Assessment of bridge expansion joints using long-term displacement measurement under changing environmental conditions

Abstract

This paper addresses the problem of condition assessment of bridge expansion joints using long-term measurement data under changing environmental conditions. The effects of temperature, traffic loading and wind on the expansion joint displacements are analyzed and interpreted, which reveal that measured displacements are observed to increase with an increase in temperature and to decrease with increased traffic loading, while the correlation between displacement and wind speed is very weak. Two regression models are developed to simulate the varying displacements under the changes in temperature and traffic loadings. Based on these models, the effects of the environmental conditions are removed to obtain the normalized displacement. Statistical process control using mean value control charts is further used to detect damage to the bridge expansion joints. The results reveal that the proposed method had a good capability for detecting the damage-induced 1.0% variances of the annual changes in the expansion joint displacements.

Keywords

structural health monitoring / displacement / expansion joint / temperature effect / wind effect / traffic loading / statistical process control / suspension bridge

Introduction

Structural health monitoring (SHM) problems have occupied many researchers in the scientific communities for the last two decades. The goal is to be able to detect, locate and assess the extent of damage in a structure so that its remaining life can be noted and possibly extended. The general methodology for detecting damage in structures is to extract meaningful features from measured data [1,2]. However, it is well known that environmental conditions, such as traffic loading and environmental temperature, will cause changes in the measured structural responses that may mask the changes caused by structural damage. Therefore, it is of paramount importance to characterize the normal variability of structural responses due to environmental effects and discriminate such normal variability from abnormal changes in structural responses caused by structural damage [3,4].

Considerable research effort has been devoted to investigating the influences of environmental conditions on the modal frequencies of bridges [3-9]. For instance, Abdel Wahab and De Roeck [5] conducted two dynamic tests for a prestressed concrete bridge in spring and winter and observed an increase of 4%-5% in the modal frequencies with a decrease in temperature. Cornwell et al. [6] observed variabilities of modal frequencies of up to 6% over a 24 h period on the Alamosa Canyon Bridge. It should be noted that the measured modal frequencies can only reflect the global dynamic characteristics of the bridge, which is difficult for local condition assessment of important bridge components. Ni et al. [9] presented a procedure for condition assessment of expansion joints based on long-term monitoring of displacement and temperature. The results revealed that temperature fluctuation mainly accounts for the movement of the expansion joint. However, in their studies, the variations in the expansion joint displacements induced by traffic loadings and wind speed were not considered.

The main focus of this paper is to present a procedure for condition assessment of expansion joints under changing environmental conditions, including temperature, traffic loading and wind using the long-term monitoring data of a long-span suspension bridge. First, this paper presents the results of a study of the variations in the expansion joint displacements as a function of temperature, traffic loadings and wind speed. Based on these results, the regression models are established, and the effects of environmental conditions are further removed to obtain the normalized displacements. Second, statistical process control using a mean value control chart is utilized for anomaly alarms if the future monitoring displacement data disobey the normal pattern. The feasibility of the proposed method is demonstrated using 148 days of health monitoring data obtained on the Runyang Suspension Bridge.

Structural health monitoring of the Runyang Suspension Bridge

The subject of this study is the Runyang Suspension Bridge, shown in Fig. 1, which is a single-span steel suspension bridge that crosses the Yangtze River along the highway between Zhenjiang and Yangzhou in China. The main span of the bridge is 1490 m, ranking first of its kind in China and third in the world.

The health monitoring system of the Runyang Suspension Bridge has been established to monitor, in real time, the responses of the bridge under various kinds of environmental conditions and mobile loads by application of modern techniques in sensing, testing, computing and network communication [4]. The displacement transducers have been used for the measurement of displacements at two expansion joints located at the northern (Yangzhou) and southern (Zhenjiang) abutments of the bridge deck. Likewise, a total of 27 temperature sensors have been installed at four sections (Sect.1, Sect.2, Sect.3 and Sect.9 in Fig. 2) of the bridge deck to measure the temperature. The detailed sensor arrangement in the deck section is illustrated in Fig. 3. The sampling rate for temperature and displacement used are both 1 Hz. A total of 148 days of data are used in this study, which covers the measurements from January to June of 2006. The data obtained in the year of 2006 are used, herein, as they reflect the behavior of a healthy bridge.

Correlations of displacement and environmental effects

Correlation between temperature and displacement

The 148-day expansion joint displacement data (from January to June of 2006) are used in this study. For each day, the 10-min average displacements at the two expansion joints and the temperatures are calculated. The temperature-displacement scatter diagrams are plotted in Fig. 4. The temperature data from all sensors were averaged to a representative temperature value of the bridge. An overall increase in displacement is observed with an increase in the temperature of the bridge. From Fig. 4, the measured expansion joint displacements at the northern and southern abutments fall in the intervals of [-23.0 cm, 28.7 cm] and [-20.6 cm, 33.0 cm], respectively. Therefore, the annual changes in expansion joint displacements are 51.7 cm and 53.6 cm, respectively.

A linear regression analysis between the 10-min average displacement (d) and the temperature (T) is further performed to model the temperature-displacement correlations [9,10] using the following equation:

(1)d={\beta }_{\mathrm{0}}+{\beta }_{\mathrm{1}}T,

where the regression coefficients {\beta }_{\mathrm{1}} and {\beta }_{\mathrm{0}} were obtained by the least-squares method as

(2){\beta }_{\mathrm{1}}={\displaystyle \frac{S_{\mathrm{d}\mathrm{T}}}{S_{\mathrm{T}\mathrm{T}}}},

(3){\beta }_{\mathrm{0}}=\overline{d}-{\beta }_{\mathrm{1}}\overline{T},

where S_dT is the covariance between the displacement and the temperature sequences; S_TT is the variance of the measured temperature sequences; and \overline{T} and \overline{d} are the means of the measured temperature and displacement sequences, respectively. Table 1 summarizes the expressions of linear regression models of the displacement versus temperature.

Correlation between traffic and displacement

Before the measured expansion joint displacements are used for the correlation analysis of traffic-displacement and wind-displacement, the temperature effect on the measured displacements should be removed. This is achieved by normalizing all of the measured displacements to a fixed reference temperature with the use of the established temperature-displacement correlation models. In this study, the reference temperature is taken as 20°C. By incorporating the reference temperature into the correlation models, a nominal displacement (d_r) is obtained for the two expansion joints. Likewise, by feeding the temperature measurement data into the model, a temperature-induced displacement (d_t) is predicted. The normalized displacement after removing the temperature effect can then be obtained by

(4)d=d_{\mathrm{m}}-(d_{\mathrm{t}}-d_{\mathrm{r}}),

where d is the normalized displacement and d_m is the measured displacement.

In this section, a correlation analysis is first conducted on the normalized expansion joint displacements and traffic conditions. The root mean square (RMS) of the vertical acceleration responses is calculated in the frequency band of 0-3 Hz [11]. RMS data obtained under weak wind conditions (10-min average wind speed less than 2 m/s) are mainly influenced by the varying traffic loadings and are utilized to characterize the traffic-displacement correlation. The normalized displacement at 10-min intervals and 10-min acceleration RMS values measured at the deck level (Sect. 5 in Fig. 2) are used in this study. Figure 5 shows the correlation diagrams of normalized displacement versus acceleration RMS for the northern and southern expansion joints, respectively. It can be observed that for the expansion joints at the northern and southern abutments, the RMS-displacement plot is somewhat dispersed, and an overall decrease in displacement is observed with an increase in acceleration RMS of the bridge.

A linear regression analysis between the normalized displacement (d) and the RMS value (M) is further performed using the least-squares method. Table 2 summarizes the expressions of linear regression models of the displacement versus acceleration RMS.

Correlation between wind and displacement

A correlation analysis is conducted on the normalized displacements and the measured wind speeds under weak wind and strong wind conditions. The wind data are collected from the WA15 anemometer located in the middle of the main span. Before the normalized displacements are used for wind-displacement correlation analysis, the traffic effect on the normalized displacements should be removed, especially for the normalized displacements at the southern abutment. This is achieved by renormalizing all of the normalized displacements to a fixed reference acceleration RMS value with the use of established regression models for RMS-displacement. Similar to Eq. (4), the renormalized displacements after removing the traffic effect are obtained by

(5)d=d_{\mathrm{m}}-(d_{\mathrm{t}}-d_{\mathrm{r}}),

where d is the renormalized displacement, d_m is the normalized displacement, d_t is the traffic-induced displacement and d_r is the nominal displacement with a reference RMS value of 1 cm/s².

The renormalized displacements for 10-min intervals and 10-min average wind speeds measured at the deck level are used in this study. Figure 6 shows the correlation diagrams of renormalized displacement versus wind speed. It can be also observed that the wind speed-displacement plot is rather scattered for both expansion joints. The correlation between displacement and wind speed is very weak and can be neglected.

Removal of environmental effects

In the previous sections, we discussed the correlations of temperature-displacement, traffic-displacement and wind-displacement. The correlation analysis results reveal the following: (i) Temperature is the critical source that causes displacement variability, and there is an overall increase in displacement with temperature. (ii) An overall decrease in displacement is observed with the increase in acceleration RMS of the bridge for the expansion joints at the northern and southern abutments. (iii) The correlation between displacement and wind speed is very weak for both the expansion joints. Therefore, the influences of temperature and traffic loading on the measured displacements should be eliminated for an accurate assessment of the condition of the bridge expansion joints. The proposed method for removing environmental effects consists of the following three steps:

1) Removal of the temperature effect: normalize all the measured displacements to a fixed reference temperature with the use of the established temperature-displacement correlation models (Table 1).

2) Removal of the traffic loading effect: renormalize all of the normalized displacements to a fixed reference acceleration RMS value with the use of the established regression models describing RMS-displacement (Table 2).

3) Removal of random variations: the renormalized displacements are averaged daily using a multisample averaging technique to eliminate the inherent randomness in the measurement data.

Figure 7 shows the measured and normalized displacements at 1-day intervals, respectively. It can be seen that the normalized displacements can effectively eliminate the environmental effects, which is suitable for real-time condition assessment for expansion joints.

Assessment using statistical process control

Statistical control charts

Control charts are used here for in situ assessment of bridge expansion joints. They are a statistical quality control tool for detecting whether the process is out of control. They plot the quality characteristic as a function of the sample number. The chart has lower and upper control limits, which are computed from the samples only when the process is assumed to be in control. When unusual sources of variability are present, the sample statistics will fall outside the control limits. When that occurs, an alarm is triggered. Different control charts exist, differing in the statistics plotted. The mean value control chart is used in this study [12]. The time series of e, taken when the structure is in good condition, will have some distribution with mean μ and variance σ². If the mean and standard deviation are known, a control chart is constructed by drawing a horizontal line CL at μ and two more horizontal lines representing the upper and lower control limits. The upper limit UCL is drawn at μ + kσ and the lower limit LCL at μ-kσ. The choice of k can be determined by all of the observation samples falling between the upper and lower control limits. When the new measurement is made, the structural abnormal condition can be diagnosed if an unusual number of samples fall beyond the control limits.

Application to the condition assessment of expansion joints

In this section, a statistical process control chart is employed to monitor the measured changes in the expansion joint displacements caused by damage. First of all, the condition index e can be defined as the difference between the normalized displacement after removing environmental effects and the annual average of the normalized displacement as follows:

(6)e={\displaystyle \frac{d_{\mathrm{m}}-d_{\mathrm{r}}}{d_{\mathrm{r}}}},

where d_m is the normalized expansion joint displacement at 1-day intervals and d_r is the annual average of the normalized displacements, which is assumed to be the baseline of the healthy structure. Figure 8 shows the mean value control chart of the time series of e using 148 days of samples. The first 100 days of samples are training data, and the latter 48 days of samples are test data. It can be seen that the mean value control charts monitor the changes in the measured expansion joint displacements in real time and effectively reduce the probability of misjudgment through the multisample hypothesis test.

For illustration, the displacements of the expansion joint under damaged conditions are simulated by subtracting a value from the normalized displacements of the 48 test samples as follows:

(7)d_{\mathrm{m}}=d_{\mathrm{m}}^{\mathrm{a}}-ϵ\overline{D},

where d_{\mathrm{m}}^{\mathrm{a}} is the normalized displacement of the test samples; d_m is the simulated displacement of the damaged structure; ϵ denotes the damage extent (in later examples, ϵ is chosen to be 1.0%); and \overline{D} is the annual change in the expansion joint displacements at the northern or southern abutment, i.e., 51.7 cm or 53.6 cm, respectively.

The differences between the simulated displacements and the annual average of the normalized displacements are calculated using Eq. (6), on the basis of which the mean value control chart is drawn as shown in Fig. 9. It can be seen that when the variance of the expansion joint displacement caused by damage reaches 1.0%, the observed samples show an obvious shift to the centerline. Some of the samples fall beyond the control limits, which indicates the existence of damage. Hence, the proposed method can effectively detect the damage-induced 1.0% variances of the annual changes in the expansion joint displacements.

Conclusions

In this paper, the variations in the expansion joint displacements under normal environmental conditions have been studied for the Runyang Suspension Bridge based on long-term continuous measurement data. The effects of temperature, traffic loading and wind on the displacements are analyzed. The results reveal that the long-term variations of displacement are highly correlated with the variation in temperature and traffic loading, whereas the correlation between displacement and wind speed is very weak. Two regression models are developed to simulate the varying displacements under the changes in temperature and traffic loading. The normalized displacements after removing the effects of environmental conditions are used to detect the damage in the expansion joints using statistical process control. In the example studied, the proposed method is able to detect the damage-induced 1.0% variances of the annual changes in the expansion joint displacements, which makes it suitable for real-time structural health monitoring.

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