Tommy H.T. Chan

Fatigue analysis and life prediction of bridges with structural health monitoring data — Part I: methodology and strategy

Abstract This paper is aimed at developing a methodology and strategy for fatigue damage assessment and life prediction of bridge-deck sections of existing bridges with online structural health monitoring data. A fatigue damage model based on the continuum damage mechanics (CDM) is developed for evaluating accumulative fatigue damage of existing bridges. A structural model for the fatigue stress analysis of bridge-deck structures is proposed, in which structures are modeled by elastic members and welded connections with possible accumulative damage. Based on the proposed model, an analytical approach for evaluating the fatigue damage and service life of bridge-deck sections based on strain history data from an online structural health monitoring system and the CDM fatigue model are suggested. The updating of the representative block of cycles of the local stress by online monitoring data in the future is included in the computational approach. In order to compare results of fatigue damage and service life prediction evaluated by the CDM fatigue damage model, a modified Palmgren–Miner rule is developed for the same fatigue problem.

Moving Force Identification—A Frequency and Time Domains Analysis

This paper addresses the problem of identifying a system of forces from vehicle crossing a guideway using only the vibration responses caused by the forces as the input without knowledge of the vehicle characteristics The vehicle is modeled as a single axle and two-axle loads with fixed axle spacing moving on a simply supported beam with viscous damping. The equations of motion of the beam are obtained through modal coordinate transformation, and the resulting set of equations relating the Fourier transforms of the responses and the moving forces are converted into time domain by a new method proposed by the authors. Correctness of the identified forces are checked by the correlation between the measured responses and the responses reconstructed with the identified forces moving on the beam. Experimental result shows that the method is effective to give good correlation when both measured bending moment and acceleration are rued, and it is faster and it gives more accurate estimate of the total mass of the vehicle than an existing method.

Fatigue analysis and life prediction of bridges with structural health monitoring data — Part II: application

Abstract This paper is a continuation of the paper titled “FATIGUE ANALYSIS AND LIFE PREDICTION OF BRIDGES WITH STRUCTURAL HEALTH MONITORING DATA — PART I: METHODOLOGY AND STRATEGY” with the emphasis on application of the developed method to the fatigue damage assessment of the Tsing Ma Bridge. Based on the methodology and strategy of the fatigue analysis presented in Part I, fatigue damage analysis and service life prediction of the bridge–deck section of the Tsing Ma Bridge (TMB) are carried out by using the strain-time history data measured by the structural health monitoring system of the bridge. The stress spectrum of the representative block of cycles at the location of strain gauges in a typical longitudinal truss is obtained by rainflow counting of cycles of stress history and statistical analysis on daily samples of daily stress spectrum. The effect of low stress cycles on the fatigue and service life is considered by modifying the stress range when it is less than a limit value of stress range. Results of fatigue damage and service life are calculated respectively by the model developed in Part I and Miners rule are compared. The influence of updating on the calculation of fatigue damage and predicted service life is numerically investigated. The result shows that the magnitude of the stress range of the bridge–deck section considered on TBM is in the region of greatest concern of bridge fatigue, and values of fatigue damage and predicted service life, as an estimation of the state of fatigue for the bridge, are found to be reasonable.

Moving force identification based on the frequency-time domain method

This paper addresses the problem on the identification of moving vehicle axle loads based on measured bridge responses using a frequency-time domain method. The focus is on the evaluation of two solutions to the overdetermined set of equations established as part of the identification method. The two solutions are (i) direct calculation of the pseudo-inverse and (ii) calculation of the pseudo-inverse via the singular value decomposition (SVD) technique. For this purpose, a bridge-vehicle system model was fabricated in the laboratory and the bending moment responses of bridge model were measured as a two-axle vehicle model moved across the bridge deck. The moving axle loads are then calculated from the measured responses via the two solutions to the over-determined set of equations. The effects of changes in the bridge-vehicle system, measurement and algorithm parameters on the two solutions are evaluated. Case studies show that the moving force identification is more feasible and its accuracy acceptable with the use of the SVD technique. This technique can effectively enhance the identification method and improve the identification accuracy over that of the direct pseudo-inverse solution.

Finite element modelling for fatigue stress analysis of large suspension bridges

Fatigue is an important failure mode for large suspension bridges under traffic loadings. However, large suspension bridges have so many attributes that it is difficult to analyze their fatigue damage using experimental measurement methods. Numerical simulation is a feasible method of studying such fatigue damage. In British standards, the finite element method is recommended as a rigorous method for steel bridge fatigue analysis. This paper aims at developing a finite element (FE) model of a large suspension steel bridge for fatigue stress analysis. As a case study, a FE model of the Tsing Ma Bridge is presented. The verification of the model is carried out with the help of the measured bridge modal characteristics and the online data measured by the structural health monitoring system installed on the bridge. The results show that the constructed FE model is efficient for bridge dynamic analysis. Global structural analyses using the developed FE model are presented to determine the components of the nominal stress generated by railway loadings and some typical highway loadings. The critical locations in the bridge main span are also identified with the numerical results of the global FE stress analysis. Local stress analysis of a typical weld connection is carried out to obtain the hot-spot stresses in the region. These results provide a basis for evaluating fatigue damage and predicting the remaining life of the bridge.

Moving force identification using an existing prestressed concrete bridge

Field measurements were carried out for a moving force identification study using an existing prestressed concrete bridge. A two-axle heavy vehicle was hired for the calibration test of the field measurements. The dynamic bending moments of the test bridge deck brought about by both hired and in-service vehicles were acquired. Dynamic axle forces were identified by means of the time-domain method. Results show that the axle forces can be identified with acceptable results for both hired and in-service vehicles. Therefore the method is valid for identifying dynamic axle forces. Gross weights were obtained by summing up the equivalent axle load of each axle. The fundamental frequencies of the vehicles were obtained by converting the corresponding axle loads identified in the time domain to the frequency domain by using fast Fourier transformation.

Vertical Displacement Measurements for Bridges Using Optical Fiber Sensors and CCD Cameras — A Preliminary Study

Bridge managers all over the world are always looking for simple ways to measure bridge vertical displacements for structural health monitoring. However, traditional methods to obtain such data are either tedious or expensive. There is a need to develop a simple, inexpensive, and yet practical method to measure bridge vertical displacements. This paper proposes two methods using either optical fiber (FBG) sensors or a charge-coupled-device (CCD) camera, respectively, for vertical displacement measurements of bridges. The FBG sensor method is based on the measured horizontal strains together with the identified curvature functions obtained by a self-developed FBG Tilt sensor. CCD cameras use a large number of pixels to form an image. The CCD camera method utilizes image processing techniques for pixel identification and subsequent edge detection. A preliminary study to validate the proposed methods in laboratory was presented. The tests include applying the methods to determine the vertical displacements separately for a concrete beam and a steel beam under various loadings. The comparisons include their installations, costs, degrees of accuracy, external factors affecting the measurement, etc. It was concluded that both methods could be used for vertical displacement measurement, and they could be complementary with one another. It was suggested to further improve the two methods developed and a successful outcome will not only help to solve an important problem for bridge management, but also prepare the way for better structural health monitoring techniques.

Statistical analysis of online strain response and its application in fatigue assessment of a long-span steel bridge

This paper covers reliability assessment of the fatigue life of a bridge-deck section based on the statistical analysis of the strain-time histories measured by the structural health monitoring system permanently installed on the long-span steel bridge under study. Through statistical analysis of online strain responses in the frequency domain using multiple linear regression, a representative block of daily cycles of strain history is obtained. It is further assumed that all cycles of online strain response during bridge service are repetitions of the representative block. The rain-flow counting method is then used to determine the stress spectrum of the representative block of daily cycles. The primary assessment of fatigue life at a given value of failure probability is undertaken for the sample component in a bridge-deck section by using the classification of details for welded bridge components and the associated statistical fatigue model provided by the British Standard BS5400. In order to evaluate bridge fatigue at any value of failure probability, a modified probability model is proposed based on BS5400. The fatigue life of the considered component in the bridge-deck section is then evaluated for some other values of probability of failure which are not included in BS5400 by use of the modified probability model. The analytical results show that the modified model is practical for reliable evaluation of the service life of existing bridges under random traffic loading.

Fatigue Damage Model for Bridge under Traffic Loading: Application Made to Tsing Ma Bridge

A fatigue damage model is developed to account for the damage accumulation process in bridges subjected to in-field traffic loading. Continuous damage mechanics (CDM) is applied to formulate damage kinetic constitutive equations. On-line strain gauge measurements are then made on the orthotropic steel deck structure of the Tsing Ma Bridge, an essential portion of the transport network for the Hong Kong airport. Fatigue life prediction analyses are then made. The results agree well with those obtained by the tests.

Efficient numerical model for the damage detection of large scale structure

A structural modeling methodology is proposed, based on the concept of Damage-Detection-Orientated-Modeling, in which a super-element representing a segment of a large-scale structure, e.g. a bridge deck, is developed. Each individual structural component is represented by a sub-element in the model. The large number of degrees-of-freedom in the analytical model is reduced, while the modal sensitivity relationship of the structural model to small physical changes is retained at the sub-element level. These properties are significant to structural damage assessment. The concept of a generic sub-element is introduced in the parameter selection strategy for model updating, and the initial finite super-element model of the structure is updated using the eigensensitivity method. Numerical studies are presented to illustrate the super-element model and model updating method. Modal frequencies and the mode shapes of the updated analytical models agree fairly well with the simulated measurements with or without noise and using incomplete measurements with a maximum error of 12%.