Identification of existing prestressing force of damaged girder using wavelet-based method

Abstract

Prestressed concrete girders have been widely used for bridge structures in Bangladesh for the last few decades. These bridges have been subjected to deterioration due to various reasons like weathering actions, accidents etc. over time. Discrepancy between the desired and the in-service prestressing forces can result in serviceability and safety problems. For retrofitting purposes of the PC girder bridges, it is important to identify the amount of effective prestress available in the girders. Identification of the existing prestressing force in damaged bridge girders are always challenging as the dynamic modal parameters along with physical properties changes with the damage. A method for identification of prestress force of a prestressed concrete bridge girder is presented using the measured structural dynamic responses. This studypresents development of a systematic procedure of implementing the Wavelet-Galerkin method for approximating solutions of the equation of motion of Euler-Bernoulli beam with axial loading. The fundamentals of wavelet analysis have been introduced by giving a brief review about different types of wavelets, continuous wavelet transform, and discrete wavelet transform. Similarities and dissimilarities between Fourier transform and Wavelet transform is also presented. Construction of wavelet systems by deriving the scaling function and filter coefficients are presented by giving an example of constructing Daubechies 6 coefficient system of wavelet scaling function. The focus of this investigation deals with solutions to the partial differential equation of aEuler-Bernoulli beam with axial loadings.Development of connection coefficients for Daubechies 6 and how the connection coefficient matrix is developed for different resolution to solve the differential equation is also derived. Finally, a case study of prestressed girders subjected to damage due to collision by a rescue ship,hasbeen presented where the prestress force of damaged and undamaged girdershas been evaluated by solving the beam equation using Wavelet-Galerkin method fordifferent loading conditions. Accelerometer data were taken from the mid-point of the damaged and undamaged girders for three different loading conditions. These loading conditions are free vibration data, vehicle axle load when the velocity of the vehicle is 7 km/hr, and vehicle axle load when the velocity of the vehicle is 25 km/hr. Frequency of the accelerometer data was 1000 hz. Data derived from the experiment were used in the Wavelet-Galerkin analysis to estimate the existing prestressing force. The variation of prestress force in damaged girders and undamaged girderswas also calculated. The analysis showed that the damaged Girder 1 has 73%, Girder 2 has 58%, and Girder 3 has 85% less effective prestress than the reference Girder 4 when the vehicle was moving at 7 km/hr velocity. And, Girder 1 has 87%, Girder 2 has 72%, and Girder 3 has 83% less effective prestress than the reference prestressing force when the vehicle was moving at 25 km/hr velocity.