness of the proposed methodology. As a result, the maximum relative error in extraction of dead load–induced cable forces accounts for 4.78% within the studied five stay cables. The precision of the extraction method is acceptable for practical applications since the relative error is less than 5%. Moreover, the bridge is continuously assessed using the dead load–induced cable forces for 5 years. Eliminating the influence of vehicle loadings, the condition of the bridge gradually degrades with time but still remains in good condition. The study not only provides a long-term condition evaluation method for stay cable systems but a dead load–induced extraction approach under random vehicle loadings, which will help bridge owners know well the condition of bridges to make appropriate maintenance decisions.

Keywords

cable force cable-stayed bridges dead load influence line long-term condition evaluation variable weight model

Introduction

In the past few decades, cable-stayed bridges have become increasingly popular due to the ability to cover large spans as well as the low cost and esthetics. Failure of these bridges is disastrous, resulting in severe casualties and disruptions in mobility and economic production. Nevertheless, existing bridges inevitably deteriorate with time and even lead to structural or functional failures due to being exposed to various external loadings and outer environments. Thus, it is urgent to investigate the condition assessment methodology for such large span bridges to ensure their safety, serviceability, and durability.

Various methodologies have been proposed for condition assessment of existing bridges, including visual inspection–based, structural health monitoring–based, and non-destructive testing–based methods (Gattulli and Chiaramonte, 2005; Kırlangıç et al., 2016; Xiong et al., 2010). Besides, great efforts have been made to model uncertainties, fuzziness, and randomness in the assessment process, including fuzzy synthesis, evidential reasoning, and cloud theory algorithms (Bolar et al., 2013; Sasmal and Ramanjaneyulu, 2008; Xu et al., 2018). The aforementioned research can be generally applied to all types of bridges. When it comes to cable-stayed bridges, some particular assessment methods are employed based on the structural characteristics. For instance, cable forces can be used to evaluate the condition of cable-stayed bridges owing to the ability to reflect the overall condition of structures (Kim et al., 2012). In addition, with the development of monitoring techniques, e.g. vibration-based, magnetism-based, and anchor load cell methods (Chen et al., 2016; Sumitro et al., 2005; Yang et al., 2016), cable force measurements can be acquired conveniently during service periods. Hua et al. (2009) presented a static-based damage detection method for cable-stayed bridges using the changes in cable forces. Xiong et al. (2011) proposed an approach for the condition assessment of stay cable forces based on the recorded cable force signals. Therefore, in view of characteristics of cable-stayed bridges, it makes sense to evaluate the structural condition by taking advantages of cable force measurements.

Based on the rationale that when damage occurs (whether it occurs gradually or instantaneously), it will result in a redistribution of dead load stress in the structure. The nature and extent of the redistribution can be used for damage detection or structural condition evaluation. Zhao and Shenton (2005) presented a damage detection method based on the best approximation of dead load stress redistribution. Hu and Shenton (2006) developed the damage identification procedure based on the redistribution of dead load in the structure. Following the idea, it is reasonable to assess the long-term condition for cable-stayed bridges on the basis of the redistribution of dead load–induced cable forces. However, the recorded measurements of cable forces are affected by various factors, such as dead weight, vehicle loadings, temperature, noise, and so on. The separation methods for measurement noise and thermal effects have been well studied at present. Signal processing approaches are always used to remove the effects of noise and temperature (Baili et al., 2009; Xu and Xia, 2011). Nevertheless, rare investigations are available to separate the effects of live loadings and dead weight due to its high uncertainties. To evaluate the condition of cable-stayed bridges, the first step is to extract response induced by dead loads from the sophisticated recorded signals.

In this article, a long-term condition evaluation methodology for stay cable systems is proposed based on the nature and extent of redistribution of the dead load–induced cable forces. First, an extraction approach for cable forces induced by dead loads is demonstrated by integrating influence lines with monitoring data. Then, the condition of cable-stayed bridges is evaluated using the changes in dead load–induced cable forces, where the rational bridging cable forces are set as the baseline. Finally, the Third Nanjing Yangtze River Bridge is taken as a case study to validate the effectiveness of both the proposed extraction and evaluation methods.

The proposed evaluation methodology

Considering that the evaluation method takes root in the dead load–induced cable forces, the first step is to extract cable forces induced by dead loads. The separation methods for the effects of noise and temperature have been well studied as aforementioned, and existing approaches have enough precisions for engineering applications (Jiang et al., 2007; Xia et al., 2013; Zhou et al., 2015). In view of the limitations of paper length, this study only focuses on separating the effects induced by live loadings and dead weights.

The simplest approach to acquire dead load–induced response is to close the bridge to exclude the influence of vehicle loadings. Nevertheless, closure of these bridges will result in great social and economic losses due to their key roles in the transportation networks. For instance, Jiangyin Yangtze River Bridge is a critical node carrying almost 85,000 vehicles per day (the corresponding toll is almost US$500,000) on the G2 Beijing–Shanghai Expressway, and it was completely closed for several times during the last 5 years owing to the extreme weather. Xiong et al. (2010) recommended to use the measurements at night when there was minimum traffic for long-term load condition assessment. To extend the application of the method, it is meaningful to develop an approach to extract dead load–induced response under random vehicle loadings. Once obtaining the dead load–induced cable forces, the variation to the rational bridging cable forces will be used to evaluate the bridge condition by taking uniform and non-uniform features into account. The flowchart of the proposed methodology is shown in Figure 1.

Figure 1.

Flowchart of the proposed evaluation methodology.

The extraction method of dead load–induced cable force

Monitoring data analysis

The monitoring cable force signals contain various components, including measurement noise, thermal effects, live load–induced effects, and dead load–induced effects. A statistical-based approach has been developed to determine the value of dead load–induced cable force (Liu et al., 2015). Weibull extreme distribution was used to fit the measured cable force data as shown in Figure 2, and the cable force corresponding to the maximum value of probability density is defined as the dead load–induced cable force. However, the statistical-based method is mainly on the basis of data analysis and lacks physical interpretations. It is better to develop a method with explicit physical meanings.

Figure 2.

Statistical-based approach to determine dead load–induced cable force (Liu et al., 2015).

A set of actual cable force monitoring data from the studied bridge (which will be introduced in section “The case study”) is taken as the instance for discussion as shown in Figure 3. The cable force data in Figure 3 have excluded the influence of measurement noise and temperature actions. The fluctuation between the upper and lower envelopes is caused by random vehicle loadings on the bridge. The value of dead load–induced cable force certainly locates between the upper and lower envelopes. Then, the dead load–induced cable force F_dead can be expressed as

F_{dead} = F_{low} + α (F_{up} - F_{low})

(1)

where F_low is the mean value of the points right on the lower envelope, F_up the mean value of the points on the upper envelope, and α is the proportionality coefficient, the geometric interpretation of which is shown in Figure 3.

Figure 3.

A set of actual cable force monitoring data.

Determination of α: influence line–based analysis

Based on the fact that the cable force will undergo the most unfavorable vehicle loading conditions as long as the bridge serves for enough long time, it is assumed herein that the upper and lower envelops shown in Figure 3 correspond to the most unfavorable conditions 1 and 2. The two most unfavorable conditions are defined by influence line–based vehicle loading distributions as shown in Figure 4(a) and (b), respectively.

Figure 4.

Influence line–based analysis of the studied cable force: (a) most unfavorable condition 1 and (b) most unfavorable condition 2.

According to the most unfavorable vehicle loading conditions, the maximum and minimum live load–induced cable forces for the studied stay cable $F_{up}^{M}$ and $F_{low}^{M}$ can be expressed by

Most unfavorable condition 1 : F_{up}^{M} = f \cdot \sum_{i = 1}^{m} S_{i}^{+}

(2)

Most unfavorable condition 2 : F_{low}^{M} = - f \cdot \sum_{i = 1}^{n} S_{i}^{-}

(3)

where f is the statistical mean of vehicle loadings, $S_{i}^{+}$ the ith area enclosed by the positive influence line and the coordinate axis, $S_{i}^{-}$ the ith area enclosed by the negative influence line and the coordinate axis, and m and n are the total numbers of areas of $S_{i}^{+}$ and $S_{i}^{-}$ , respectively.

Based on the above assumption that the upper and lower envelops from the monitoring data in Figure 3 are in line with the vehicle loading distributions shown in Figure 4, the ratios of the maximum and minimum live load–induced cable forces under the two cases (i.e. monitoring data analysis and influence line–based analysis) are identical, namely

\frac{F_{up}^{M}}{F_{low}^{M}} = \frac{F_{up} - F_{dead}}{F_{low} - F_{dead}}

(4)

Based on equations (2) and (3), the solution of equation (4) is

F_{dead} = F_{low} + \frac{\sum_{i = 1}^{n} S_{i}^{-}}{\sum_{i = 1}^{m} S_{i}^{+} + \sum_{i = 1}^{n} S_{i}^{-}} (F_{up} - F_{low})

(5)

When compared to equation (1), the value of α is equal to $\sum_{i = 1}^{n} S_{i}^{-} / (\sum_{i = 1}^{m} S_{i}^{+} + \sum_{i = 1}^{n} S_{i}^{-})$ .

The long-term condition evaluation algorithm

The cable force is a kind of series index, which is a group of sequential numbers as X = (x₁, x₂, …, x_n), where x_i is the dead load–induced force of stay cable i. Uniform and non-uniform characteristics are usually used to interpret series indexes, where the uniform feature indicates the average distance to the baseline, while the non-uniform feature illustrates the fluctuation range around the baseline. Since the most common method for series indexes takes root in variable weight theory (Wu and Xiang, 2006), the variable weight–based evaluation approach will be utilized in this study, in which the uniform and non-uniform characteristics will be taken into account. The flowchart of the proposed evaluation algorithm is shown in Figure 5.

Figure 5.

Flowchart of the proposed evaluation algorithm.

Step 1: calculate evaluation result y_i

Since the rational bridging cable forces could make the bridge in the optimal state, it is set as the baseline for condition evaluation using dead load–induced cable forces. The distance to the baseline can be used to evaluate the state of bridges (Xiong et al., 2010). In this study, the relative distance to the baseline of ±40% is defined as an unacceptable point, which deserves an evaluation result of y_i = 0 (Ren et al., 2015). Then, the other values of y_i could be determined via linear interpolation, namely

y_{i} = {\begin{matrix} \frac{x_{i} - 0.6 x_{i}^{0}}{x_{i}^{0} - 0.6 x_{i}^{0}}, 0.6 x_{i}^{0} < x_{i} < x_{i}^{0} \\ \frac{1.4 x_{i}^{0} - x_{i}}{1.4 x_{i}^{0} - x_{i}^{0}}, x_{i}^{0} < x_{i} < 1.4 x_{i}^{0} \\ 0, x_{i} \leq 0.6 x_{i}^{0}, x_{i} \geq 1.4 x_{i}^{0} \end{matrix}

(6)

where $x_{i}$ is the recorded dead load–induced cable force of stay cable i and $x_{i}^{0}$ is the baseline value.

Step 2: allocate variable weight ω_i

To overcome the limitations of the constant weight model, the variable weight model is applied in this study. Compared to the constant weight model, the variable weight model can highlight the severe localized damages in the overall evaluation result. For instance, for the case that one stay cable has a great distance to the baseline while the others are all close to the baseline, the variable weight model is able to make the final evaluation result in line with the actual situation via increasing the weight of the target stay cable to lower the evaluation result. The most common variable weight model is used in this study (Lan and Shi, 2001), namely

ω_{i} = \frac{y_{i}^{α_{f} - 1}}{\sum_{k = 1}^{n} y_{k}^{α_{f} - 1}}

(7)

where n is the total number of stay cables used for evaluation and α_f (0 ≤ α_f ≤ 1) is the coefficient that decides the effectiveness of weight adjustment. In view of structural safety, the value of α_f is set as 0.2 in this study (Ren et al., 2015).

Step 3: acquire non-uniform coefficient r

Correlation degree is used to assess the non-uniformity of the dead load–induced cable force series. In consideration of the request of order preserving, the slope correlation degree is adopted herein, namely

r = \frac{1}{n - 1} \sum_{i = 1}^{n - 1} {[1 + | \frac{x_{i}}{x_{i + 1}} - \frac{x_{i}^{0}}{x_{i + 1}^{0}} |]}^{- 1}

(8)

Step 4: aggregate y_i into the comprehensive evaluation result V

The comprehensive evaluation result should take both the uniform and non-uniform characteristics of the dead load–induced cable force series into account, namely

V = r \times U = r \times \sum_{i = 1}^{n} y_{i} ω_{i}

(9)

where U is the evaluation result with the uniform feature.

The case study

The Third Nanjing Yangtze River Bridge that opened to traffic in 2005 is located in Jiangsu Province, China. This bridge is a vital transportation link standing over the middle and lower Yangtze River and connecting Nanjing and its Liuhe District, and also a part of the G42 Shanghai–Chengdu Expressway, the site plan of which is shown in Figure 6(a). This cable-stayed bridge has two steel towers with a main span of 648 m, the front view of which is shown in Figure 6(b). A unique feature of this bridge is the arc-shaped steel tower that is the first bridge among such long-span cable-stayed bridges in the world. The deck superstructure is a 3.2-m-deep and 37.5-m-wide orthotropic steel box girder that accommodates three lanes of traffic in each direction. The deck is supported by 168 stay cables and each cable is formed by 109–241 wires of 7 mm diameter.

Figure 6.

General information regarding the Third Nanjing Yangtze River Bridge: (a) site plan and (b) front view.

In the second year after the completion of the bridge, a sophisticated long-term monitoring system was devised and implemented to monitor its structural health state. The goal of the structural health monitoring system was to monitor the structural behavior in conditions of extreme traffic, high temperature, humidity, or wind. In order to achieve this goal, the following sensor applications were selected: anchor load cells for cable forces, connected pipes for vertical deflections, strain gages, thermometers, and so on. The detailed sensor layout is shown in Figure 7. As shown in Figure 7, the sensors in the Third Nanjing Yangtze River Bridge studied in this article include the following: (1) anchor load cells to monitor the cable forces of stay cables. The load cells are installed in the anchors of stay cables, which measure cable force directly. Compared to the other cable force measurement approaches (e.g. vibration frequency measurement), the anchor load cells have a high precision. The pre-tension forces will not greatly influence the measurements of anchor load cells if the supports (below and above the load cell) are rigid enough. However, due to the degradation of the material and uneven tensions, the measurement accuracy will decrease over time. Moreover, anchor load cells are difficult to replace since the sensors are embedded in the anchor system. The total 168 stay cables are all equipped with anchor load cells with a relative error of ±1%. The sample frequency of the anchor load cell is 10 Hz; (2) thermometers. A total of six R.M.YOUNG-41372 thermometers are installed for the whole structure, for which the precision is ±0.3°C. One thermometer is installed outside the lower cross beam of the south tower to monitor the ambient temperature. Another thermometer is installed inside the steel box girder at the south tower to monitor the temperature inside the girder. The other four thermometers are installed inside the lower cross beam of both towers to monitor the temperature inside the towers. The sample frequency of thermometers is 10 Hz. The temperature sensors, HBL-type strain temperature compensators, are used to measure temperature distributions of the girder and tower, which acquire a datum each half an hour (a frequency of 1/1800 Hz) and have a resolution of ±0.5°C.

Figure 7.

Layout of the sensors in the Third Nanjing Yangtze River Bridge.

Extraction of dead load–induced cable forces under random vehicle loadings

The SA-E15 stay cable of the Third Nanjing Yangtze River Bridge as shown in Figure 6 is used to verify the effectiveness of the proposed extraction approach. The components of the recorded cable force signals include noise, thermal effects, live load effects, and dead load effects. First, the wavelet transform denoising method, a powerful tool in signal processing, is applied to improve the quality of the measured data. The wavelet denoising approach is suitable for processing non-stationary signals owing to its availability for evaluating the time and frequency domains (Kaloop et al., 2015). Aiming to reach a satisfactory denoising result, six wavelet delamination and “db8” wavelet basis are determined for denoising after a preliminary test. The continuously monitored 600-s cable force data were employed to illustrate the effectiveness of the denoising method as shown in Figure 8. As a result, the signal is smoother after denoising using the wavelet filter. Then, a regression method is employed to fit the correlation between the ambient temperature and cable force. The linear regression model is proper to fit the relationship between the ambient temperature and cable force as shown in Figure 9. According to the regression result, the cable force of the studied stay cable increases 2.7055 kN/°C. Finally, 4-month (January–April 2007) cable force monitoring data without the effects of noise and temperature are prepared for the following discussion as shown in Figure 10, where each point represents the quarter-hourly mean of the cable force.

Figure 8.

Denoising results based on the wavelet filter: (a) original cable force signals and (b) noise-free cable force signals.

Figure 9.

Correlation of the temperature and the cable force.

Figure 10.

The 4-month cable force data without the effects of noise and temperature.

The mean values of the points on the upper and lower envelopes are as follows:

Most unfavorable condition 1: $F_{up} = 3264.55 kN$ ;

Most unfavorable condition 2: $F_{low} = 3113.22 kN$ .

A two-dimensional (2D) frame finite element (FE) model for the bridge was built using the program ANSYS R15.0 based on the engineering drawings. Beam188 and Link10 were used to simulate the steel box girder and stay cable. A total of 5515 nodes and 3805 elements are in the whole bridge model as shown in Figure 11. The model updating was then performed based on both the static and the dynamic test responses. The typical five steps for model updating are shown in Figure 12. Seven parameters are first selected as the updating parameters, including vertical spring stiffness and transverse spring stiffness of the supports at the towers, auxiliary piers and transition piers as well as the longitudinal spring stiffness of the supports at the towers. Then, parameter sensitivity analysis is carried out on the basis of the frequency and deflections. The sensitivity analysis results based on the natural frequency and deflections are shown in Figure 13. As a result, the sensitivity of the longitudinal stiffness of the supports at the towers is relatively small both in the frequency and deflection sensitivity analyses. Next, the objective function is defined as

J = a \sum_{i = 1}^{k} λ_{fi} {(\frac{f_{i} - f_{it}}{f_{it}})}^{2} + b \sum_{i = 1}^{k} λ_{Mi} {(\frac{1 - \sqrt{MA C_{i}}}{MA C_{i}})}^{2} + c \sum_{j}^{n} \sum_{i = 1}^{m} λ_{dji} {(\frac{d_{ji} - d_{jit}}{d_{jit}})}^{2}

(10)

where a, b, and c are the model coefficients, λ the weight coefficient, f the natural frequency, MAC the modal assurance criterion, and d is the deflection response. According to the parameter sensitivity analysis results, the dynamic responses are more sensitive to the parameters than the static ones. The values of a, b, and c are determined to be 1.0, 1.0, and 0.2, respectively, according to the ratios of the maximum sensitivity values between the dynamic and static responses. Due to the higher measurement accuracy for the lower mode frequencies, the first five mode frequencies are included in the objective function, and the weight λ is uniformly assigned to each mode. The first-order optimization algorithm is employed in this study and the algorithm requires the gradient to be calculated with respect to all the updating parameters. More specific updating process will not be described in this article and for details on the effectiveness of the updated model refer to Li (2013).

Figure 11.

The FE model of the Third Nanjing Yangtze River Bridge.

Figure 12.

Five steps of the model updating process.

Figure 13.

Sensitivity analysis results of the seven updating parameters: (a) sensitivity analysis results to the natural frequency and (b) sensitivity analysis results to the deflection.

The updated FE model was validated by means of comparing the dynamic and static predictions with the field measurements. The static standard truck test was implemented in September 2005. The referenced structural response (e.g. natural frequency) was measured in situ. The natural frequency was measured using the ambient vibration test, while the deflection for model validation was under the truck loading mode as shown in Figure 14(b). The field-measured frequencies and deflections are presented in Figure 14 along with the respective predictions from both the initial and updated FE models. It is seen from Figure 14 that the predictions of both the frequency and deflection response from the updated model agree better with the field measurements than those calculated by the initial model.

Figure 14.

The FE model validation results: (a) model validation based on the natural frequency and (b) model validation based on the deflection.

The influence line of the cable forces of interest (SA-E15) can be drawn based on the updated FE model as shown in Figure 15. According to equation (5), the dead load–induced cable force of stay cable SA-E15 is 3152.39 kN.

Figure 15.

Influence line of the SA-E15 stay cable force.

Cable force measurements during bridge closure windows are used to verify the effectiveness of the proposed extraction method. The cable force monitoring data of the stay cable SA-E15 during the bridge closure period (17 January 2007) are shown in Figure 16 which are not influenced by noise and temperature. According to Figure 16, the cable forces fluctuate slightly between 3158.40 and 3159.00 kN during the bridge closure window, which may result from the measurement stability of the sensors. The average value can be taken as a typical value to represent the dead load–induced cable force of $F_{dead}^{clo} = 3158.60 kN$ .

Figure 16.

Cable force induced by the dead load during the bridge closure period.

It is known that the calculated value of the dead load–induced cable force of stay cable SA-E15 is 3152.39 kN, while the value obtained from the monitoring data during the bridge closure period is 3158.60 kN (the baseline). As a result, the absolute error of the extraction method is 6.21 kN, the relative error of which to the cable force fluctuation range accounts for 4.10%.

To avoid contingency, another four stay cables were selected to verify the accuracy of the proposed method and the validation results are listed in Table 1. The maximum absolute error and relative error account for 7.67 kN and 4.78% within all the five stay cables, respectively. The maximum relative error of the extraction method is less than 5% that is proper for engineering applications.

Table 1.

Validation results of all the five cables.

No.	$\sum S_{i}^{+}$	$\sum S_{i}^{-}$	F_up (kN)	F_low (kN)	F_dead (kN)	$F_{dead}^{clo}$ (kN)	Error (kN)	Relative error (%)
SA-E4	398.25	88.20	1770.26	1560.90	1598.86	1600.21	1.35	0.64
SJ-W9	493.20	14.4	2477.95	2358.06	2361.46	2363.48	1.89	1.68
NA-W12	450.72	39.24	2585.37	2444.10	2455.41	2462.16	6.75	4.78
SA-E15	367.05	128.20	3264.55	3113.22	3152.39	3158.60	6.21	4.10
NA-W21	369.28	132.96	4150.01	3936.59	3993.09	3985.42	7.67	3.59

Long-term condition evaluation

The 5-year (2007–2011) dead load–induced cable force data were extracted based on the proposed approach, which are used to discuss the variation trend of the dead load–induced cable force over time. The variation rate of dead load–induced cable force is defined herein to evaluate the variation extent, namely

ρ = \frac{x_{i} - x_{i}^{0}}{x_{i}^{0}} \times 100 %

(11)

where $x_{i}$ is the recorded dead load–induced cable force of stay cable i and $x_{i}^{0}$ is the rational bridging cable force (the baseline). Stay cables SJ-W18, SA-E21, and SA-E7 are used to illustrate the three typical variation trends as shown in Figure 17.

Figure 17.

Typical variation trends for dead load–induced cable force.

It can be seen from Figure 17 that the dead load–induced cable force of each cable varies with time. In general, there are three typical variation trends herein: (1) variation rate ρ fluctuates close to the line of ρ = 0 as stay cable SJ-W18; (2) ρ increases with time as stay cable SA-E21; and (3) ρ decreases over time as stay cable SA-E7.

Based on the evaluation process in section “The long-term condition evaluation algorithm”, the long-term condition of the cable-stayed bridge is assessed using the dead load–induced cable force. To highlight the advantages of the proposed methodology, the evaluation results using cable forces including live loadings are calculated for comparison. The 5-year evaluation results of the bridge are listed in Table 2 under the two circumstances. Based on the evaluation results in Table 2, the condition of the bridge evaluated using dead load–induced cable forces gradually degrades with time but still remains in a good condition. However, the assessment results corresponding to cable forces including live loadings show strong randomness since live load–induced cable forces influence uniform and non-uniform features greatly.

Table 2.

The 5-year evaluation results of the bridge.

Year	2007	2008	2009	2010	2011
Cable forces including live loadings
U_li	86.11	81.10	88.41	89.28	89.83
r_li	0.968	0.952	0.962	0.960	0.978
V_li	83.35	77.25	85.12	85.75	87.89
Dead load–induced cable forces
U_de	98.58	97.80	94.08	93.24	90.46
r_de	0.993	0.992	0.978	0.977	0.965
V_de	97.93	97.03	92.02	91.06	87.63

Conclusion

This article has proposed a long-term condition evaluation method for stay cable systems using dead load–induced cable forces. The following conclusions can be drawn from the study:

A novel methodology for extraction of dead load–induced cable force under random vehicle loadings is developed. The method integrates influence lines with long-term monitoring data to determine the proportionality coefficient between the maximum and minimum recorded cable forces. The proposed extraction method has an explicit physical significance.

A long-term condition evaluation approach for stay cable systems is presented based on the uniform and non-uniform features of cable force series. The rational bridging cable force is set as the baseline and the long-term condition of cable-stayed bridges is evaluated by the variation degree of dead load–induced cable force to the baseline.

The Third Nanjing Yangtze River Bridge is used to demonstrate the effectiveness of the proposed methodology. The SA-E15 stay cable was used to verify the effectiveness of the proposed extraction method. The maximum absolute error accounts for 6.21 kN when compared to the value derived from the measurements during the bridge closure window. To avoid contingency, another four stay cables were selected and the maximum relative error accounts for 4.78% among all the five stay cables. Then, the 5-year cable force monitoring data are used to evaluate the long-term condition of the bridge. As a result, the condition of the bridge gradually degrades with time but still remains in a good condition.

The study not only provides a long-term condition evaluation method for stay cable systems but a dead load–induced extraction approach under random vehicle loadings, which will help bridge owners know well the condition of bridges and make maintenance decisions.

Footnotes

Acknowledgements

The authors thank the anonymous reviewers for their constructive comments that greatly improved the quality of this manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research reported in this article was supported in part by the National Natural Science Foundation of China under Grant No. 51208096, the Basic Research Program (Natural Science Foundation) of Jiangsu, China under Grant No. BK20181278, the Key Science and Technology Project of Jiangsu Transport Department, China under Grant No. 2014Y02, the Scientific Research Foundation of Graduate School of Southeast University under Grant No. YBJJ1845, and China Scholarship Council.

ORCID iD

Xiang Xu

References

Baili

Lahouar

Hergli

et al . (2009) GPR signal de-noising by discrete wavelet transform. NDT & E International 42(8): 696–703.

Bolar

Tesfamariam

Sadiq

(2013) Condition assessment for bridges: a hierarchical evidential reasoning (HER) framework. Structure & Infrastructure Engineering 9(7): 648–666.

Chen

Leu

et al . (2016) Tension determination of stay cable or external tendon with complicated constraints using multiple vibration measurements. Measurement 86: 182–195.

Gattulli

Chiaramonte

(2005) Condition assessment by visual inspection for a bridge management system. Computer-Aided Civil & Infrastructure Engineering 20(2): 95–107.

Shenton

III (2006) Damage identification based on dead load redistribution: effect of measurement error. Journal of Structural Engineering 132(8): 1264–1273.

Hua

Chen

et al . (2009) Structural damage detection of cable-stayed bridges using changes in cable forces and model updating. Journal of Structural Engineering 135(9): 1093–1106.

Jiang

Mahadevan

Adeli

(2007) Bayesian wavelet packet denoising for structural system identification. Structural Control and Health Monitoring 14(2): 333–356.

Kırlangıç

Cascante

Polak

(2016) Assessment of concrete beams with irregular defects using surface waves. ACI Materials Journal 113(1): 73–81.

Kaloop

Sayed

(2015) Bridge performance assessment based on an adaptive neuro-fuzzy inference system with wavelet filter for the GPS measurements. ISPRS International Journal of Geo-information 4(4): 2339–2361.

10.

Kim

Jun

(2012) Application of laser vibrometer to the measurement and control of cable tensile forces in cable-stayed bridges. International Journal of Distributed Sensor Networks 8(10): 810682.

11.

Lan

Shi

(2001) Degree of grey incidence and variable weight synthesizing applied in bridge assessment. Journal of Tongji University (Natural Science) 29(1): 50–54 (in Chinese).

12.

(2013) Research on data fusion between maintenance management and health monitoring systems for long-span cable-stayed bridge. Master’s Dissertation, Southeast University, Nanjing, China (in Chinese).

13.

Liu

Huang

Ren

et al . (2015) Extraction of cable forces due to dead load in cable-stayed bridges under random vehicle loads. Journal of Southeast University (English Edition) 31(3): 407–411.

14.

Ren

Liu

Huang

(2015) The long-term trend analysis and assessment of the cable forces due to dead load in cable-stayed bridges. Journal of Harbin Institute of Technology 47(6): 103–108 (in Chinese).

15.

Sasmal

Ramanjaneyulu

(2008) Condition evaluation of existing reinforced concrete bridges using fuzzy based analytic hierarchy approach. Expert Systems with Applications 35(3): 1430–1443.

16.

Sumitro

Kurokawa

Shimano

et al . (2005) Monitoring based maintenance utilizing actual stress sensory technology. Smart Materials & Structures 14(3): S68.

17.

Xiang

(2006) Assessment the cable tension and the linetype state of cable-stayed bridge based on variable weight synthesis. China Railway Science 27(6): 42–48 (in Chinese).

18.

Xia

Chen

Zhou

et al . (2013) Field monitoring and numerical analysis of Tsing Ma Suspension Bridge temperature behavior. Structural Control and Health Monitoring 20(4): 560–575.

19.

Xiong

Xiao

(2011) Condition assessment of stay cable forces based on variation and trend coefficients. Journal of Tongji University (Natural Science) 39(11): 1575–1580 (in Chinese).

20.

Xiong

Xiao

Deng

et al . (2010) Methodology of long-term real-time condition assessment for existing cable-stayed bridges. Advances in Structural Engineering 13(1): 111–126.

21.

Huang

Ren

et al . (2018) Condition assessment of suspension bridges using local variable weight and normal cloud model. KSCE Journal of Civil Engineering 22(10): 4064–4072.

22.

Xia

(2011) Structural Health Monitoring of Long-span Suspension Bridges. London: Spon Press.

23.

Yang

Nagarajaiah

et al . (2016) Real-time output-only identification of time-varying cable tension from accelerations via complexity pursuit. Journal of Structural Engineering 142(1): 04015083.

24.

Zhao

Shenton

IIIHW

(2005) Structural damage detection using best approximated dead load redistribution. Structural Health Monitoring 4(4): 319–339.

25.

Zhou

Xia

Brownjohn

et al . (2015) Temperature analysis of a long-span suspension bridge based on field monitoring and numerical simulation. Journal of Bridge Engineering 21(1): 04015027.

Long-term condition evaluation for stay cable systems using dead load–induced cable forces

Abstract

Keywords

Introduction

The proposed evaluation methodology

The extraction method of dead load–induced cable force

Monitoring data analysis

Determination of α: influence line–based analysis

The long-term condition evaluation algorithm

Step 1: calculate evaluation result yi

Step 2: allocate variable weight ωi

Step 3: acquire non-uniform coefficient r

Step 4: aggregate yi into the comprehensive evaluation result V

The case study

Extraction of dead load–induced cable forces under random vehicle loadings

Long-term condition evaluation

Conclusion

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

ORCID iD

References

Step 1: calculate evaluation result y_i

Step 2: allocate variable weight ω_i

Step 4: aggregate y_i into the comprehensive evaluation result V