Simulation and Experimental Study on Bridge–Vehicle Impact Coupling Effect under Pavement Local Deterioration

Abstract

With the rapid development of China’s transportation network, the demand for bridge construction is increasing, the traffic volume is increasing yearly, and the average vehicle speed and the frequency of overloaded vehicles crossing bridges are soaring. When a vehicle passes over a highway bridge, it can easily form a coupling vibration between the vehicle and bridge due to the excitation of the expansion joint, the unevenness of the bridge deck, and the existing coating-hole. The impact effect is significant, which seriously affects the operation safety of both the vehicle and bridge, seriously damaging the service life of the bridge. Due to the influence of construction technology, it is common for the vibration to meet transverse and longitudinal expansion joints of a prefabricated girder bridge, where an aging bridge deck frequently results in bulges and potholes in asphalt pavement. The bridge vibration amplification effect under the dynamic load of heavy, high-speed vehicles is significant, and research about the large impact coefficient of bridges with local pavement deterioration is urgently needed. This study used SIMULINK simulation software and involved conducting several bridge model tests. Dynamic simulation analyses and running vehicle tests on scaled and real bridge models were carried out to study the coupling vibration response of bridge decks in the presence of different pothole sizes. The results show that the impact effect of low-speed vehicles passing through a larger-sized pothole is relatively significant, and the impact coefficient can be amplified to 214% of the original value under good road surfaces in extreme cases. The vehicle–bridge coupling impact effect of potholes is similar to bulges. This relevant work could provide suggestions for the operational performance evaluation and maintenance of bridges with local pavement deterioration.

1. Introduction

Bridges are essential parts of urban transportation, and the need for their serviceability and maintenance is highly recognized by local governments. However, due to the existence of expansion joints as well as road irregularities, vehicles, especially overloaded ones, always impose dynamic impact onto bridge structures during their operation, causing the bridge–vehicle impact coupling effect, which is largely represented by the impact coefficient.

The impact coefficient in real bridges varies a lot and is random in most cases [1]. Depending on the type of vehicle [2], an impact coefficient analysis can be conducted with the structural form of the bridge considered [3,4,5]. The ANSYS software package can be applied to establish numerical models and simulate bridge–vehicle coupling effects [6], where the impact coefficient is more significant with the growing vehicle speed and the increasing unevenness of the irregularities at the bridge deck [7,8]. In contrast with the regular unevenness at the road surface, uncertainties [9] like potholes and bulges caused by repeated abrasion and temperature softening effects are also common in the asphalt layer, and the resultant pounding between overloaded vehicles and prominent obstacles separates the contact point [10] and deteriorates the service life of the bridge [11].

Apparently, existing potholes and bulges can significantly increase the impact coefficient from bridge–vehicle coupling effects [12], and a similar finding was also reached from the results of scaled running vehicle testing, where different-sized bumps were installed [7]. Apart from the size of the potholes and bulges, the number of these obstacles also matters, and an amplification factor considering a different arrangement was put forward accordingly [13], indicating that bridges are more likely to be impaired by multiple or periodic potholes or bulges.

Moving vehicles [14,15,16] and advanced algorithms [17,18,19,20] are frequently used to identify the structural condition of bridges. The pounding problem is frequently discussed in rigid-body dynamics [21,22], where the geometry [23] and sliding friction [24] can also affect the interaction between the rigid deck and moving vehicles. Overloaded vehicles are often inevitable, and there are occasions when potholes and bulges are not repaired in time. It is important that proper strategies are implemented to alleviate the drastic effects of vehicle pounding [25].

General impact coefficient analysis focuses more on the overall irregularity at the bridge deck surface, and deep learning methods and properly trained machine learning methods can be used to solve complicated parametric problems [26,27,28]. Similar types of advanced algorithms successfully applied in bridge structural health monitoring [29], fatigue detection [30], and composite material design [31] can also be introduced to better solve this complicated coupling problem in the future. Until recently, more and more bridges have suffered from pothole and bulge problems, and the induced impact problem is much more severe than common bridge–vehicle coupling effects.

In this paper, the exaggerated dynamic amplification phenomena in bridges, which is caused by the impact of vehicles passing over local pavement deterioration, is discovered through systematic analyses with numerical and experimental methods. The severe deterioration of the bridge deck is considered, and the corresponding impact and pounding effect are analyzed using running vehicle experiments through a scaled bridge model. Dynamic simulations were additionally carried out to study the coupling vibration response of bridge decks under different pothole-size conditions. The results indicate a counter-intuitive result, showing that low-speed passing vehicles can induce a larger impact effect with respect to large-size pothole scenarios, and the impact coefficient can be amplified to 214% of the original value under conventional pavement scenarios. This relevant work can provide suggestions for the operational performance evaluation and maintenance of bridges with local pavement deterioration.

2. Numerical Simulation of Impact Coefficient under Deterioration of Bridge Deck Driving Condition

2.1. Construction of Vehicle–Bridge Coupling Dynamics Simulation Model

In order to explore the influence of bridge deck deterioration on bridge traffic risk, a SIMULINK (2020a) simulation model was established to simulate the vehicle–bridge coupling vibration response during a vehicle passing through a bridge structure. The simulation model is shown in Figure 1.

The modeling techniques of contact connection in SIMULINK are fundamental, and the interaction between vehicle and bridge sub-systems follows the basic formulation of motions, as expressed in Equation (1):

$$\left[\begin{array}{cc}{M}_v& \\ & M_B\end{array}\right]\left\{\begin{array}{c}{\ddot{x}}_v\\ {\ddot{q}}_B\end{array}\right\}+\left[\begin{array}{cc}{C}_v& C_{vB}\\ C_{Bv}& C_B+C_B^v\end{array}\right]\left\{\begin{array}{c}{\dot{x}}_v\\ {\dot{q}}_B\end{array}\right\}+\left[\begin{array}{cc}{K}_v& K_{vB}\\ K_{Bv}& K_B+K_B^v\end{array}\right]\left\{\begin{array}{c}{x}_v\\ q_B\end{array}\right\}=\left\{\begin{array}{c}{F}_v^r\\ F_B^{rG}\end{array}\right\}$$

(1)

where:

$X_v,{\dot{X}}_v,{\dot{\ddot{X}}}_v$	denote the displacement, velocity, and acceleration of the vehicle;
$q_B,{\dot{q}}_B,{\ddot{q}}_B$	denote the modal displacement, velocity, and acceleration of the bridge;
$M_v,C_v,K_v$	denote the mass, damping matrix, and stiffness matrix of the vehicle;
$M_B,C_B,K_B$	denote the modal mass, damping matrix, and stiffness matrix of the bridge;
$C_{vB},C_{Bv}$	denote the augmented damping matrix of the bridge considering the vehicle–bridge coupling effect;
$K_{vB},K_{Bv}$	denote the augmented stiffness matrix of the bridge considering the vehicle–bridge coupling effect;
$C_B^v,K_B^v$	denote the augmented damping and stiffness matrix of the bridge considering the vehicle-loading effect;
$F_v^r,F_B^{rG}$	denotes the interaction force imposed onto the vehicle and the bridge;

There are four sub-systems in the simulation of the vehicle-driving process:

• The bridge deck local deterioration sub-system. It is used to input local deterioration information of the bridge deck, such as the shape and the location parameters of the bridge deck pothole, and to represent specific potholes.
• The overall bridge deck unevenness sub-system. It is used to input the parameters of the deck unevenness, to represent a specific unevenness of the bridge deck, to combine with the bridge deck local deterioration sub-system, to form the bridge deck contour elevation, and to provide a displacement excitation input.
• The vehicle sub-system. It is used to input the vehicle physical parameter information and the bridge displacement excitation of the HC vehicle model, as well as to output the tire contact force.
• The bridge sub-system. It is used to input the physical parameter information of the bridge and the tire contact force and to output the modal displacement response of each mode of the bridge through the modal-superposition method.

The separated literation procedure and explicit time integration were adopted to output the time–history of the dynamic deflection in the bridge. In each literation step, the bridge sub-system is firstly assumed to be rigid, and the motion of the vehicle is calculated based on the combined statuses from the bridge and the local unevenness; the motion of the bridge is subsequently derived, and the step moves forward as convergence is reached. The displacement of the bridge is recorded in each step, and the time–history can be output accordingly. However, the time interval of the step should be carefully reduced to avoid accumulative error embedded in this method.

In the vehicle sub-system, the two-axle overloaded vehicle is mainly considered, and the parameters of the two-axle overloaded vehicle are transformed into the HC vehicle model. The physical parameters of the vehicle are shown in

Table 1. List of HC vehicle model parameters for overloaded vehicles.

Parameter Name	Symbol	Unit	Numerical Value
Body mass	$m_b$	$\mathrm{kg}$	11,800
Body pitch moment of inertia	$I_x$	$\mathrm{kg}\cdot {\mathrm{m}}^2$	21,670
Front axle mass	$m_f$	$\mathrm{kg}$	2200
Rear axle mass	$m_r$	$\mathrm{kg}$	2000
Front spring stiffness	$k_f$	$\mathrm{N}/\mathrm{m}$	950,000
Rear spring stiffness	$k_r$	$\mathrm{N}/\mathrm{m}$	3,640,000
Front spring damping	$c_f$	$\mathrm{N}\cdot \mathrm{s}/\mathrm{m}$	15,880
Rear spring damping	$c_r$	$\mathrm{N}\cdot \mathrm{s}/\mathrm{m}$	4980
Front tire stiffness	$k_{tf}$	$\mathrm{N}/\mathrm{m}$	2,780,000
Rear tire stiffness	$k_{tr}$	$\mathrm{N}/\mathrm{m}$	2,340,000
Distance from front axle to body center of mass	$L_f$	$\mathrm{m}$	3.125
Distance from rear axle to body center of mass	$L_r$	$\mathrm{m}$	1.875

, and the total weight of the vehicle is about 16 t.

In the bridge sub-system, a typical simple supported hollow slab beam bridge on the Third Ring road in Wuhan was taken as the research object, with a span of 25 m and 14 transverse beams. The design load level is city-A, and the pedestrian load level is 4.02 kN/m². The model parameters of the bridge sub-system are shown in

Table 2. List of model parameters of the hollow slab beam bridge.

Parameter Name	Span $\mathbf{m}$	$\mathbf{Flexural}\mathbf{Rigidity}\mathbf{of}\mathbf{Section}\mathbf{N}\cdot {\mathbf{m}}^2$	$\mathbf{Unit}\mathbf{Mass}\mathbf{of}\mathbf{Section}\mathbf{kg}/\mathbf{m}$
Numerical value	25	4.9794 × 1010	18,450.36

.

2.2. The Impact of Overall Deterioration of Bridge Deck on Impact Coefficient

The deterioration of the driving condition on the bridge deck is reflected as the bridge deck becomes uneven on the whole, resulting in increased vehicle vibrations while traveling on the bridge deck.

The impact coefficient is considered when vehicles pass over different levels of pavement roughness in bridge decks at different running speeds, where events A, B, and C denote the relative roughness of pavement in descending order [32]. The numerical simulation results are shown in Figure 2.

In the figure below, it can be seen that as the bridge deck becomes rougher, the overall impact coefficient of the bridge increases while the same vehicle crosses the bridge, and the influence becomes more stabilized as the running speed exceeds 9 m/s. The greater the impact coefficient, the more unfavorable it is to the safety of the bridge structure; that is, the deterioration of the bridge deck driving condition will significantly increase the safety risk of the bridge structure.

2.3. The Impact of Local Deterioration of Bridge Deck on Impact Coefficient

The deterioration of the bridge deck also covers the local pavement defects such as potholes and bulges, and the vehicle will experience severe impact when passing through these local deteriorations. To find a representative model to describe the major dynamic impact effect from all kinds of locally deteriorated bridges, the geometric shape is vital. Considering that a vehicle runs over a bridge with the same shape and size at different running speeds, the bridge deck pothole and bulge are set at the middle span, and the depth of the pothole or the height of the bulge is 0.06 m, and the width is 0.6 m. Curved and rectangular potholes and bugles are simulated, and the results are shown in Figure 3.

As shown in the above figure, when the bridge deck potholes and bulges are of the same geometric shape, their influence on the impact coefficient is almost the same, while the curved and rectangular convex bulge or concave pothole share a similar descending trend of impact coefficient as the running speed increases, despite the variation of impact coefficient being noticeable during low-speed conditions. It should be noted that, due to the circular shape of the tires, the contact point between the wheel and the bridge deck is always curved, even if they pass through rectangular potholes or bulges. Although the simulation analysis of the rectangular pothole is carried out, considering the real practicing scenario, the curved pothole is mainly used in the following simulation analyses.

According to the SIMULINK simulation model established in Section 2.1, the roughness of the bridge deck was set to class-A to minimize the general influence, and the curved pothole adopted a typical local deterioration of the bridge deck, as shown in Figure 4.

As shown in the figure above, the parameters describing the bridge deck pothole are as follows:

$LD$: the distance between the bridge deck pothole and the bridge head;

$L$: the width of the bridge deck pothole;

$H$: the depth of the bridge deck pothole.

2.3.1. Impact Analysis of Bridge Deck Pothole Locations

The width of the bridge deck pothole is 0.6 m, the depth of the bridge deck pothole is 0.06 m, and the distance between the bridge deck pothole and the bridge head is set according to

Table 3. List of the distance from the bridge deck pothole to bridge head (bridge span is 25 m).

LD value	3.125	6.25	9.375	12.5	15.625	18.75	21.875
Position description	1/8	2/8	3/8	4/8	5/8	6/8	7/8

.

The statistical results of the impact coefficient of the measuring point when the same vehicle passes through an identical bridge deck pothole at different locations from the bridge head at different speeds are shown in Figure 5.

The following can be seen from the picture above:

• In the curve comparison between the non-deck pothole and the 1/8 span away from the bridge head, it can be seen that the local deterioration of the bridge deck at the bridge head will significantly increase the impact coefficient. A bridge head jump often occurs at the bridge head due to the expansion joint step effect, roadbed settlement, etc., which not only affects driving comfort and driving safety but also significantly amplifies the impact effect of vehicles on the bridge.
• According to the comparison of curves at 1/8 span, 7/8 span, 2/8 span, 6/8 span, 3/8 span, and 5/8 span from the bridge head, it can be seen that the impact coefficient of the bridge deck pothole is greater than that at the bridge tail—that is, the impact of the bridge deck pothole on the safety of the bridge structure is greater on the upper bridge side than on the lower bridge side;
• The impact coefficient reaches its maximum when the bridge deck pothole is at the mid-span location. In addition, there is an obvious low-speed zone, which makes the measured impact coefficient reach its maximum value, and it is not affected by the location of the bridge deck pothole.

2.3.2. Impact Analysis of Bridge Deck Pothole Width

The pothole was set at the mid-span of the model bridge, the depth of the bridge deck pothole was 0.06 m, and the width of the bridge deck pothole was set according to

Table 4. List of bridge deck pothole width settings.

Pothole Type	No Pothole	Small Pothole	Medium Pothole	Large Pothole
L	0 m	0.3 m	0.6 m	1.0 m

.

The statistical results of the impact coefficient of the measuring point when the same vehicle pasesg through the bridge deck with different widths at different driving speeds are shown in Figure 6.

Through analysis of the figure above, the following conclusions can be obtained:

• With the increase in the width of the bridge deck pothole, the velocity interval at which the impact coefficient reaches the maximum value also increases, and the velocity interval is roughly linearly related to the width of the bridge deck pothole. However, the maximum value of the measured impact coefficient hardly changes. Preliminary judgment suggests that it may be related to the huge difference between the frequency of the jumped vehicle and that of the bridge structure.
• The fundamental frequency of the bridge structure is approximately 5.87 Hz based on the known conditions. For a small pothole, the maximum impact coefficient is achieved at the speed of about 2 m/s, and the excitation frequency of the vehicle under and on the bridge deck pothole is about 6.67 Hz. For medium potholes, the maximum impact coefficient is achieved at the speed of about 4 m/s, and the excitation frequency of the vehicle under and on the bridge deck pothole is about 6.67 Hz. For large potholes, the maximum impact coefficient is achieved at the speed of about 6 m/s, and the excitation frequency of the vehicle under and on the bridge deck pothole is about 6 Hz. It can be seen that when the excitation frequency is close to the fundamental frequency of the bridge, it can easily cause bridge resonance, resulting in a significant increase in the impact coefficient.

2.3.3. Impact Analysis of Bridge Deck Pothole Height

The impact coefficient is considered when a vehicle crosses a bridge deck pothole with the same width but a different depth at a fixed speed. The distance between the bridge deck pothole and the bridge head is 7 m. When the width of the bridge deck pothole is 0.6 m, take the speed interval of 4 m/s corresponding to the maximum impact coefficient for that pothole. When the width of the bridge pothole is set to 1.0 m, the vehicle speed interval corresponding to the maximum impact coefficient of the pothole is taken as 6 m/s. The statistical results of the impact coefficient of the bridge pothole with different depths when crossing the bridge are shown in Figure 7.

It can be seen in Figure 7 that when the bridge deck pothole width is fixed, the impact coefficient is proportional to the depth of the bridge deck pothole. The following conclusions can be drawn: when there is a bridge pothole, the ratio of the maximum impact coefficient corresponding to the driving speed and the width of the bridge pothole is close to the fundamental frequency of the bridge structure. The existence of the bridge deck pothole for low-speed vehicles makes it easy to reach the resonance in the bridge structure, and the deeper the bridge pothole is, the larger the maximum impact coefficient will be.

3. Scaling Model Test of Impact Coefficient under Local Deterioration of Bridge Deck Pothole

3.1. Overview of the Test

A scaled-down steel–concrete composite simply supported model bridge is proposed to be established to verify the above simulation test rules, and a scaled-down model test is conducted to investigate bridge impact coefficients under localized deterioration of the bridge deck pothole.

The span of the steel–concrete composite simply supported model bridge is 2 m + 10 m + 2 m, the bridge deck width is 3 m, and the transverse layout is 1 m + 1 m + 1 m. The bottom of the model bridge body consists of four 100 mm × 100 mm × 10,000 mm H-shaped steel, and the upper part of the beam body is 40 mm thick cement mortar with a concrete compression strength of about 30 MPa. The height of the beam is 140 mm. The layout and construction information of the model bridge is shown in Figure 8.

The steel–concrete composite simply supported model bridge is shown in Figure 9.

The vehicle load is applied by a 1/5 RC model car, as shown in Figure 10.

3.2. Working Condition Design

In the model test, potholes resulting from localized deterioration of the bridge deck can be simulated by slotting in the concrete layer of the steel–composite model bridge. The model tests were carried out under the following conditions according to the orthotropic experimental design.

As shown in Figure 11, Figure 12 and Figure 13, there are three lanes involved and the more unfavorable lane #1 and lane #3 were used, and the experimental conditions for the scaled bridge-running vehicle are set as follows:

Working condition 1: When there is no bridge deck pothole, the car drives back and forth on lane #1 and records measurements at points ④ and ③.

Working condition 2: Slot at 1/4 cross-section of lane #1, with a width of 10 cm and a depth of 1 cm, and drive from left to right on lane #1. Measure at points ④ and ③;

Working condition 3: Slot at 1/4 cross-section of lane #1, with a width of 10 cm and a depth of 1 cm, and drive from right to left in lane #1. Measure at points ④ and ③;

Working condition 4: Slot at 2/4 cross-section of lane #3, with a width of 10 cm and a depth of 1 cm, and drive back and forth in lane #3. Measure at points ① and ②;

Working condition 5: Slot at 2/4 cross-section of lane #3, with a width of 20 cm and a depth of 1 cm, and drive back and forth in lane #3. Measure at points ① and ②;

Working condition 6: Slot at 2/4 cross-section of lane #3, with a width of 30 cm and a depth of 1 cm, and drive back and forth in lane #3. Measure at points ① and ②;

Working condition 7: Slot at 2/4 cross-section of lane #3, with a width of 30 cm and a depth of 2 cm, and drive back and forth in lane #3. Measure at points ① and ②;

Working condition 8: Slot at 2/4 cross-section of lane #3, with a width of 30 cm and a depth of 3 cm, and drive back and forth in lane #3. Measure at points ① and ②;

Working condition 9: After repairing the slot opened in working condition 2, a slot is created at the 2/4th cross-section of lane #1, with a width of 30 cm and a height of 2 cm, and the car is running back and forth in lane #1. Measurements at points ④ and ③ are taken.

3.3. Data Acquisition

The dynamic deflection measurement points were arranged under four H-shaped steel beams at the bottom of the mid-span of the model bridge. The dynamic deflection curves were measured using a WBD-type dial indicator and an INV3062V signal acquisition analyzer. The actual arrangement of the measuring points of the sensors is shown in Figure 14.

3.4. Analysis of Test Results

3.4.1. Analysis of Bridge Modal Test Results under Different Working Conditions

The frequencies of each mode of the model bridge measured after each slotting operation are shown in

Table 5. Frequency list of each stage of model bridge under different working conditions.

Serial Number	Description of Working Conditions	Rank 1		Rank 2
		②	③	②	③
1	Working condition 1	2.3467	2.3467	4.4998	4.4998
2	Working condition 2, 3	2.3437	2.3437	4.5189	4.5189
3	Working condition 4	2.3071	2.3071	4.3626	4.3626
4	Working condition 5	2.3261	2.3261	4.5079	4.5079
5	Working condition 6	2.3783	2.3783	4.5897	4.5897
6	Working condition 7	2.3355	2.3355	4.5653	4.5653
7	Working condition 8, 9	2.2975	2.2975	4.5286	4.5286

.

3.4.2. Impact Analysis of Bridge Deck Pothole Locations

The test results of working conditions 1, 2, 3, and 4 were taken for analysis, and the test results are shown in Figure 15. The data points in the figure represent the speed and impact coefficient calculated by the dynamic deflection curve of running vehicle tests, with the horizontal axis indicating the car speed and the vertical axis representing the impact coefficient.

In Figure 15, it can be seen that when the shape and size of the bridge deck potholes are the same, the location of the bridge deck pothole in the longitudinal direction also affects the impact coefficient, and the impact coefficient is the largest when the bridge deck pothole is at the mid-span. As the distance between the pothole and the bridge head becomes further, the measured impact coefficient increases first and then decreases overall. The comparison of Figure 4 in Section 2 is consistent with the conclusion obtained by numerical simulation. However, due to the small number of model test conditions set, all of the data are close to the center of the bridge span.

3.4.3. Impact Analysis of Bridge Deck Pothole Width

Working conditions 1, 4, 5, and 6 are taken here for analysis, and the comparison of test results is shown in Figure 16.

In Figure 16, with the increase in the bridge pothole width, the range of the maximum impact coefficient for the vehicle speed increases. The fundamental frequency of the model bridge is 2.34 Hz, and the second-order frequency is 4.59 Hz. The excitation frequency of the vehicle under and on the bridge pothole is 6 Hz, which is close to the second-order frequency of the model bridge.

A comparison of Figure 5 shows that the model test law and simulation test law are more consistent. There are two differences: first, the excitation frequency of the model test is close to the second-order frequency of the bridge, while the excitation frequency of the simulation test is close to the fundamental frequency of the bridge. Second, the model test of the impact coefficient did not increase with the increase in the width of the bridge deck pothole. The preliminary analysis is related to the coupling effect between the pothole in the longitudinal-direction location and the width of the bridge pothole. In the model test, the longitudinal location of the bridge deck pothole is the mid-span section. In the simulation, the longitudinal location of the bridge deck pothole is a 7/25 span section position, which is not set in the mid-span.

3.4.4. Impact Analysis of Bridge Deck Pothole Height

Taking working conditions 1, 6, 7, and 8 for analysis, the comparison of test results is shown in Figure 17.

In the above figure, it can be obtained that as the width of the bridge deck potholes is fixed, the speed range corresponding to the maximum impact coefficient is relatively fixed. As the depth of the bridge deck potholes increases, the impact coefficient also increases at the same speed, and it is roughly in a linear relationship.

Compared with Figure 6, it can be seen that the model test and the simulation conclusions are consistent in the analysis of the impact coefficient of the depth of the bridge deck pothole.

3.4.5. Analysis of Impact Coefficient of Bridge Deck Potholes and Bridge Deck Bulges

The test results of working conditions 1, 7, and 9 were taken for analysis, considering the influence of the same shape and size of bridge deck potholes and bridge deck bulges on the impact coefficient. The test results are shown in Figure 18.

In the above figure, it can be known that as the shape and size are the same, the influence of the bridge deck potholes and the bridge deck bulges on the impact coefficient is basically the same. Compared with Figure 7, the law of the model test and the numerical simulation are the same. It can be seen that whether it is a bridge deck pothole or a bridge deck bulge, there is essentially a local collision between the vehicle and the bridge. However, it should be noted that bridge deck potholes are not equivalent to the bridge deck bulges under high-speed driving conditions; due to the influence of gravity, the process of the wheel falling from outside the bridge deck pothole into the bottom of the bridge deck pothole is similar to a horizontal parabolic motion, and it is very likely to directly fly over the bridge deck potholes without touching the bottom face. For a bridge deck bulge, the process of the wheel driving from outside the bridge deck bulge onto the bridge deck bulge is always inevitable.

4. Real Bridge Testing

4.1. Test Profile

A real bridge test on a practical bridge of the Third Ring Road in Wuhan was conducted in September 2021. A regular inspection was performed, and cracks were found in the deck pavement on the right main line of the bridge. There were multiple diagonal or longitudinal cracks, with a total length of 16 m, and no evident bridge deck pothole was observed. According to the evaluation criteria for the intact condition of the bridge, the intact condition level of the right side of the main line of the bridge is class-A—intact condition.

One year later, during the daily inspection of this bridge, it was found that cracks, due to inadequate maintenance, continued to deteriorate and develop into obvious bridge deck potholes under the repeated rolling of overloaded vehicles and rainwater erosion on the original bridge deck pavement. After actual measurement, bridge deck potholes at this location were found to be about 0.3 m in length, about 0.2 m in width, and about 0.03 m in depth. They were located near the right wheel track line of the second lane on the right main line, about 7 m away from the end of the bridge side beam of the vehicle.

To investigate the impact of the bridge deck potholes at this location on the impact effect of the bridge, a non-contact measurement method of a photoelectric deflection instrument and a strong light source target were used to monitor the dynamic deflection response of this bridge under the operating environment. The dynamic deflection measuring point was set at the mid-span of the #14 hollow slab beam on the right main line, as shown in Figure 19.

4.2. Data Acquisition and Result Analysis

We used a motion camera to capture the driving events of social vehicles passing over the bridge deck bulges and matched them with the dynamic deflection monitoring data. Four driving events of overloaded vehicles driving in the second lane on the right main line and the wheels passing over the bridge deck pothole were screened out, which were recorded as driving events A, B, C, and D [32], respectively. The dynamic deflection time–history curves corresponding to each driving event are shown as the “solid line” in Figure 20, and the filtered time–history curves are shown as the “dotted line” in Figure 20.

The passing time, maximum dynamic deflection amplitude, and maximum static deflection of each driving event were extracted, respectively, from Figure 20, and the driving speed and impact coefficient were calculated, as shown in

Table 6. Calculation results table of deflection characteristic values.

Driving Event	Bridge Crossing Time s	Driving Speed m/s	Maximum Dynamic Deflection Amplitude mm	Maximum Static Deflection mm	Impact Coefficient
A	2.43	10.29	0.357	0.182	0.962
B	2.47	10.12	0.250	0.145	0.724
C	2.95	8.47	0.266	0.153	0.739
D	2.80	8.93	0.521	0.276	0.888

.

It can be known from the above table that when overloaded vehicles pass through the bridge deck potholes, the impact effect of the vehicle on the bridge structure significantly increases. The average impact coefficient is 0.828, and the maximum impact coefficient is 0.962, which exceeds the maximum value of 0.45 stipulated in the domestic code “JTG D60-2015 General Specifications for Design of Highway Bridges and Culverts”. This indicates that the bridge deck pothole significantly increases the impact effect of the bridge by 214%.

4.3. Cross-Verification of Practical Bridge Test

Using the same modeling techniques adopted in the aforementioned SIMULINK model in Section 2, parameters regarding the vehicle model, real bridge model, real bridge deck roughness coefficient, and real bridge deck potholes were input in the new SIMULINK model. The driving speed of the running vehicle was set as 10 m/s. The dynamic deflection response at the mid-span of the bridge when the vehicle passes the bridge can be simulated. The time–history curve is shown in Figure 21.

It can be known from Figure 21 that the dynamic deflection time–history curve of the bridge fluctuates greatly when the vehicle passes over the bridge pothole. At this time, the maximum amplitude of dynamic deflection is 0.230 mm, the maximum static deflection calculated is 0.132 mm, and the impact coefficient calculated is 0.745, which is relatively close to the measured result of driving event B under a 10 m/s running speed at about 0.8 in Figure 2 in Section 2.

5. Conclusions

In this paper, based on SIMULINK simulation software (2020a) and a scaled bridge model, the dynamic simulation analysis and running vehicle test were adopted, while numerical simulation and reduced-scale and real bridge experimental analysis were carried out for the coupling vibration response of vehicle and bridge under different sizes of bridge deck pothole conditions. The following conclusions can be drawn:

• Through the vehicle–bridge coupling dynamics simulation model based on SIMULINK, it is found that the overall deterioration of the bridge deck driving condition will increase the overall impact coefficient of the bridge, which significantly enlarges the risk of the bridge structure;
• Through the simulation test, model test, and real bridge test, it is shown that the local deterioration of bridge deck driving condition (the location, width, and depth of bridge deck potholes) has different degrees of influence on the impact coefficient. The impact effect of low-speed vehicles passing through larger-size potholes is relatively significant, and the impact coefficient under good pavement can be amplified to 214% of the original value in deteriorated cases.
• The same-size bridge deck potholes and bulges have similar impact effects on vehicle and bridge coupling. The impact coefficient obtained through measurement and simulation is much larger than the calculated value from code regulations. Therefore, the bridge should be maintained in time based on the physical conditions, such as the location, width, and longitudinal height of potholes and bulges on the bridge deck, so as to reduce the drastic effect of traffic.

The pothole mentioned is ideal and rigid, while overloaded vehicles can induce massive impact force and would probably further deteriorate the local damage on the pavement. More simulations regarding interactions between overloaded vehicles and existing potholes or bugles will be conducted in the future.