Evaluation of lateral cooperative working performance of assembled beam bridge based on the index of strain correlation coefficient

Abstract

The assembled beam bridge is one of the most commonly used and most developed structural types in rapid industrialized bridge construction technology. The hinge joint is the key to the overall cooperative performance of this type of structure, and it is also the most vulnerable part in the service period. This article proposes a monitoring and evaluation method for the lateral collaborative working capability of this type of bridge based on the dynamic strain correlation coefficient index. The proposed method has the advantages of no need to interrupt traffic, easy implementation, concise physical meanings, being independent of short-term traffic load, and so on. Its potentialities to be used in the monitoring and evaluation of the technical state of the hinge joint and the lateral collaborative working performance of the whole bridge have been expatiated theoretically. Through numerical simulation analysis and real bridge monitoring data analysis, it is proved that the method is effective and accurate, and can be applied to the health monitoring system of such bridges.

Keywords

assembled beam bridge correlation coefficient dynamic strain lateral collaborative working performance monitoring and evaluation

Introduction

In recent years, China has built 823,000 highway bridges and the number has ranked first in the world. In spite of this, it is still unable to meet the rapid development of transportation demand, and there are still urgent bridge construction needs across the country. In some of the busy central and eastern regions or western cities, not only it is necessary to continue constructing a large number of bridges, but also it requires that construction and transportation network operations develop simultaneously and in parallel. This imposes restrictive requirements on the construction period and construction speed of the bridge. Accelerated bridge construction technology can speed up the construction of bridges, reduce the total construction cost, and minimize the adverse impact on existing traffic, so it has been rapidly developed in various parts of the world in recent years (Culmo, 2011; He et al., 2012; Khan, 2014; Li et al., 2009; Marsh, 2011). In China, accelerated bridge construction with assembly beam bridges as the major bridge type has been developed for almost 30 years. It is currently the bridge type with the highest proportion. In recent years, with the requirements for construction efficiency and environmental protection, this trend has been translated into the national government’s policy needs (The General Office of the State Council of the People’s Republic of China, 2016).

The assembled beam bridge has a high degree of industrialization, a low cost, and a simple, rapid, and efficient construction, and therefore it has become one of the important bridge types when highways and other infrastructures cross obstacles such as mountains and rivers. The assembled beam bridge has a simple structure and a small and medium span. The girder section is mainly composed of a hollow slab, a T-shaped girder, and a small box girder. The mechanical properties are relatively clear and the design theory is mature. Benefiting from the advantages of easy control of the quality of factory processing, the mechanical properties of the prefabricated girder can generally be fully guaranteed (Jahromi et al., 2018a, 2018b). However, the overall performance of assembly beam bridges does not depend solely on the mechanical properties of the monolithic prefabricated girder but also the co-stressing capacity of the individual beams after they are assembled as a whole (Bakht and Jaeger, 1992; Shah et al., 2007), that is, the role of external loads is distributed to all monolithic girders through the lateral connection system. The lateral connection system is mainly composed of longitudinal hinge joints between the prefabricated girders of each piece and cross girders. The strength of the lateral connection system will directly affect the force distributed by each beam.

In the service process, the main problem of this kind of bridge lies in the degradation of the lateral connection capacity and the destruction of the hinge joints. The damage of the hinge joint makes the lateral connection of the assembled beam bridge weakened, which will cause uneven distribution of forces between the girders and plates, and increase the internal force of the single girder. This will cause not only its own safety problems, but also other kinds of damages. Understanding the lateral cooperating ability of assembled beam bridges and the state of hinge joints between prefabricated girders in a timely manner helps to form a correct and timely decision-making on custody in service and thus plays a role in ensuring the safety and durability of bridges (Abendroth et al., 1995; Wen et al., 2017). How to use the monitoring and evaluation measures to achieve the above objectives during the operation period of an assembled beam bridge without disrupting the traffic is very necessary. The purpose of this article is to provide a monitoring and evaluation method for the lateral collaborative working capability of an assembled beam bridge based on strain monitoring information.

Strain monitoring information–based lateral collaborative performance indicators for assembled beam bridge

As mentioned above, the condition of hinge joints directly affects the lateral collaborative ability between the prefabricated girders of the assembled beam bridge. When the hinge joints break, the distribution ratio of the external load between the girders will change, and the mechanical response of each girder under the external load will also change. This means that the failure information of the hinge joint is necessarily implied in the mechanical response of each prefabricated girder. Therefore, if the mechanical response of each prefabricated girder under external loads can be monitored, it is theoretically possible to retrospect the information on the failure of hinge joints or the degradation of lateral collaborative performance.

However, the above direct and simple reasoning is difficult to achieve in monitoring and evaluation of the actual service bridges. The reason is that the response of each piece of girder depends not only on the condition of hinge joints, but also on the structural form of the bridge, the stiffness of the prefabricated girder, and other factors. More unfortunately, it is still largely dependent on external loads, including size and position of action. Because of the randomness and time variation of traffic flow loads, the responses are also time varying and random. The changes in responses are mostly due to the contribution of traffic loads, while the contribution of hinge joints, prefabricated girder stiffness, and other factors is submerged. How to find the latter through the former has become one of the difficult problems that have plagued the engineering community for a long time. For this reason, this article will focus on solutions below.

Indicator definition

For this purpose, we propose a method to extract the change information of the characteristics of the structure from the measured strain response information of the prefabricated girder, that is, by defining the correlation coefficient of the dynamic strain at the adjacent girder bottom as the lateral collaborative performance indicator of the assembled beam bridge and then to reflect the strength of weak joints between the girders via the proposed indicators (Wen et al., 2017). This indicator is defined as the correlation coefficient of the longitudinal strain at the midpoint of each prefabricated girder on the same cross section, that is

ρ_{ij} = \frac{Cov (ε_{i}, ε_{j})}{\sqrt{D (ε_{i}) \cdot D (ε_{j})}}

(1)

where $ε_{i}$ are $ε_{j}$ are the longitudinal strain time series of the prefabricated girders of the ith and jth slabs monitored, respectively, where $i, j = 1, 2, \dots, n$ ; $n$ is the total number of prefabricated girders; Cov is the covariance; and D is the variance.

The indicator can be given in its analytical expression form by the simplified mechanical model shown in Figure 1. In this model, regardless of whether the cross-section is a plate girder, T-beam, small box girder, or in other forms, each prefabricated girder can use vertical stiffness $K_{i}$ and torsional stiffness $K_{i}^{m}$ to reflect the mechanical behavior of its individual girder. Each prefabricated girder is connected laterally by a vertical spring $k_{i (i + 1)}$ , namely, hinge joint stiffness, as a whole. Here, the hinge joint stiffness is used to quantify the articulation of the hinge joint, which can be regarded as the sum of the lateral interactions of the fabricated girder along the longitudinal direction.

Figure 1.

The transverse mechanical model of the assembled beam bridge.

In practice, the prefabricated girder of the assembled beam bridge has the same vertical stiffness, torsional rigidity, flexural rigidity, elastic modulus, beam width, and beam span. Therefore, their subscripts are removed and marked as $K$ , $K^{m}$ , $W$ , and $E$ , respectively. The width and span of each prefabricated girder are also the same, denoted as $b$ and $l$ , respectively. Although the initial state of the hinge joints can be considered approximately the same, the degradation rate of the lateral connection is fast or slow during long-term use. Therefore, from the perspective of long-term monitoring, the stiffness of each joint should be assumed to be unequal, that is

k_{12} \neq k_{23} \neq \dots \neq k_{(n - 1) n}

Consider the vehicle load as a concentrated load $P$ and that it acts on the coordinates (x,y). $P$ is assigned in both longitudinal and transverse directions so that the assembled beam bridge is flexed in the longitudinal and transverse directions, respectively, as shown in Figure 1. The load assigned to the ith beam can be assigned as follows

F_{i} = P \cdot η_{x, i} (x)

(2)

In the formula, $F_{i}$ is the force assigned to the ith beam and $η_{x, i} (x)$ is the lateral influence line of the ith beam. $η_{y, i} (y)$ is the longitudinal influence line of the mid-span bending moment of the ith beam, then there is

M_{i} = P \cdot η_{i} (x, y) = P \cdot η_{x, i} (x) η_{y, i} (y) = F_{i} \cdot η_{y, i} (y)

(3)

Generally, the longitudinal influence line function of the bending moment of each girder is the same, and the following are all written as $η_{y} (y)$ . To denote $M = {M_{i}}^{T}$ and $F = {F_{i}}^{T}$ , then equation (3) can be written in its matrix form

M = F \cdot η_{y} (y)

(4)

The force vector $F$ in the above formula can be related with the external load $P$ by the force law principle

F = P \cdot [I_{1} {(δ_{0} - δ_{1})}^{- 1} Δ_{P} + I_{2}]

(5)

where $δ_{0}$ is the flexibility matrix for hinge joints in the original system, $δ_{0} = λ^{- 1} / K$ ; $δ_{1}$ is the flexibility matrix for hinge joints in the basic system, $δ_{1} = I_{3} / K$ ; and $Δ_{P}$ is the hinge displacement vector of the basic system when $P = 1$ , $Δ_{P} = I_{4} / K$ .

$I_{1}$ is the constant location matrix in the $n \times (n - 1)$ dimension, $I_{1} = (a_{ij})$ , $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, (n - 1)$ . When $i = j$ , $a_{ij} = - 1$ , and when $j = i - 1$ , $a_{ij} = 1$ ; in other cases, $a_{ij} = 0$ .

$I_{2}$ is an $n \times 1$ lateral location matrix of external load. When the load acts on the $i th$ girder, the value is equal to 1 in the $i th$ element, and the rest are 0, that is, $I_{2} = [\begin{matrix} 0 & \dots & 1 & \dots & 0 \end{matrix}]^{T}$ .

$λ$ is a matrix of diagonal elements with relative stiffness of hinge joints, $λ = diag (λ_{i})$ , in which the relative stiffness $λ_{i}$ is defined as the ratio of the $i th$ hinge joint’s stiffness to the vertical stiffness of the $i th$ prefabricated girder, that is, $λ_{i} = k_{i (i + 1)} / K$ .

$I_{3}$ is an $(n - 1) \times (n - 1) - dimensional$ matrix, $I_{3} = (b_{ij})$ , $i = 1, 2, \dots, n - 1$ and $j = 1, 2, \dots, n - 1$ . When $i = j$ , $b_{ij} = - (2 + 2 ζ)$ , and when $j = i \pm 1$ , $b_{ij} = 1 - ζ$ ; in other cases, $b_{ij} = 0$ . Here, $ζ$ is the ratio of torsional deformation and vertical deformation of the girder

ζ = \frac{K b^{2}}{4 K^{m}}

$I_{4}$ denotes the influence vector of the lateral position of the external load (acting on the $i th$ girder) to each hinge joint, with its length $n - 1$ . When its element value is other than 0, it means that there is an effect, and if it is 0 means no effect

\begin{matrix} I_{4} = & [0, \dots, 0, - {1 + 2 ζ \cdot [(i - 0.5) - \frac{x}{b}]}, \\ 1 - 2 ζ \cdot [(i - 0.5) - \frac{x}{b}], 0, \dots, 0]^{T} \end{matrix}

Denote $ε = {ε_{i}}^{T}$ , where $ε_{i}$ is the longitudinal strain at the midpoint of the beam bottom of the $i th$ girder in mid-span cross section where the strain sensors are installed. Then the analytical expression of the strain and external load at the bottom of each girder can be given by

ε = ε_{0} \cdot [I_{1} {(λ^{- 1} - I_{3})}^{- 1} I_{4} + I_{2}]

(6)

where $ε_{0}$ is a scalar, which denotes the strain of the girder at the monitoring section when the external loads $P$ are taken fully by a single beam (still acting at the location $y$ ), which can be expressed as follows

ε_{0} = \frac{P η_{y} (y)}{EW}

Equation (6) can be further written using the following expression

ε = B ε_{P}

(7)

where $B$ is an $n \times (2 n - 1) - dimensional$ constant matrix, which is independent of the external load and reflects the parameters of the intrinsic properties of the assembled beam bridge

B = [B_{1}; B_{2}; \dots; B_{n}] = [\begin{matrix} I_{1} {(λ^{- 1} - I_{3})}^{- 1} & I_{n} \end{matrix}]

In this formula, $I_{n}$ is an $n - dimensional$ unit matrix and $ε_{P}$ is a column vector with its length being $2 n - 1$ , $ε_{P} = {I_{4}; I_{2}} ε_{0}$ , which reflects the strain response of each girder under the external load.

Equation (7) is an expression at a time of measurement. When measuring m times continuously, $ε$ is then augmented as an $n \times m - dimensional$ measurement matrix, still identified as $ε$ ; each element $ε_{i}$ in $ε$ is then augmented as a vector of time series, designated as $ε_{i} = {ε_{i 1}, ε_{i 2}, \dots, ε_{im}}$ , which is a $1 \times m$ strain vector measured form the $i th$ girder. Then, it can be written as $ε = {ε_{1}; ε_{2}; \dots; ε_{n}}$ . Correspondingly, $ε_{P}$ in the right-hand side of equation (7) has also been augmented to a $(2 n - 1) \times m - dimensional$ matrix, still identified as $ε_{P}$ . Equation (7) can be rewritten in the following form

ε_{i} = B_{i} ε_{P}

(8)

Substituting equation (8) into equation (1), we obtain the analytical expression of the indicator under traffic load as follows

ρ_{ij} = \frac{Cov (ε_{i}, ε_{j})}{\sqrt{D (ε_{i}) \cdot D (ε_{j})}} = \frac{B_{i} Γ_{P} B_{j}^{T}}{\sqrt{B_{i} Γ_{P} B_{i}^{T} B_{j} Γ_{P} B_{j}^{T}}}

(9)

where $Γ_{P} = E (ε_{P} ε_{P}^{T}) - E (ε_{P}) E (ε_{P}^{T})$ , which is a parameter that reflects the statistical characteristics of the load–strain effect of the traffic flow and is determined entirely by the external load.

Characterization of indicators

Equation (9) shows that the magnitude of the correlation coefficient of the beam bottom strain of the prefabricated girders is related to the structural characteristic parameters $B$ and the statistical parameters of external load effects $Γ_{P}$ .

Generally speaking, in the long term, the statistical model of traffic flow load on the road surface or bridge surface in the traffic network is stable and constant. Therefore, the statistical characteristic parameters of the load–strain effect of the traffic flow $Γ_{P}$ are also basically unchanged, which means that the indicator $ρ_{ij}$ has long-term statistical stability and will not be changed by variations in short-term external loads. In the literature (Wen et al., 2017), it has already been proved through numerical simulation that as long as the time is long enough (48 h in this case), under any arbitrary type of traffic flow load model, the indicator $ρ_{ij}$ does statistically converge to a specified value. This value is independent of the size and position of any single moving vehicle on the deck, but is related to the statistically stable model of traffic load on the deck.

On the other hand, from the abovementioned derivation, it can be seen that the ratio of torsional deformation and vertical deformation of the girder $ζ$ and the relative stiffness of the hinge joint $λ$ are two factors that affect the structural characteristic parameters $B$ . As mentioned earlier, during the life cycle of the entire assembled beam bridge, the hinge joints are weak parts, not only because the on-site construction quality is not easy to control and cause initial damage, but also it is easy to have performance degradation during service. Compared with the prefabricated girder itself, the hinge joint is more prone to damage and is a controlling factor in the degradation of the structural characteristics of the fabricated beam bridge. In other words, during the service period, $ζ$ remains basically the same and $λ$ is easy to reduce.

In summary, as a matter of fact, the relative stiffness of the hinge joint $λ$ is the only reason that may cause the index $ρ_{ij}$ change. This means that $ρ_{ij}$ has the ability to characterize the lateral cooperative performance of prefabricated girders of assembled beam bridges, as demonstrated in the simulation case below.

The effect of hinge joint stiffness on correlative coefficient index

In Wen et al. (2017), we obtained the simulation data of the longitudinal strain at the beam bottom of the cross-section of a mid-span cross-section under a random traffic load simulation model of a simply supported assembled beam bridge with nine prefabricated girders. All the indexes $ρ_{ij}$ are calculated according equation (1), and the statistical convergence is proved by examining the change of the index over time under various random traffic load model conditions. Based on this, this article further investigates the change of the statistical stability value of the indicator when the hinge joint stiffness changes. The parameters of the bridge model and the parameters of the traffic flow load model imposed on it are used in the literature (Wen et al., 2017) and will not be repeated here.

In the simulation calculation in this article, the random traffic flow status is updated every 0.1 s, and the strain effect of each piece of beam is calculated. For a certain length of time, a certain length of strain time series sample is obtained and the corresponding correlation coefficient value $ρ_{ij}$ can be calculated. These values should be verified to be statistically stable before being used. The change rule of the index is investigated in three case studies: case 1 is to change the relative stiffness of the joint as a whole, case 2 is to change the relative stiffness of the single hinge joint, and case 3 is to change the relative stiffness of the hinge joint in a single lane.

Influence of the overall variation of hinge stiffness

First, when the relative stiffnesses of all the eight joints are equal and the changes are in accordance with the monotonically increasing law, the variation of strain correlation coefficient between two adjacent prefabricated girders of each hinge joint is investigated. At this time, the relative stiffness of each hinge joint is collectively denoted as $λ$ , its value ranges from 0.1 to 1.0, and in each stage it increases by 0.1. In the course of the study, except for the joint stiffness, other parameters of the assembled beam bridge remain unchanged. After determining the relative stiffness of the hinge joints at each stage, we calculate the strain correlation coefficients corresponding to the eight hinges $ρ_{12}$ , $ρ_{23}$ , …, $ρ_{89}$ , as shown in Figure 2.

Figure 2.

Influence of the overall variation of the hinge stiffness.

As shown in Figure 2, as the relative stiffness of the hinge joint becomes larger, the correlation coefficient gradually becomes larger. This rule is also consistent with the effect of the variation of hinge joint stiffness of the assembled beam bridge on the lateral cooperative working performance: when the hinge joint stiffness in the actual assembled beam bridge becomes smaller, the lateral connections between the adjacent girders will be weakened. Even in severe cases, hinge joints are vacated, there is no connection between the girders, and lateral cooperative working does not occur. As a result, single-beam bearing phenomenon and single-beam damage will occur. At the same time, due to the symmetry in the transverse direction of the structure, the rule of correlation coefficients corresponding to four pairs of symmetrical positions, $ρ_{12}$ and $ρ_{89}$ , $ρ_{23}$ and $ρ_{78}$ , $ρ_{34}$ and $ρ_{67}$ , $ρ_{45}$ and $ρ_{56}$ , conforms to the same law practically, which is also consistent with the lateral deformation law of the assembled beam bridge.

Influence of variation of the single hinge stiffness

During the actual use of prefabricated girder bridges, the probability of vehicles traveling in the middle lane is greater than that of both sides of the lanes, and the locations of damage on hinge joints are also unevenly distributed. Some individual hinge joints will have priority in damage and destruction. Therefore, it is more important to study the influence of the change in the stiffness of a single hinge joint on the lateral collaborative working performance. Figure 3 shows the curve of the strain correlation coefficient between two adjacent prefabricated girders of each hinge joint when the first to the fourth hinge joints are increased from 0.1 to 1. The rest of the hinge joint stiffness is set to be 0.5 and the other parameters of the assembled beam bridge are maintained unchanged.

Figure 3.

Influence of variation of the single hinge stiffness: (a) Change of strain correlation coefficient when stiffness of the 1st hinge joint increase, (b) Change of strain correlation coefficient when stiffness of the 2nd hinge joint increase, (c) Change of strain correlation coefficient when stiffness of the 3rd hinge joint increase, and (d) Change of strain correlation coefficient when stiffness of the 4th hinge joint increase.

From Figure 3, it can be seen that from the relative stiffness of hinge 1 to the relative stiffness of hinge 4, the corresponding correlation coefficient increases from a small value to a large value, and the magnitude of change becomes larger. The correlation coefficient of the other hinges remains unchanged. This is consistent with the effect of changes in the stiffness of a single hinge joint of an actual assembled beam bridge on lateral collaborative working performance. During the actual use of the assembled beam bridge, when a single hinge joint is damaged, the connection between the adjacent two girders weakens, that is, the correlation decreases, which is reflected in the decrease of the strain correlation coefficient. The phenomena such as loss of hinge joints and single-beam stressing will occur when the damage continues. It will eventually make the single girder bear the load alone and lose its lateral connection with the adjacent girders finally.

Influence of variation of the hinge joint stiffness in a single lane

Many of the actual bridge damage surveys have found that during the actual use of prefabricated girder bridges there is a clear distinction between hinge failures in different lanes. This is due to the difference in density and load of traffic flow loads in each lane. It is necessary to study the influence of changes in hinge stiffness on the correlation coefficient in a single lane in the lane. Similarly, take lanes 1 and 3 for example, the corresponding hinge joints include $ρ_{12}$ , $ρ_{23}$ , $ρ_{34}$ and $ρ_{67}$ , $ρ_{78}$ , $ρ_{89}$ . Figure 4(a) and (b), respectively, shows the curve of the strain correlation coefficient of the two adjacent prefabricated girders of each hinge joint when the relative stiffness of each hinge joint in lanes 1 and 3 increases from 0.1 to 1, and the rest of the hinge joint stiffnesses are set to be 0.5, other parameters of the assembled beam bridge remain unchanged.

Figure 4.

Influence of variation of the hinge joint stiffness in a single lane: (a) Change of strain correlation coefficient when stiffness of the hinge joints in lane 1 increase, and (b) Change of strain correlation coefficient when stiffness of the hinge joints in lane 3 increase.

Let $λ_{lane 1}$ and $λ_{lane 3}$ be the relative stiffness of hinge joints in lanes 1 and 3, respectively. As shown in Figure 4, when the relative stiffness of hinge joints in lanes 1 and 3 becomes larger, the corresponding correlation coefficient also becomes larger, while the other correlation coefficients remain almost unchanged. $ρ_{34}$ and $ρ_{67}$ are the boundaries between the two lanes and their adjacent lanes, respectively. Both of them are smaller than the corresponding coefficients of other hinges in the same lane. This shows that when the vehicle load acts on a single lane, the hinge joints in the lane are more likely to be damaged and destroyed, which is consistent with the phenomenon that the cracking rules of hinge joints in different lanes are different.

Real-bridge lateral cooperative performance evaluation based on monitoring information

In order to further explore the ability of the indicators to characterize the laterally cooperative performance of the actual fabricated girder bridge, a study on a Hougangtang bridge with a service life of 16 years is carried out in this study. The bridge is located on the main line of a highway around the city in the south of Shanghai. The superstructure consists of 12 two-hole prefabricated hollow slabs. The bridge is 12 m wide and 22 m long. Every four spans are connected to form a continuous beam system by construction measures, which is known as a simply supported continuous system. The cross section of the pier can withstand the negative bending moment caused by the second-stage dead load and traffic flow load. Through field inspections, it was found that the bridge has a typical damage of an assembled beam bridge, which is mainly manifested in the leakage of the hinge joints and longitudinal cracking of the bridge deck, as shown in Figure 5(a). A fiber Bragg grating (FBG) strain monitoring system was installed in the mid-span of the bridge to collect the strain data continuously without interrupting the bridge traffic (Figure 5(b)). Based on this, the lateral collaborative working performance of the bridge was studied.

Figure 5.

Image of the technology status and monitoring system of Hougangtang bridge: (a) Location and disease of the bridge, and (b) FBG monitoring system of the bridge.

In order to measure the longitudinal strain of each girder, an FBG strain sensor with a temperature self-compensation function is installed at the bottom of each prefabricated slab of the second span’s mid-span section. The measurement system consists of 12 FBG strain sensors and 3 FBG temperature sensors, as shown in Figure 5(b). Dynamic monitoring is performed at a frequency of 50 Hz for a total of 72 h. Figure 6 shows the raw strain data obtained by 12 sensors over a period of time and the strain data after deducting noise and temperature trends.

Figure 6.

Strain monitoring data of each channel (23 November 2016).

The fitting correlation coefficient of the original strain data

Obtaining the original strain data of the Hougangtang Bridge, without any treatment, the fitting linear relationships between the strain data of two adjacent girders are analyzed, as shown in Figure 7. The correlation between two adjacent girders can be reflected through the linear fitting correlation coefficient of the original data, which can be used to determine the health status of the hinge joint between two adjacent girders.

Figure 7.

Linear correlation between raw strain monitoring data between two adjacent girders.

From the above figure, it can be seen that the strain shows a very good linear relationship between most of the adjacent two beams, the linearity is very good, and all are close to 1, such as the 1st and 2nd girders, the 9th and 10th girders, the 10th and 11th girders, as well as the 11th and 12th girders, whereas the strain linearity between the 6th and 7th girders, the 7th and 8th girders, and the 8th and 9th girders is relatively low, with their values being 0.5, 0.5, and 0.2, respectively. Based on these facts, it can be preliminarily determined that the hinge joints between these beams are abnormal.

Lateral variation of strain correlation coefficient of prefabricated girders

Based on the original strain data, the effect of noise and temperature was removed and the strain effect monitoring data under traffic load were obtained. Based on these data, the variation law of the strain correlation coefficient between a piece of beam and other pieces of beam can be analyzed to determine the lateral collaborative state of the assembled beam bridge. Figure 8 shows the lateral variation of the correlation coefficients when the 2nd and 3rd girders are referenced.

Figure 8.

Lateral variation of strain correlation coefficient when (a) the 2nd girder is referenced and (b) the 3rd girder is referenced.

According to the theoretical analysis, in an assembled beam bridge, the correlation between a certain girder and other girders is related to their distance. The farther the distance between the girders is, the lower the correlation coefficient is. As shown in Figure 8, the correlation coefficients between the 2nd and 3rd girders and the rest of the girders basically conform to this feature. The measured data points are approximately in line with the prediction trend line, but there is a sudden change in the 7th and 8th beams, and in the 8th at the minimum position of the slats, they all significantly deviated from the forecast trend line. In addition, the correlation coefficient between the 2nd and 8th girders is 0.534; the correlation coefficient between the 3rd and 8th girders is 0.396, and the abrupt change is more severe, because the third girder is closer away from the 8th girder. According to the other girders, the strain correlation coefficient shows the same change along the lateral direction, and the strain correlation coefficient shows abrupt changes at the 7th and 8th girders. This shows that the adjacent hinge joints of the 7th and 8th girders have been damaged, resulting in the reduction of the lateral connection stiffness of the bridge at this point and the weaker cooperative working ability.

Similar conclusions can also be obtained by analyzing the correlation coefficient between the two girders. On the basis of the above analysis, the correlation coefficient between the strain data of any two beams in the 12 beams of the Hougangtang Bridge is further obtained and is shown in Figure 9 in the form of a cloud map. As can be seen from this figure, the cloud diagrams composed of the correlation coefficients are clearly divided into the upper left, lower left, upper right, and lower right areas. Among them, the colors of the lower left and upper right areas are light, indicating that the correlation coefficient of each girder in the area is large and the hinges are good; the left upper and lower right areas are darker, indicating that the correlation coefficient of each girder in the area is small, the hinge joints are in poor condition, and the connection stiffness is degraded.

Figure 9.

Cloud maps of the correlation coefficients.

In addition, there is a clear line of demarcation between the 6th and 7th beams, which separates the dark areas from the light areas. The color in the light-colored area does not change much, but the color fluctuation in the dark-colored area changes greatly. There are obvious color changes between the 6th and 7th girders, the 7th and 8th girders, and the 8th and 9th girders. The deepest color is located at the 8th beam. This further illustrates that possible hinge breaks occur between these girders.

Validation by visual survey

In the previous section, the evidences, including the linear fitting correlation coefficient based on the original strain data of adjacent girders, the strain correlation coefficient between a piece of girder and other pieces of the post-processed data, and the strain correlation coefficient between any two girders, show that the joints between the 6th and 7th girders, the 7th and 8th girders, and the 8th and 9th girders of the Hougangtang Bridge have been damaged. Whether this conclusion is reliable or not depends on the results of on-site field surveys.

Figure 10 shows a site survey photograph of the beam bottom of the bridge. As can be seen from the figure, there are multiple water seepage phenomena between the 6th and 7th beams, the 7th and 8th beams, and the 8th and 9th beams; at the bottom of the beam, the 7th and 8th girders have the most serious water seepage. They have leakage along the full span and extend to the bent cap. Notice that at the end of the beam the most serious seepage situations occur at the hinge joint between the 7th and 8th girders, the leakage is along the whole span, and it has been extended to the cap. Leakage is the external manifestation of the destruction of the hinge joints. Obviously, the hinge joints between the 6th and 7th beams, the 7th and 8th beams, and the 8th and 9th beams have been destroyed to varying degrees. The strain data analysis results are in good agreement with the actual bridge observations. This verifies the conclusions of this article based on the strain monitoring and strain correlation coefficient indicators, and also shows that the strain correlation coefficient proposed by Wen et al. (2017) has a good ability to characterize the lateral cooperating performance of an assembled beam bridge.

Figure 10.

Damages of Hougangtang bridge.

Conclusion

Among the rapid industrialized bridge construction technologies, assembled beam bridges are the most mature structural types. Although the factory-made bridge girder and plate members have very good quality assurance, the high quality of this component level does not necessarily translate into the high quality of the entire bridge structure. The hinge joints are the key for the cooperative force between the prefabricated girders or the other parts. Their construction quality and performance state during the service period are the key to the overall cooperative performance of the structure.

Because the structure of hinge joints tends to be degraded and the force transmission function is easily lost in service, this article proposes a method to evaluate the capacity of laterally cooperating work of assembled beam bridges by means of strain monitoring. The proposed method is an easy-to-implement solution to the problem without interruption of traffic conditions. The proposed strain correlation coefficient has clear physical meaning and is not affected by short-term external loads. Theoretically, it has a good monotonically increasing mapping relationship with hinge joint stiffness, which can be used to characterize the joint state of hinge joints and the performance of the entire bridge.

Numerical simulation analysis and real bridge monitoring data analysis results prove that this index has a good ability to characterize the function of hinge joint degradation and damage and can successfully identify the location and degree of hinge joint damage. It can be used as a core monitoring model to serve the safety and health monitoring systems of such bridges during the service period.

Footnotes

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: This work was supported by the National Key R&D Program of China (2017YFF0205605), Shanghai Urban Construction Design Research Institute Project “Bridge Safe Operation Big Data Acquisition Technology and Structure Monitoring System Research,” and the Ministry of Transport Construction Science and Technology Project “Medium-Small Span Bridge Structure Network Level Safety Monitoring and Evaluation.”

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