Bridge Displacement Research Articles

A simplified weak coupling dynamic analysis method for running safety evaluation of train on bridges under earthquake excitation

This study proposes a simplified analysis method that couples the bridge and train-track subsystem in a weak form to facilitate the dynamic analysis of the train-track-bridge coupled system (TTBS) under earthquakes. The method includes three main steps: (i) performing dynamic analysis of the bridge under seismic conditions to obtain the response of the bridge deck; (ii) interpolating the bridge displacement beneath each wheelset based on the train's velocity, departure time, and the initial positions of the wheelsets; and (iii) assessing the running safety of the train by incorporating the interpolated bridge response as track irregularity into the train-track coupled system. Steps (i) and (iii) can be analyzed separately using finite element and multibody dynamics software, eliminating the need to create a complex TTBS model that is challenging to achieve within a single software platform. Additionally, based on the method’s assumptions, the earthquake excitation on the train can be separated into the seismic inertial effect and seismic-induced bridge deformation, enabling a quantitative analysis of the impact of these two types of excitations on train safety. Taking a 10-span simply supported bridge and a long-span cable-stayed bridge as examples, the proposed method’s assumptions are verified by comparing its results with those obtained from a complex TTBS model. Furthermore, the impact characteristics of inertial effects and seismic-induced bridge deformation on train safety for these two types of bridges are analyzed. The proposed method offers robust support for seismic design of bridges and facilitates a comprehensive analysis of the mechanisms through which seismic excitations affect train safety.

A Sparsely-Measured Fitting Method for Identifying the Coefficients in the Governing Equation of a Beam

This study proposes a method for identifying the coefficients in the governing equation of a beam from the sparsely measured response of bridge displacement. The following three steps constitute the procedure: First, the full-field displacement is reconstructed by the compressive sensing theory, which is innovatively applied in the spatial domain with a proposed general basis matrix. Then, the reconstructed displacement is fitted by the B-spline surface basis functions, and the derived control points are further adopted to compute the derivatives of displacement. The genetic algorithm is finally applied to seek the coefficients of the governing equation by substituting the fitted response into the equation. The proposed method is validated numerically and experimentally, including a parametric study to evaluate the performance subjected to various practical conditions. The salient advantages of the proposed method lie in that it requires few sensors for measurement, and the derivatives of displacement are computed robustly.

Full-field displacement measurement of long-span bridges using one camera and robust self-adaptive complex pyramid

Full-field motion with a high spatial resolution can reflect the health state of long-span bridges. Traditional structural health monitoring (SHM) systems measure the structural displacement at sparse points only. Despite the development of various methods for obtaining high-resolution responses, they fail to estimate the multi-scale motions of real long-span bridges. A novel full-field motion estimation method is proposed to directly measure the entire structural responses using one digital camera. In this approach, multi-scale motions of different components under unknown excitations are encoded in a complex pyramid. The parameters of the complex pyramid are determined by the localization index to record robust local phases at each measurement point. Two indices, namely, the spatial Laplacian of the phase and the amplitude value degradation index, are designed to adaptively estimate multi-scale displacements contained in the complex pyramid. The proposed method estimates the full-field displacements of a steel frame accurately in an experimental test. Moreover, the full-field displacement of the 1377-m long main span Tsing Ma Bridge is estimated using only one shot. Results suggest that the displacement estimated by the proposed method matches well with the GPS data and further visualizes the bridge mode shapes with a high resolution.

UAS displacement measurement using a three point homography method with potential bridge monitoring applications

Measuring bridge displacements using Unmanned Aerial Systems (UAS) is an emerging field offering the advantage of a remote non-contact approach for measuring bridge displacements. Unfortunately, UAS measurements contain the motion of the UAS which needs to be compensated for to get true bridge displacements. So far, UAS bridge displacement studies have compensated the unwanted motion of the UAS from measurements by tracking a minimum of 4 stationary points required as the minimal solution to calculate a Projective homography between two UAS camera views. While this has been shown to be effective, a reduction in the minimal solution would make these methods more robust to factors such as loss of stabilising points or temporary occlusion to an object entering the scene. In this paper, by combining recent advances to the Perspective-3-Point problem that make camera pose calculation from 3 points reliable and calculating a Euclidean homography instead of a Projective homography, we show in a laboratory experiment that structural displacements can successfully be made to submillimetre accuracy using only 3 points instead of the traditional 4 points. This is done with only visual information from video feed without the need for any additional sensors.

Study on Vehicle-Bridge Coupled Vibration of Curved Girder Bridges under Different Road Surface Grades

This study explores the impact of different levels of road surface smoothness on the dynamic response of bridges. By conducting a detailed analysis under five different conditions of road surface smoothness, the mechanisms by which road surface irregularities affect the dynamic characteristics and safety performance of bridge structures are revealed. The research employs the finite element simulation method to compare and analyze the changes in key dynamic indicators such as vertical displacement, torsional angle, torque, and bending moment of bridges under different grades of road surface smoothness. The results indicate that a decrease in road surface smoothness significantly increases the dynamic response of bridges. The findings provide important reference information for bridge engineers in the design and maintenance of bridges.

Phase shift-based resonance assessment for in-service high-speed railway bridges

Resonance in high-speed railway bridges can deteriorate the structural integrity and running safety of a train; thus, the resonant speed needs to be identified. Previous studies have proposed resonant conditions analytically, but their applications to in-service bridges are limited. Free vibration after the passage of a train was utilized to assess resonance, but it could not capture the natural frequency of the coupled system because the train-bridge interaction was neglected. This study proposed a practical framework for quantifying the resonance in a high-speed railway bridge using a phase shift. The static displacement of the railway bridge was numerically reconstructed using the train loading history. Phase angles were extracted by comparing the static and dynamic displacements, which were directly utilized to develop a novel resonance indicator in this study. Numerical simulations and field demonstrations validated the applicability of the proposed method for understanding the resonance behavior of full-scale railway bridges.

Bridge Monitoring Strategies for Sustainable Development with Microwave Radar Interferometry

The potential of a coherent microwave radar for infrastructure health monitoring has been investigated over the past decade. Microwave radar measuring based on interferometry processing is a non-invasive technique that can measure the line-of-sight (LOS) displacements of large infrastructure with sub-millimeter precision and provide the corresponding frequency spectrum. It has the capability to estimate infrastructure vibration simultaneously and remotely with high accuracy and repeatability, which serves the long-term serviceability of bridge structures within the context of the long-term sustainability of civil engineering infrastructure management. In this paper, we present three types of microwave radar systems employed to monitor the displacement of bridges in Japan and Italy. A technique that fuses polarimetric analysis and the interferometry technique for bridge monitoring is proposed. Monitoring results achieved with full polarimetric real aperture radar (RAR), step-frequency continuous-wave (SFCW)-based linear synthetic aperture, and multi-input multi-output (MIMO) array sensors are also presented. The results reveal bridge dynamic responses under different loading conditions, including wind, vehicular traffic, and passing trains, and show that microwave sensor interferometry can be utilized to monitor the dynamics of bridge structures with unprecedented spatial and temporal resolution. This paper demonstrates that microwave sensor interferometry with efficient, cost-effective, and non-destructive properties is a serious contender to employment as a sustainable infrastructure monitoring technology serving the sustainable development agenda.

Quantifying the Impact of Environment Loads on Displacements in a Suspension Bridge with a Data-Driven Approach.

Long-span bridges are susceptible to damage, aging, and deformation in harsh environments for a long time. Therefore, structural health monitoring (SHM) systems need to be used for reasonable monitoring and maintenance. Among various indicators, bridge displacement is a crucial parameter reflecting the bridge's health condition. Due to the simultaneous bearing of multiple environmental loads on suspension bridges, determining the impact of different loads on displacement is beneficial for the better understanding of the health conditions of the bridges. Considering the fact that extreme gradient boosting (XGBoost) has higher prediction performance and robustness, the authors of this paper have developed a data-driven approach based on the XGBoost model to quantify the impact between different environmental loads and the displacement of a suspension bridge. Simultaneously, this study combined wavelet threshold (WT) denoising and the variational mode decomposition (VMD) method to conduct a modal decomposition of three-dimensional (3D) displacement, further investigating the interrelationships between different loads and bridge displacements. This model links wind speed, temperature, air pressure, and humidity with the 3D displacement response of the span using the bridge monitoring data provided by the GNSS and Earth Observation for Structural Health Monitoring (GeoSHM) system of the Forth Road Bridge (FRB) in the United Kingdom (UK), thus eliminating the temperature time-lag effect on displacement data. The effects of the different loads on the displacement are quantified individually with partial dependence plots (PDPs). Employing testing, it was found that the XGBoost model has a high predictive effect on the target variable of displacement. The analysis of quantification and correlation reveals that lateral displacement is primarily affected by same-direction wind, showing a clear positive correlation, and vertical displacement is mainly influenced by temperature and exhibits a negative correlation. Longitudinal displacement is jointly influenced by various environmental loads, showing a positive correlation with atmospheric pressure, temperature, and vertical wind and a negative correlation with longitudinal wind, lateral wind, and humidity. The results can guide bridge structural health monitoring in extreme weather to avoid accidents.

Real‐time displacement measurement for long‐span bridges using a compact vision‐based system with speed‐optimized template matching

AbstractThis paper introduces a new accelerating algorithm, efficient match slimmer (EMS), specifically designed to lighten computational loads of sophisticated template matching algorithms, enabling these algorithms to be effectively run on single‐board computers. Utilizing EMS in conjunction with a robust template matching algorithm, we have developed Raspberry Vision—a compact, cost‐effective, and real‐time vision‐based system. Its compactness and portability facilitate a practical measurement strategy that not only minimizes the camera‐to‐target distance but also simplifies the camera calibration process in bridge displacement monitoring, thereby enhancing measurement accuracy. The performance of the system is estimated on two operational suspension bridges. The results demonstrate that Raspberry Vision, equipped with the measurement strategy, can significantly improve the measurement accuracy in the long‐span bridge test and is also suitable for cross‐sea bridge measurements.

Satellite Synthetic Aperture Radar, Multispectral, and Infrared Imagery for Assessing Bridge Deformation and Structural Health—A Case Study at the Samuel de Champlain Bridge

A space-borne remote sensing method was applied, validated, and demonstrated in a case study on the Samuel de Champlain Bridge in Montreal, Canada. High-resolution C-band radar satellite imagery was analyzed using the Persistent Scatterer Interferometric Synthetic Aperture Radar technique to derive bridge displacements and compare them against theoretical estimates. Multispectral and long-wave thermal infrared satellite imagery acquired during the InSAR observation period and historical environmental data were analyzed to provide context for the interpretation and understanding of InSAR results. Thermal deformation measurements compared well with their theoretical estimates based on known bridge geometry and ambient temperature data. Non-thermal deformation measurements gave no evidence of settlement during the 2-year monitoring period, as would normally be expected for a newly constructed bridge with its foundation on bedrock. The availability of environmental data obtained from multispectral and thermal infrared satellite imagery was found to be useful in providing context for the bridge stability assessment. Ambient temperature measurements from thermal infrared satellite imagery were found to be a suitable alternative in cases where data from in situ temperature sensors or nearby weather stations are not available or not fit for purpose. No strong correlation was found between the river conditions and bridge deformation results from the InSAR analysis; this is partly due to the fact that most of these effects act along the river flow in the north–south direction, to which the satellite sensor is not sensitive.

Computer Vision-Based Pier Settlement Displacement Measurement of a Multispan Continuous Concrete Highway Bridge under Complex Construction Environments

Various concrete bridges have been built across oceans, valleys, and mountains; however, the settlement displacement of bridge piers caused by environmental changes or self-weight during construction phases often leads to uneven stresses, cracking, and eventual collapse. To address the labor-intensive and high-cost issues of pier displacement monitoring using contact-type sensors, this paper proposes an automatic vision-based method for measuring pier settlement displacement under complex construction environments, such as complex image backgrounds, varying ambient light, and camera movement. In the proposed method, a deep learning network was first employed to eliminate the adverse effect of complex image backgrounds and varying ambient light on the accuracy of target detection; then, an adaptive displacement extraction algorithm without a human-computer interaction process was developed to automatically extract the center coordinates of targets attaching to the bridge piers and reference platform; finally, the pier settlement displacement was calculated by using the relative displacements obtained by a dual camera system to eliminate the measurement error caused by camera translation and rotation movements. Laboratory tests of a cantilever beam and field tests of a continuous multispan concrete girder highway bridge under construction have successfully validated the effectiveness and robustness of the developed methodology. The results obtained in this paper can provide some insights for engineers in applying computer vision technology for the real-time monitoring of bridge displacements.

Bridge Displacement Prediction from Dynamic Responses of a Passing Vehicle Using CNN‐GRU Networks

Dynamic displacement is an important indicator for bridge safety estimation but is difficult to measure due to economic or technological limitations. Dynamic responses of a passing vehicle include the bridge dynamic response information. This study proposes a framework utilizing artificial neural networks to efficiently and accurately predict bridge displacements from the dynamic response of a passing vehicle. The input and the output of the networks are the vehicle acceleration responses and the bridge dynamic displacement responses, respectively. The implemented framework consists of convolutional neural network (CNN) and gated recurrent units (GRU). CNN is adept at feature extraction in the microcosm of short‐term time series, revealing intricate nuances. As a complement, GRU plays a crucial role in extracting features of macroscopic long‐term time series. The CNN‐GRU network can efficiently extract higher‐order features contained in the input data. Numerical experiments are conducted using the developed vehicle‐bridge interaction (VBI) system model to obtain requisite data for training the deep neural network. The impact of the presence or absence of roadway irregularities and the number of vehicles are discussed, indicating the accuracy of the framework. Furthermore, a laboratory experiment is conducted to further assess the performance of the CNN‐GRU network. Results indicate that the CNN‐GRU network offers an effective alternative for bridge displacement measurements.

A Deep Learning Estimation Method for Temperature-Induced Girder End Displacements of Suspension Bridges

A Deep Learning Estimation Method for Temperature-Induced Girder End Displacements of Suspension Bridges

Nonlinear modeling of temperature-induced bearing displacement of long-span single-pier rigid frame bridge based on DCNN-LSTM

Long-span single-pier rigid frame bridge may experience excessive bearing displacement under temperature variation, which can result in structural deformation or instability, causing significant engineering accidents and immeasurable losses on society. This paper proposes a spatial-temporal nonlinear modeling method for temperature and temperature-induced bearing displacement (TIBD) of long-span single-pier rigid frame bridge based on DCNN-LSTM network with elastic modulus fusion, relying on the monitoring data of the Second Yangtze River Bridge in Wuhan. This framework introduces a dynamic autoregressive method for model inference to improve the prediction accuracy of the model. This study addresses three major issues: Insufficient rational selection of temperature characteristic values; Inadequate research on correlation between structural temperature and TIBD for the bridges; Poor prediction accuracy of temperature-TIBD regression models. The method proposed in this study achieves prediction accuracy of up to 99.8 % for TIBD, and this model is not affected by seasonal variation.

Critical application zone of the jet grouting piles in the vicinity of existing high-speed railway bridge in deep soft soils with medium sensibility

Jet grouting piles were widely employed for ground reinforcement in building and infrastructure engineering due to the low cost and construction convenience. However, this foundation treatment method is not allowed to be used in high-speed railway involved constructions in China because of the concerning of the negative effect on the lateral displacement of the existing high-speed railway. To find a reasonable application distance of jet grouting piles away from existing high-speed railway bridge in deep soft soils with medium sensibility, a series of laboratory and in-situ tests on the influence of the jet grouting piling on the deformation of surrounding soils and adjacent high-speed railway bridge are carried out. The geological characteristics of the construction site and the mechanical properties of the soft soil are deeply investigated by utilizing field and laboratory tests. The piling induced lateral displacement of the surrounding soils is monitored as well as the displacement of an adjacent high-speed railway bridge. The monitoring data reveal that the influence area of the jet grouting piling is approximately 1.75 ∼ 1.85 times of the pile length in deep soft soils. The critical distance of the jet grouting piles from the existing high-speed bridge should be larger than 2 times of the pile length.

Influence Line Identification Method Based on VMD Combined with Improved Wavelet Threshold Denoising

The influence line of bridge can reflect the performance of the bridge under the moving vehicle load. It has a wide range of applications in structural damage detection, performance evaluation, model correction and bridge weigh-in-motion. Fast moving vehicles will cause the dynamic effect of the bridge, resulting in the change of the bridge response curve and the difficulty of identifying the influence line. In this paper, an influence line identification method based on variational mode decomposition (VMD) combined with improved wavelet threshold denoising is proposed. Firstly, the mathematical model of influence line identification is established based on vehicle load matrix and bridge response. Then, VMD combined with improved wavelet threshold denoising method is used to eliminate dynamic fluctuation effect and noise. Finally, the elastic net penalty term is introduced in the influence line identification problem, and the B-spline basis function is used to reconstruct the influence line. In order to verify the effectiveness of the proposed method, a vehicle-bridge coupling model is established for numerical calculation, and the identification of bridge displacement influence lines under different conditions such as vehicle speed, noise level, road roughness and vehicle weight is investigated. The results show that the proposed method can effectively eliminate the dynamic fluctuation components and noise of the bridge response. In the case of good road roughness, the influence line can still be accurately identified when the vehicle speed reaches 15 m/s.

Longitudinal seismic displacement analysis of Quasi Seismic Isolation Bridge based on Energy-based Multimodal Pushover Method with and without collision

This paper aims to evaluate the longitudinal seismic displacement of the Quasi Seismic Isolation Bridge (QSIB) based on the Energy-based Multimodal Pushover Method (EMPM), including the pier-beam relative displacement and the collision effect. As a simplified seismic analysis method, the EMPM invokes the concept of energy balance into the modal pushover analysis to assess the nonlinear seismic behavior of Laminated Rubber Bearing (LRB) on bridges. In this method, the energy-based capability curve is obtained by the modal pushover analysis, while the energy-based demand curve is estimated under the ground motion record. The target performance criterion can be derived by intersecting the capability curve with the demand curve. The effect of several key factors in EMPM, such as the mode classification and selection, collision effect, energy coefficient and ductility factor, are studied by a case study of a prototype QSIB under ChiChi and El Centro earthquakes. The results of EMPM are compared with those from Nonlinear Time History Analysis (NTHA), to illustrate the effectiveness and accuracy of this method for evaluating the maximum seismic displacement, and the pier-beam relative displacement with and without collision. Results show that the EMPM is found to be able to estimate the longitudinal seismic displacement of the QSIB with and without collision, and can be used as an effective alternative for rapid assess the seismic performance of bridges. The results also indicate that LRB stiffness for modal analysis should be taken as the stiffness pre- or post-sliding when without or with the gap element. Collision effect enlarges the peak displacement and the maximum bias of EMPM.

A non-contact vehicle weighing approach based on bridge weigh-in-motion framework and computer vision techniques

Bridge weigh-in-motion (BWIM) system plays increasingly important role in vehicle load monitoring and bridge maintenance due to advantages of high efficiency and little impact on traffic. However, the contact-type sensors in a traditional BWIM system should be installed in advance and is environment-sensitive, which hinders its application. To this end, a vision-based contactless BWIM (cBWIM) system is proposed. The core idea of the current method is to replace the traditional contact-type sensors by two consumer cameras to realize real-time monitoring of bridge displacement and vehicle trajectory. The cBWIM system consists of three modules, including the axle weight identification algorithm, the bridge displacement monitoring system and the vehicle trajectory tracking system. The influence line-based Moses algorithm is utilized for identification of axle weight. For bridge displacement monitoring, the minimum bounding rectangle-based similarity matching method is proposed to achieve high accuracy measurement of displacement and real-time data processing. For vehicle trajectory tracking, a deep learning-based YOLOv5s algorithm is adopted as a detector, combined with DeepSort algorithm to realize real-time tracking of vehicle position. The cBWIM system is applicable for non-uniform motion and vehicle occlusion cases. Laboratory tests covering various cases (i.e. uniform motion, non-uniform motion and visual occlusion) and field measurement on a full-scale bridge have demonstrated that the proposed method is effective and reliable and can provide alternative tool to the current vehicle weighing methods.

Shaking table test of the seismic performance for railway simply-supported girder bridge isolated by self-centering bearing

In order to solve the problem of the residual displacement of a railway simply-supported girder bridge and realize the aim of a rapid recovery in traffic after earthquake events, we designed a self-centering seismic isolation bearing and created a typical simply-supported girder bridge model with 1/10 ratio. Three peak ground acceleration (PGA) shaking table tests were performed, with the test procedures further described in detail. The test results show that the bearing provides an overall good self-centering performance. Other than the case of a 0.5 g transverse earthquake, where the bearing remains outside of the sliding surface and therefore cannot be self-centering, all the tests show that the bearing is completely self-centering. At the same time, during all the earthquake scenarios, the main structure of the bridge was not damaged in any discernable way, the longitudinal frequency did not change, and the transverse frequency decreased given that the bearing remained outside of the sliding surface. In addition, it was found that the large bearing displacement in the longitudinal direction may lead to a collision of adjacent girders, resulting in a sharp increase in the acceleration of the girders. In cases without collisions between the girders, the acceleration of the girder is effectively reduced compared with the acceleration of the pier top. The results also show that the pier can be effectively protected by the self-centering bearing, as well as indicating that the reinforcement strain of the pier does not reach the yield value under all tests. Due to the large displacement of the bearing, it is necessary to increase the allowable displacement or install a limiting device. Finally, the finite element model (FEM) of the test model is established, with the calculation results compared with the test results, in this way proving the correctness of the FEM and providing a reference for designing the seismic isolation of the railway simply-supported girder bridge.

Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology

This paper presents a study on applying satellite Interferometric Synthetic Aperture Radar (InSAR) technology for the remote monitoring of road bridges and interpreting the results from a structural standpoint. The motivation behind this study arises from the widespread deterioration observed in many road bridges worldwide, leading to the need for large-scale, economic, and effective structural health monitoring (SHM) techniques. While traditional contact-type sensors have cost sustainability limitations, remote sensing techniques, including satellite-based InSAR, offer interesting alternative solutions. The objective of this study is three-fold: (i) to process InSAR data specifically for road bridges in operational conditions through the Multi-Temporal InSAR technique and extract displacement time series of reflective targets on their decks; (ii) to interpret the observed millimetric bridge displacements to verify the consistency with expected response to environmental loads and the possibility to detect unexpected behaviours; and (iii) to investigate the correlation between bridge displacements and environmental loads as temperature and river water flow variations. The study focuses on the multi-span prestressed concrete A22 Po River Bridge in Italy, utilising a dataset of X-Band HIMAGE mode Stripmap images acquired over eight years by the satellite constellation COSMO-SkyMed. The study demonstrates the effectiveness of InSAR-based SHM in detecting temperature-induced displacements and identifying different bridge spans simply by studying the sign of the correlation between displacements and temperature variation. It also reveals an unexpected behaviour in a portion of the bridge retrofitted to prevent scour issues a few years before the dataset start date. Furthermore, the correlation between pier displacements and river level variations underscores the importance of considering environmental factors and the geotechnical characteristics of the foundation soils in bridge monitoring. The results obtained from this study are significant with a view to using this satellite InSAR-based monitoring for early detection of anomalous bridge behaviour on a large scale.