Automated Bridgehead Settlement Detection on the Non-Staggered-Step Structures Based on Settlement Point Ratio Model

Abstract

The bridgehead settlement problem continues to be one of the most chronic issues affecting long-term bridge performance. In addition, the magnitude of non-staggered-step settlement across the bridge approach transition has not been quantified. Non-contact measurement is considered an alternative to manual inspection, enabling automated damage evaluation for structural maintenance. This paper proposes an inexpensive automatic system using an inertial navigation sensor and a line scanning camera to evaluate the non-staggered-step bridgehead settlement with acceptable accuracy. By analyzing road longitudinal slope data, driving distance, and pavement images, this paper established a calculation model and algorithm of non-staggered-step bridgehead settlement, in which case, a new calculation index named the settlement point ratio (SPR) was proposed. Moreover, the effect of the vehicular detection system and the distance gradient tested at three speeds were measured. The results illustrate that the system has a good performance in longitudinal slope data with an absolute error of less than 1.5%. In addition, 31 bridges in China, Ningbo city, were selected. Combined with the test data, 50 groups of SPR were output using the established model and algorithm. By validating the system’s output with the standard measurement method, correlation, and regression analysis were carried out in order to verify the SPR model’s reliability. The correlation coefficient is 0.934, and the determination coefficient of the regression model is 0.872, which confirms its capability for accurate data collection and settlement measurement. Therefore, the proposed method is scientific and reasonable for detecting and quantifying non-staggered-step bridgehead settlement, effectively completing the research blank of bridgehead settlement detection.

1. Introduction

Bridges, as a vital constituent of the road network, exert an influence on the vehicles traversing them, thereby impacting traffic safety [1]. The differential settlement between bridge structures and road foundations gives rise to differential height at the bridgehead, where the bridge and the road interface. This phenomenon occurs due to the combined effects of natural factors and traffic loads. When the degree of differential settlement at the bridgehead surpasses a certain threshold, it results in bridgehead bumping occurrences [2]. The vehicle bumps caused by the bridge will directly affect the vehicle’s comfort, indirectly affecting the driver’s ability to control the vehicle. When the speed is fast, the car easily loses control, causing severe traffic crashes [3].

In order to avoid bridgehead bumping, real-time monitoring of bridge settlement is essential. Currently, there are four main methods used for monitoring bridgehead settlement: stagger height [4], road roughness [5,6,7,8,9,10,11], vehicle bumps [12,13,14], and ride comfort [15,16,17].

Due to the uneven settlement of the bridgehead, there will be a height difference between the road and the bridge in the connection area. Liu et al. used elevation measurement tools such as level and electronic total station to directly measure the stagger height and evaluate the settlement of the bridgehead [4]. However, this method can only measure settlement in the form of step settlement, and it has low measurement efficiency. Moreover, it significantly affects the normal operation of traffic during the measurement process.

In 1982, a research team composed of multiple countries and organized by the World Bank conducted a large-scale road roughness experiment in Brazil and introduced the International Roughness Index (IRI) as a measure of road roughness. The International Roughness Index (IRI) is commonly used to assess the smoothness of road surfaces [18]. Methods for measuring road roughness include the walking profiler produced by Australian Road Research Board (ARRB) [5], continuous roughness meters [6], and laser road roughness meters [7]. However, the walking profiler has relatively low efficiency as it requires manual pushing, and continuous roughness meters and laser road roughness meters have relatively low sensitivity to non-staggered-step settlement. Liu et al. proposed a semi-supervised learning method to comprehensively evaluate the IRIs based on multi-vehicle vibration data. Although the errors of the model were significantly affected by the iteration order. The roughness of large-scale road and bridge transition sections can be quickly assessed [8]. With the development of information technology, some scholars have started to use information technology to measure road roughness. Buttlar et al. compared a laser vehicle section meter and a smartphone with a pavement roughness test app. The correlation between the two was good on pavements in good condition but not rough conditions [9]. Janani et al. analyzed the correlation between IRI measured using a smartphone and IRI measured using a roughometer. They also investigated the impact of vehicle speed on the correlation and determined a reliable speed range for estimating road surface roughness using a smartphone [10]. Eriksson et al. developed an in-vehicle sensor-based pavement roughness detection system, which uses signal processing and machine learning-based methods to collect data to achieve model recognition of road anomalies. However, the method is susceptible to the background environment [11].

When vehicles pass over bridgeheads with differential settlement, it can lead to vehicle vibrations and oscillations. Therefore, some scholars evaluate the differential settlement of bridgeheads by studying the vibrations of vehicles. The vibration model of the car-body-seat system was established by Zhi et al. Zhi et al. assessed the differential settlement of roads by measuring the vibration response of the car-body-seat system [12]. Tomonori Nagayama et al. transformed the measured vertical acceleration of the vehicle into the acceleration of the on-spring mass in a standardized quarter car model. This acceleration was subsequently utilized to estimate the road roughness through an approximate calculation [13]. Mohan et al. used sensing elements such as accelerometers, microphones, radios, and GPS that come with smartphones to collect acceleration, vehicle bumps, and other data to assess differential settlement of roads and bridges [14].

The ISO International Vibration Standard [19] establishes a link between vehicle vibration and riding comfort. Some scholars reflect the differential settlement of bridgeheads by testing the physiological signs of drivers and passengers as the vehicle passes over them. Du et al. selected the driver’s heart rate as an indicator to assess the impact of bridgehead bumping on vehicle performance. They observed a significant correlation between variations in the driver’s heart rate and the severity of bridgehead bumping [15]. Zhang et al. utilized the vehicle dynamics simulation software Carsim to conduct simulations and found that bridgehead height differences significantly impact passenger comfort. They observed that when the height difference exceeded 20 mm and the vehicle speed exceeded 100 km/h, the comfort level decreased [16]. Pan et al. found a significant correlation between driver’s heart ratio variation and the severity of bridgehead bumping through investigation and driving experiments. The results of the study showed that the driver’s heart ratio increased by more than ten times/min when the bumping was severe than when driving was stable [17]. These indicators are indirect and do not directly measure the specific settlement of the bridgehead surface. In addition, different people have different sensitivities to bridgehead bumping, so the results obtained from the experiments are closely related to the experimental population, and it is relatively difficult to obtain standard experimental results.

The research on bridgehead bumping is mainly focused on the staggered-step settlement, a step-like settlement at the road and bridge connection. Pavement bumping is added to the Highway Performance Assessment Standards [20]. The standard stipulates the use of section-type equipment to detect pavement bumping. After removing the influence of abnormal values, the extreme difference of pavement elevation within the unit length is calculated with 0.1 m as the sampling interval and 10 m as the statistical unit, and then according to the relevant calculation formula to obtain the pavement bumping index (PBI) [20]. The standard concern is mainly caused by the local pavement bump, depression, and road and bridge abnormal connection of bumping cars, that is, only for the staggered-step platform type bridgehead settlement. The research on the bridgehead bumping caused by the non-staggered-step settlement is still blank, and the scholars and the existing standards only focus on detecting and evaluating the staggered-step settlement.

In summary, current research focuses on staggered-step settlement, while studies on non-staggered-step settlement are still lacking. Non-staggered-step settlement lacks abrupt changes in height, making it less sensitive to detection using roughness measurement devices. Moreover, when vehicles pass over areas with non-staggered-step settlement, the vibration response of the vehicle is less pronounced compared to staggered-step settlement, making it challenging to assess non-staggered-step settlement at bridgeheads based on vibration response alone. Therefore, there is a need to establish a new objective evaluation index and evaluation model specifically for non-staggered-step settlement.

To address the aforementioned issues, this paper proposes a non-staggered bridgehead settlement detection method based on the settlement point ratio. The method utilizes a vehicular system to collect road images, vehicle travel distance, and longitudinal slope data. Subsequently, the bridgehead settlement point ratio is calculated using the proposed settlement point ratio algorithm. The main contributions of this paper are as follows:

(1)

We achieve automatic detection of road longitudinal profile curves using multi-source data. We propose an inexpensive automatic system using an inertial navigation sensor and a line scanning camera to evaluate the differential settlement in bridge approach.

(2)

We introduce a novel bridgehead settlement evaluation indicator, namely SPR.

(3)

We perform detection of non-staggered bridgehead settlements based on the proposed bridgehead settlement evaluation indicator.

The remainder of this paper is organized as follows. Section 2 introduces the types of bridgehead settlement and the detection techniques employed in this study. Section 3 provides a detailed description of the proposed method. Section 4 presents the experiments, discussions, and analysis. Finally, Section 5 provides a summary of this paper.

2. Settlement Types and Detection Technology

2.1. Types of Bridgehead Settlement

Bridgehead settlement is caused by uneven settlement at the junction of the road and bridges. At present, scholars have divided it into gradual type, saddle type, staggered-step type, curve type, exponential type, and broken line type based on linear characteristics [21]. This paper summarizes bridgehead settlement as staggered step type, broken line type, and curve type (Figure 1). The staggered step settlement refers to the step-alike settlement at the bridge-road junction caused by differential settlement of the road and bridge or spalling of pavement materials (Figure 1a,d). The broken-line settlement often occurs at the transition section of the road and bridge to the bridgehead slab, showing a more uniform broken line of longitudinal slope change (Figure 1b,e). The curve settlement refers to the road profile showing a curve characteristic after the bridgehead settlement (Figure 1c,f). The broken line and curve line bridgehead settlement is called the non-staggered-step bridgehead settlement.

In the above three types of bridgehead settlement, the staggered-step bridgehead settlement presents the characteristics of local uplift. With the settlement with a sudden change in the road profile, the pavement bumping content in the standard in China has made regulations for its detection and calculation. However, the broken line and curve line bridgehead settlement are no longer applicable to the relevant content of pavement bumping due to its gradual change and sectional features. These two types of non-staggered-step bridgehead settlement are this paper’s research object and focus.

2.2. Detection Technology

Two types of non-staggered-step bridgehead settlements show different characteristics on road profiles. Thus, this paper will study the detection method based on the road profile line. Road profile detection technology detects two types of settlements while carrying road image detection equipment. Subsequently, a vehicular detection system for non-staggered-step bridgehead settlement is formed, as shown in Figure 2.

The vehicular detection system mainly includes a detection vehicle, inertial navigation system, line scanning camera, photoelectric encoder DMI. The inertial navigation system is used to collect road longitudinal slope data. The photoelectric encoder DMI is used to obtain real-time vehicle speed and driving distance, which together provide a data basis for calculating the road profile. In addition, the line scanning camera can capture continuous road images as a pavement image detection device. When the road profile line corresponds to the road image position, the junction of road and bridge can be quickly located on the line.

3. Methodology

3.1. Data Preprocessing

The vehicular detection system can obtain the distance, speed, tri-axial acceleration, tri-axial angular velocity, and other information of the detection vehicle. Firstly, we need to use the tri-axial acceleration and tri-axial angular velocity to obtain the vehicle’s pitch angle, which is the road’s longitudinal slope, and establish the spatial right angle coordinate system, where the pitch angle is the angle of vehicle rotation around the X axis. Tri-axial acceleration and tri-axial angular velocity, as part of the data from Zhang [22], can be used to calculate the pitch angle of the vehicle. According to Formula (1), the pitch angle can be calculated using tri-axial acceleration. According to Formula (2), the vehicle’s pitch angle can be calculated using tri-axial angular velocity.

$$pitc{h}_a=\arctan \left(\frac{a_x}{\sqrt{a_y^2+a_z^2}}\right)$$

(1)

$$pitc{h}_w={\int }_0^T{w}_{x}dt$$

(2)

where $pitc{h}_a$ is the pitch angle obtained using tri-axial acceleration at the time of T, $pitc{h}_w$ is the pitch angle obtained using angular velocity at the time of T, $a_x$, $a_y$, and $a_z$ are tri-axial acceleration, and $w_x$ is the angular velocity of rotation about the X-axis. Since there is no exact expression for $w_x$, in the calculation, the angular velocity of the starting point during the period is used as the angular velocity of that period.

There is no cumulative error in calculating the pitch angle using tri-axial acceleration, but it contains too much noise, such as acceleration when the vehicle is moving and acceleration when the vehicle is vibrating; the integration of the angular velocity can obtain the inclination angle, which is more accurate and insensitive to external vibration but will produce a cumulative error, so the tri-axial acceleration and tri-axial angular velocity cannot be used alone to obtain the inclination angle. The two need to be combined. Therefore, the Kalman filter algorithm is considered below to fuse the two data. The Kalman filter algorithm consists of the system state prediction Formula (3) and the system state observation Formula (4) [23]:

$$X_k=F{X}_{k-1}+B{U}_k+W_k$$

(3)

$$Z_k=H{X}_k+V_k$$

(4)

where $X_k$, $X_{k-1}$ are the system states of the system at moments k and k − 1, $U_k$ is the control quantity of the system at moment k, $W_k$ is the noise of the system state at moment k and its covariance at moment k is Q, F and B are the system state transfer coefficients, $Z_k$ is the observed value of the system at moment k, H is the system observation transfer coefficient, $V_k$ is the system observation noise at moment k and its covariance at moment k is R. The subscript k|k − 1 indicates that the a priori information up to, but not including, time step k is used, which is found in the prediction step of the algorithm. The subscript k|k is the corrected estimate using information up to and including time step k.

The first step is the prediction, and the system state prediction value ${\widehat{x}}_{k|k-1}$ and the system state prediction error $P_{k|k-1}$ at moment k are obtained.

$${\widehat{x}}_{k|k-1}=F{\widehat{x}}_{k-1|k-1}+B{u}_k$$

(5)

$$P_{k|k-1}=F{P}_{k-1|k-1}{F}^T+Q_{k-1}$$

(6)

The second step is an update to obtain the optimal estimate of the Kalman gain $K_k$ and the system state ${\widehat{x}}_{k|k}$ at moment k.

$$K_k=\frac{P_{k|k-1}{H}^T}{H{P}_{k|k-1}{H}^T+R_k}$$

(7)

$${\widehat{x}}_{k|k}={\widehat{x}}_{k|k-1}+K_k\left(Z_k-H{\widehat{x}}_{k|k-1}\right)$$

(8)

$$P_{k|k}=\left(I-K_{k}H\right)P_{k|k-1}$$

(9)

In this paper, there is no control quantity, i.e., $U_k$ is 0, the pitch angle calculated by acceleration is taken as the measured value $Z_k$ at k moments, and the pitch angle calculated by angular velocity is taken as the state prediction value ${\widehat{x}}_{k|k-1}$ at k moments. Based on several experiments, the covariance of prediction noise Q is fixed as 0.03, the covariance of observation noise R is fixed as 0.3, and the initial value of state prediction error is fixed as 0.

Based on the driving distance and pitch angle, the elevation of each acquisition point is calculated relative to the starting point. According to Formula (10), the starting point elevation is fixed as 0. The graph formed by smoothly connecting the two-dimensional points of driving distance and elevation is the road profile line.

$$H_i=H_{i-1}+\left(d_i-d_{i-1}\right)\times \mathit{sin}{\theta }_{i-1},i=\mathrm{2,3},4,..,n$$

(10)

where H_i is the elevation (m) of point i relative to the starting point; n is the total number of points collected by the system; d_i or d_i−1 is the cumulative driving distance (m) of the detection vehicle at point i and i − 1, respectively; θ_i−1 is the pitch angle of the point i − 1 collected by the system, where it is positive when uphill and negative when downhill.

To ensure the consistency of the test conditions, it is necessary to use the road image to determine the starting and ending points of the bridge section detection. However, this paper uses a low-cost line scan imaging device without a light supplement. The original image shows the characteristics of dark on both sides and bright in the middle. In addition, the overall brightness of the image is relatively black. Therefore, the preprocessing step, which uses a uniform light method, is devised to reduce the noise to sharpen or enhance the linear features of the raw images [24]. An example of the preprocessed image is depicted in Figure 3. As can be seen, the image visualization effect is better than that before processing.

3.2. The Calculation Model and Algorithm

3.2.1. Calculation Indicators and Threshold Requirements

This paper uses the longitudinal slope difference before and after the bridge joint to quantify the bridgehead settlement. Unlike the traditional research method, this study focuses on investigating the longitudinal slope difference before and after each point uniformly selected in the study section. The proportion of points exceeding the threshold of the longitudinal slope difference to the total number of points is used to characterize the non-staggered-step bridgehead settlement. The above points that exceed the longitudinal slope threshold are called settlement points, and the ratio is defined as the settlement point ratio (SPR).

The calculation of SPR is based on selecting the longitudinal slope difference threshold. In this paper, Ningbo city is taken as an example to study bridgehead settlement. According to Ningbo Municipal Administration Office [25], the maximum longitudinal slope difference under different speeds is defined. In the meantime, considering that the speed limit on urban bridges and roads is generally 80 km/h, the longitudinal slope difference threshold under different speeds is defined in

Table 1. Regulation of longitudinal slope difference threshold under different speeds.

Speed V/(km/h)	>60, ≤80	>40, ≤60	≤40
Threshold of Longitudinal Slope Difference	3%	3.5%	4%

.

3.2.2. Model and Algorithm

Since bridgehead settlement mainly occurs at the junction of road and bridges, the research section should cover the distance before and after the bridge joint. Therefore, the mark should be made for the case without bridge joints to identify the junction of road and bridge on the pavement images. Moreover, after the road profile line and the road image position correspond, the bridge joint is located on the line. At this time, the starting point of the road profile line is the acquisition starting point, and the joint bridge position is reset to the horizontal zero point of the profile line, as illustrated in Figure 4.

The calculation model is suitable for the bridgehead settlement of the entering bridge and exiting bridge. Take the entering bridge as an example. As shown in Figure 4a, the bridge joint point is located on the profile line, and the starting point of the transition section is located at the elevation mutation point on the line. The horizontal distance between the bridge joint point and the transition section starting point is defined as D. The profile line at −D~D in the horizontal direction is intercepted. Moreover, the points are evenly selected along the horizontal direction with Δd as the interval. Inspired by Zhang’s research [22], as shown in Figure 4b, the distance d₀ (d₀ > Δd) from the front and rear of each point is drawn along the horizontal direction. Since d₀ is greater than Δd, only part of the points in Figure 4a participates in the determination of whether they are settlement points. Unlike Zhang’s study [22], we optimize the calculation of the absolute value of the difference between the fore-slope and the back-slope. These points are called effective calculation points, and their number is defined as n_e, and the sort of points is k. The value rules of the above parameters will be described in the following test and data analysis.

The calculation model of non-staggered-step bridgehead settlement is as follows:

Step 1: The absolute value ΔS_k (%) of the difference between the fore-slope and the back-slope of each effective calculation point after the slope drawing is calculated:

$$∆S_k=\left|\frac{H_{k+1}-H_k}{d_0}-\frac{H_k-H_{k-1}}{d_0}\right|,k=\mathrm{1,2},3,\dots ,n_e$$

(11)

where H_k denotes the elevation (m) of the k^th effective calculation point; H_{k − 1} is the elevation (m) of the k − 1^th effective calculation point, namely, the starting point at the front slope of the k^th effective calculation point; H_{k + 1} is the elevation (m) of the k + 1^th effective calculation point namely the ending point at the back slope of the k^th effective calculation point; while H₀ is denoted as 0, and $H_{n_e+1}$ is the elevation of the ending point of the profile line. The meanings of other parameters are the same as before.

Among them, the number of effective points n_e is calculated by Formula (12), where the result is an integer.

$$n_e=\frac{2\left(D-d_0\right)}{∆d}+1$$

(12)

Step 2: The longitudinal slope difference threshold, as seen in Table 1, denoted as ΔS₀, is determined according to the test speed. If ΔS_k exceeds the threshold ΔS₀, then the corresponding effective calculation point is determined as the settlement point, so that n_k is denoted as 1, and n_k is denoted as 0 conversely, which is:

$$n_k=\left\{\begin{array}{c}0\\ 1\end{array}\right.\genfrac{}{}{0pt}{}{,\mathsf{\Delta }{S}_k\le \mathsf{\Delta }{S}_0}{,\mathsf{\Delta }{S}_k>\mathsf{\Delta }{S}_0}$$

(13)

Step 3: The number of settlement points N and its ratio to effective calculation point n_e are calculated, where the ratio is called the SPR, namely, the settlement point ratio:

$$N=\sum _{k=1}^{n_e}{n}_k$$

(14)

$$SPR=\frac{N}{n_e}\times 100\%$$

(15)

Based on the algorithm, the relevant computer programs can be written to realize the automatic and rapid calculation of non-staggered-step bridgehead settlement.

4. Analysis and Discussion

4.1. Accuracy Verification of Road Longitudinal Slope Automatic Detection

To ensure that the longitudinal slope results collected by the vehicular detection system are within the allowable error range, the accuracy of longitudinal slope automatic detection should be verified before the formal test. Before this, the distance automatic measurement test was carried out according to the accuracy verification requirements in the Specifications of Automatic Pavement Condition Survey [26]. The test results meet the specifications requirements, which require that the distance automatic measurement error does not exceed 0.1%.

The following experiments are conducted in accordance with the standard specifications of the Specifications of Automatic Pavement Condition Survey [26] regarding the automated longitudinal slope detection. The MOT Standard [26] stipulates that the automated longitudinal slope detection of pavement needs to meet the following two points: the absolute error of 95% detection value ≤1.5% or relative error ≤10%, and the absolute error of all detection values ≤6%. According to the provisions of the MOT Standard [26], a straight-line test section with a length of 150 m and a significant longitudinal slope change is selected to mark the section’s starting and ending positions and a measuring point position every 10 m along the driving direction. DSZ05 leveler is used to measure the elevation of two adjacent measuring points along the driving direction. According to Formula (16), Figure 5a,b, the longitudinal slope value between two adjacent measuring points is calculated, and the result is used as the known longitudinal slope between the two measuring points. Moreover, the vehicular detection system detects the test section at a constant speed of 20 km/h, 30 km/h, and 40 km/h. As illustrated in Figure 5c, the system collects longitudinal slope data at an interval of 0.1 m and outputs the average longitudinal slope every 10 m as the automatic measurement results.

$$S_{HM}^{\prime }=\frac{\frac{h_{AB}}{d_{AB}}}{\sqrt{1-{\left(\frac{h_{AB}}{d_{AB}}\right)}^2}}$$

(16)

where S_HM denotes the longitudinal slope value (%) between two adjacent measuring points measured manually, h_AB denotes the height (m) between two adjacent measuring points measured by the leveler, and d_AB represents the distance (m) between two adjacent measuring points, which was taken as 10 m in this case.

In order to better develop the bridge slope generality test, it is necessary to calibrate the automatic test results, as shown in Equation (17).

$$S_{AM}={\alpha \ast S}_{AM}^{\prime }+\beta$$

(17)

where α and β is the empirical correction factor, in this work, we fix the focusing parameter α as 1.02 and β as 0.03. $S_{AM}^{\prime }$ is the automatic longitudinal slope measurement before calibration, and $S_{AM}$ is the automatic longitudinal slope measurement after calibration.

Error analysis is carried out on the measurement results, and the absolute error and relative error are selected as the accuracy verification parameters of longitudinal slope automatic measurement, whose calculation formulas are as follows:

$$E_{AE}=\left|S_{AM}-S_{HM}\right|$$

(18)

$$E_{RE}=\frac{\left|S_{AM}-S_{HM}\right|}{\left|S_{HM}\right|}\times 100\%$$

(19)

where E_AE denotes the absolute error (%) of the longitudinal slope measurement between two adjacent measuring points, E_RE denotes the relative error (%) between two adjacent measuring points, and S_AM is the average longitudinal slope value (%) between two adjacent measuring points output by the vehicular detection system every 10 m.

The analysis results are shown in

Table 2. Error analysis between vehicular detection system and manual measurement results.

Distance Range/m	SAM/%			SHM/%	EAE/%			ERE/%
	20 km/h	30 km/h	40 km/h		20 km/h	30 km/h	40 km/h	20 km/h	30 km/h	40 km/h
0~10	−8.91	−9.15	−9.32	−10.10	1.19	0.95	0.78	11.83	9.41	7.69
10~20	−9.29	−9.49	−9.67	−10.20	0.91	0.71	0.53	8.89	6.99	5.19
20~30	−9.55	−9.92	−9.71	−10.20	0.65	0.28	0.49	6.39	2.79	4.79
30~40	−10.07	−10.55	−10.27	−10.36	0.29	0.19	0.09	2.82	1.81	0.85
40~50	−10.60	−10.99	−10.76	−10.40	0.20	0.59	0.36	1.91	5.63	3.48
50~60	−10.32	−10.49	−10.25	−10.42	0.10	0.07	0.17	0.93	0.64	1.62
60~70	−10.16	−10.30	−10.04	−10.51	0.35	0.21	0.47	3.33	1.97	4.50
70~80	−10.02	−9.96	−9.92	−10.10	0.08	0.14	0.18	0.82	1.43	1.83
80~90	−10.29	−10.12	−10.18	−10.24	0.05	0.12	0.06	0.51	1.18	0.58
90~100	−9.98	−9.74	−9.97	−10.12	0.14	0.38	0.15	1.42	3.74	1.52
100~110	−9.76	−9.76	−9.58	−10.11	0.35	0.35	0.53	3.44	3.44	5.26
110~120	−9.99	−10.02	−9.95	−10.22	0.23	0.20	0.27	2.29	1.99	2.68
120~130	−9.90	−9.81	−9.87	−10.20	0.30	0.39	0.33	2.89	3.79	3.19
130~140	−9.63	−9.43	−9.61	−10.17	0.54	0.74	0.56	5.32	7.32	5.52
140~150	−9.15	−9.00	−9.27	−10.03	0.88	1.03	0.76	8.77	10.30	7.55

. There are 15 groups of longitudinal slope results measured automatically and manually, distributed every 10 m, namely, 0~10 m, 10~20 m, …, 140~150 m. It can be seen from Table 2 that the absolute error E_AE of 15 groups of longitudinal slope measurement results under three speeds are all less than 6%. Meanwhile, the percentage of detection values with relative errors less than 10% at 20 km/h, 30 km/h, and 40 km/h speeds are 93.33%, 93.33%, and 100%. Although at 20 km/h and 30 km/h, the proportion of detection values that meet the requirements of relative error is less than 95%, the absolute error of 100% detection values is less than 1.5%. In other words, the proportion of detection values with absolute error less than 1.5% is more than 95%. In summary, the error analysis results under three vehicle speeds comply with the relevant regulations in JTG/T E61-2014 Standard in China [27], proving that the vehicular detection system used in this study meets the longitudinal slope accuracy requirements.

4.2. Correlation Analysis

4.2.1. Automatic and Manual Test Scheme

As shown in Figure 6, the detection vehicle equipped with the detection system passes through the bridge-road transition section and bridge section at a constant speed after acceleration, collects data and images, and stops after deceleration. Considering driving safety and reducing the influence of vehicle bumping on the test results, the vehicle runs at a constant speed of not more than 40 km/h after acceleration. Based on the built bridgehead settlement calculation model and algorithm, the data and images collected by the detection system are input. Then, the SPR of each test object will be obtained.

Additionally, considering that the bridgehead settlement is caused by the uneven settlement between the road and bridge, the bridgehead settlement condition is described by measuring the longitudinal slope difference [28]. As shown in Figure 7, the leveler measured three elevation points at the bridge joint, the l₀ distance before the bridge joint, and the l₀ distance after the bridge joint.

The longitudinal slope value and the absolute value of the difference between the transition section and the bridge section are calculated by Formula (20).

$$∆S=\left|\frac{\frac{∆h_1}{d_0}}{\sqrt{1-{\left(\frac{∆h_1}{d_0}\right)}^2}}-\frac{\frac{∆h_2}{d_0}}{\sqrt{1-{\left(\frac{∆h_2}{d_0}\right)}^2}}\right|$$

(20)

where d₀ denotes the front (rear) distance (m) of the bridge joint in the manual measurement of the longitudinal slope, which means the same as l₀ in the above calculation model. Δh₁ and Δh₂ are the height (m) of the transition section and the bridge section, respectively. ΔS is the absolute value (%) of the longitudinal slope difference before and after the bridge joint in manual measurement.

4.2.2. Correlation Analysis of Results

In practice, the staggered-step bridgehead settlement often occurs where the road and bridge are straight connected (no significant longitudinal slope change) or the pavement material of bridge joints is significantly exfoliated. In contrast, the non-staggered-step bridgehead settlement is studied in this paper. To make the proposed detection method applicable to the correct object, the bridge with significant longitudinal slope change and no obvious material exfoliation at the bridge joints is selected as the test object.

For the value of model parameters in this paper, the MOT Standard [29] regulations on pavement bumping detection sampling interval with 0.1 m and considering the influence of point density on the calculation results in the practical application model. Meanwhile, the Guidelines [25] provisions on the axle distance of the detection vehicle and the influence of the slope drawing length on the calculation results in the practical application model are considered. In summary, the model parameters are valued according to the following rules:

(1)

For D in the model: data is accurate to 0.05 m and the value is different according to different road profile lines of the test objects.

(2)

For Δd in the model: it takes 0.5 m when D > 5.0 m, on the contrary, it takes 0.1 m.

(3)

For d₀ in the model: it takes 2.0 m when D > 5.0 m, on the contrary, it takes 1.0 m.

(4)

For $∆$S₀ in the model: the test speed of each group is less than 40 km/h, according to Table 1, $∆$S₀ is 4%.

The research team behind this paper selected the data of entering and exiting bridges in Ningbo, Zhejiang Province, as test objects. The vehicular detection system collected the longitudinal slope data and continuous pavement images simultaneously. To ensure the uniformity of the trials, 50 groups of SPRs, including the entering and exiting bridge, were obtained through the established calculation model and algorithm. In the meantime, according to the manual test scheme, the longitudinal slope difference between the transition section and the bridge section was measured at the bridge-road junction of each test object, forming 50 sets of manual test results. SPRs and ΔS are illustrated in Appendix A.

To further analyze the correlation between the output results of the calculation model and the manual measurement results, the above 50 groups of SPRs and the absolute value of the longitudinal slope difference ΔS by manual measurement are analyzed for correlation. The correlation coefficient r = 0.934, indicates that the two are significantly correlated. Furthermore, we use SPSS software to establish a linear regression model between the two. The model-fitting results are shown in Figure 8. The analysis shows that the determination coefficient of SPRs and manual measurement results is 0.872, indicating that the established regression model has high fitting accuracy. This study confirms the capability of using this methodology for measuring the non-staggered-step bridgehead settlement.

5. Conclusions

For the non-staggered-step bridgehead settlement, the existing national standards do not stipulate its detection methods. The existing methods have low efficiency, intense subjectivity, low sensitivity to sectional settlement, and are vulnerable to the interference of deformation distresses. Given the above problems, this paper proposes to use the vehicular detection system to rapidly collect the longitudinal slope data and pavement images, forming the road profile line corresponding to the image position. Based on this, a calculation model and algorithm of the non-staggered-step bridgehead settlement are established. Moreover, a calculation index, namely, the settlement point ratio (SPR), is proposed and verified. The main conclusions of this paper are as follows:

The accuracy of the road longitudinal slope collected by the vehicular detection system was verified by comparative tests. By testing three different vehicle speeds, the proportion of detection values with absolute error less than 1.5% is more than 95%. The results show that the longitudinal slope errors between the automatic detection and the manual measurement of 15 groups of distance gradients meet the requirements of relevant standards.

The rules for selecting test objects and selecting model parameters were stipulated. Automatic and manual tests were carried out on 31 Ningbo, Zhejiang Province, bridges. In total, 50 SPRs were output through the established model based on automatic detection data. In addition, the correlation and regression analysis were carried out on the absolute value of 50 groups of longitudinal slope difference by manual measurement. The results indicate that the correlation coefficient of the two is 0.934, and the determination coefficient of the regression model is 0.872. The two are significantly correlated, confirming the capability of using this methodology to measure the non-staggered-step bridgehead settlement.

Overall, the detection method proposed in this paper effectively supplements the research blank of bridgehead settlement detection and has significant application value for its automatic quantitative detection. However, this method is suitable for single-lane detection. Further research is needed for one-time detection of bridgehead settlement under multi-lanes. In the future, data sets from other regions need to be added to optimize the proposed detection method further to enhance the model’s universality.