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  • The response quantities obtained from both the response-spectrum analysis and the timehistory¬†analysis included bending moments, shear forces, axial forces, and displacements. A¬†detailed review of the response results showed that the observations from the shear forces¬†and the axial forces were the same as those from the bending moments. Given this, only the¬†bending moments and the displacements were used for the evaluation of the seismic¬†performance of the bridge. However only the results for bending moments are shown there,¬†the results for deflections can be found in [17].
    For simplicity in discussing the results, the simultaneous excitations in the longitudinal and vertical directions are referred to as excitations in the longitudinal direction (or longitudinal excitations), and those in the transverse and vertical directions are referred to as excitations in the transverse direction (or transverse excitations). This is the case for both the responsespectrum and the time-history analyses.
    To assist in understanding the results from the analyses, it is useful to describe the¬†convention for the moments, as used in this study. In reference to the coordinate system¬†shown in Fig. 5, longitudinal moments in the bridge girder are those that act about the Yaxis,¬†and transverse moments are those that act about the Z-axis. For the piers, the moments¬†that result from longitudinal excitations and act about the Y-axis are referred to as “moments¬†in the longitudinal direction”, and those that result from transverse excitations and act about¬†the X-axis are referred to as “moments in the transverse direction”.
    The moments at the joints of the model resulting from the response-spectrum analysis represent the maximum absolute values and by definition are positive. The time-history analysis provided a comprehensive set of results for each excitation motion. Time histories and maximum positive and negative values for the moments and displacements were obtained for the joints of the model. Moment and displacement envelopes for both the girder and the piers were determined using the largest absolute values of the computed (positive and negative) maxima for each of the selected sets of ground motions.
    The comparisons of bending moments are shown in Figs. 15 and 16. Figure 15(a) shows the¬†envelopes of the longitudinal moments in the bridge girder for seismic actions in the¬†longitudinal direction, and Fig. 15(b) shows the envelopes of the transverse moments for¬†seismic actions in the transverse direction. The moment envelopes are plotted using the¬†corresponding values at selected sections along the bridge girder. Similarly, Figs. 16(a) and¬†16(b) present the moment envelopes for pier P31 for excitations in the longitudinal and¬†transverse directions respectively. The moment envelopes for the other piers are similar to¬†those for pier P31, and they are not shown here. The designation “Design” in Figs. 15 and 16 is for the design responses which were calculated by [7], and “UHS” is for the responses due¬†to seismic actions represented by the uniform hazard spectrum. Furthermore, the¬†designations “World-wide”, “Saguenay”, “Miramichi”, and “Simulated” are respectively for¬†the responses due to the selected world-wide records ‚Äď short-period set (Fig. 10), the¬†Saguenay records (Fig. 12), the Miramichi records (Fig. 13), and the simulated motions ‚Ästshort-period hazard set (Fig. 14(a)).

    For the purpose of clarity, the results from the response-spectrum analysis (i.e., the “Design”¬†and the “UHS” results) are discussed first. It can be seen from Fig. 15(a) that for the seismic¬†actions in the longitudinal direction, the UHS envelope of the moments in the bridge girder¬†is somewhat higher than the design envelope. Also, the values of the UHS envelope for the¬†pier (Fig. 16(a)) resulting from the longitudinal seismic actions are larger than those of the¬†design envelope in the upper 25 m of the pier. The largest differences are approximately¬†20%. These observations for the longitudinal seismic actions were expected because the¬†periods of the predominant longitudinal and vertical modes of the bridge are shorter than¬†1.5 s, i.e., these are within the range in which the uniform hazard spectrum is higher than¬†the design spectrum (Fig. 3). For seismic actions in the transverse direction, the UHS¬†envelopes of the moments in the bridge girder and in the pier (Figs. 15(b) and 16(b),¬†respectively) are all smaller than the design values. This is because the uniform hazard¬†spectrum is lower than the design spectrum for the periods of the predominant transverse¬†modes, i.e., periods longer than approximately 2.0 s (Fig. 3).

    The 20% exceedance of the design responses by those from the UHS seismic actions in the¬†longitudinal direction does not represent any concern regarding the seismic safety of the¬†bridge. This is because of the following two reasons. First, conservative assumptions are¬†involved in the design through the use of factored material strengths and specified safety¬†factors, and therefore the actual capacity (i.e., resistance) of the bridge is substantially larger¬†than the demands due to design loads. For example, considering only the resistance factors for¬†concrete and reinforcing steel used in the design (i.e., ŌÜc=0.75 and ŌÜs=0.85, as specified in the¬†Design Criteria [5]), the nominal flexural resistance of the bridge is about 20% larger than the¬†design resistance. Other safety factors involved in the design, associated with the specified¬†safety index [5], provide even larger resistances relative to the design resistance of the bridge.
    The second reason is related to the conservatism of the response resulting from the uniform hazard spectrum. By definition, the uniform hazard spectrum at the bridge location represents the envelope of the spectral contributions of all possible earthquakes in the surrounding area that affect the seismic hazard at the location. This implies that the seismic response resulting from the uniform hazard spectrum represents the envelope of the response contributions from earthquakes with different magnitudes and at different  distances from the bridge location, assuming that all the earthquakes occur at the same time.
    Obviously, the response from such combined earthquake actions is much larger than the responses from each of the earthquakes considered separately. These considerations clearly show that the response-spectrum analysis using the uniform hazard spectrum provides significantly larger responses than those from expected seismic ground motions represented by that spectrum.

    In regard to the response results obtained from the time-history analysis of the model  subjected to the selected sets of excitations, it can be seen in Figs. 15 and 16 that the maximum moments are all smaller than the design responses for both the longitudinal and transverse excitations. This was expected based on the spectral characteristics of the excitation motions. As described earlier, the response spectra of the excitation motions used in the analysis (i.e., the World-wide short-period set, the Saguenay set, the Miramichi set, and the simulated short-period set) are all lower than the design spectrum for periods longer than approximately 0.5 s (Figs. 10, 12-14), i.e., within the period range of the longitudinal and transverse modes that produce almost the entire response. The contributions of the modes with periods below 0.5 s, where the spectra of the excitation motions exceed the design spectrum, are very small.

  • The objective of this study was to investigate the performance of the Confederation Bridge¬†due to seismic excitations expected at the bridge location. A finite element model of a typical¬†segment of the bridge was subjected to selected seismic motions representative of the¬†seismic hazard for the bridge location. The response results obtained from the dynamic¬†analysis of the model were compared with the seismic design parameters. The following are¬†the main conclusions from this study:
    Ôā∑ The responses from the linear time-history analyses (displacements and forces) were¬†found to be smaller than those used in the design of the bridge.
    Ôā∑ The longitudinal responses of some sections of the bridge obtained from the response¬†spectrum analysis (i.e., for seismic actions represented by the horizontal and vertical ¬†uniform hazard spectra) were found to be about 20% larger than the design values.

    Considering the conservatism in the design through the use of factored material strengths and specified safety factors, as well as the characteristics of the uniform hazard spectra, the exceedance of the design responses by 20% does not represent any concern regarding the safety of the bridge.
    Ôā∑ The general conclusion is that the seismic effects considered in the design are¬†appropriate for the required safety during the service life of the bridge.
    Ôā∑ A finite element model consisting of 3D beam elements is suitable for the Confederation¬†Bridge provided that the foundation flexibility is taken into account in the modeling.
    Ôā∑ The modeling method used in this study is considered to be applicable to single-box¬†girder bridges in general.

  • For the purpose of the seismic evaluation of the bridge, dynamic analyses were conducted¬†on the bridge model to determine the responses due to seismic actions represented by the¬†uniform hazard spectrum and the selected sets of records. Elastic material properties of the¬†model were assumed in the analyses. The dynamic analyses included both responsespectrum¬†analyses and time-history analyses.
    Response-spectrum analyses
    Response-spectrum analyses were performed for seismic actions represented by the uniform hazard spectrum. Separate response-spectrum analyses were carried out for the following two cases of seismic actions: (i) seismic actions in the longitudinal and vertical directions of the model; and (ii) seismic actions in the transverse and vertical directions. These two cases were considered appropriate since the longitudinal and the transverse modes are well separated, and the vertical modes are combined mainly with the longitudinal modes. The horizontal and the vertical actions were applied simultaneously at the bases of the piers. The horizontal seismic actions were represented by the horizontal uniform hazard spectrum (UHS) (Fig. 3), and the vertical actions were represented by a spectrum obtained by multiplying the horizontal UHS by 2/3. The factor of 2/3 is commonly used for defining vertical design spectra relative to horizontal spectra [9].
    The analyses included the first 100 modes, which covered all natural periods above 0.02 s. A modal damping of 5% was used for all the modes. The response maxima at each joint of the models were computed by combining the modal responses using the complete quadratic combination (CQC) rule.
    As required by the Canadian Highway Bridge Design Codes [24], the mass participation of the modes considered in the analysis is larger than 90% in each of the three principal directions of the model. Namely, the amounts of the mass participation of the longitudinal, transverse and vertical modes used in the analysis are 95.3%, 95.5% and 93.6% respectively.
    Time-history analyses
    Time-history analyses were conducted to determine the responses of the model subjected to the records of the selected sets. As in the response-spectrum analysis, simultaneous seismic excitations in the longitudinal and vertical directions, and in the transverse and vertical directions of the model were used in the time-history analysis. In each analysis, the seismic excitations consisted of a pair of scaled horizontal and vertical acceleration time histories applied at the bases of the piers.

    The mode-superposition method was used in the time-history analysis. As in the responsespectrum analysis, the first 100 modes and modal damping of 5% for all the modes were considered in the time-history analysis. The response time histories were obtained at equal time interval of 0.005 s.

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  • Given the uncertainties in the estimation of the seismic hazard for eastern Canada, a number¬†of time-history analyses were conducted using excitation motions well beyond the scenario¬†earthquake motions for the bridge location determined from the seismic hazard analysis as¬†discussed in Section 3.3. In total, five groups of different seismic excitations were¬†considered.

    Because of lack of strong seismic motion records in eastern Canada, two ensembles of ground motion records obtained during strong earthquakes around the world were used in this study. The ensembles are described in [18, 19] and are characterized by different peak ground acceleration to peak ground velocity ratios (A/V ratios). The average A/V ratio (A in g, and V in m/s) of the records of one of the ensembles is 2.06, and that of the other ensemble is 0.48. Based on the A/V ratios of the records, the ensembles are referred to as the high and low A/V ensembles. In general, high A/V ratios are characteristics of seismic motions from small to moderate earthquakes at short distances, and low A/V ratios are characteristics of seismic motions from large earthquakes at large distances. Regarding the frequency content, high A/V motions normally have a high frequency content, and low A/V motions have a low frequency content. Seismic motions with a high frequency content are characterized by predominant frequencies higher than approximately 2 Hz (i.e., periods lower than 0.5 s), and seismic motions with a low frequency content are characterized by predominant frequencies lower than 2 Hz (i.e.,periods longer than 0.5 s).

    In addition to the foregoing ensembles, ground motion records obtained during the 1988 Saguenay, Quebec earthquake, and the 1982 Miramichi, New Brunswick earthquake were used as excitation motions. Also, stochastic seismic motions generated for eastern Canada were used.

    High A/V excitations

    It is well known that seismic ground motions in eastern Canada are characterized by high frequency content and high A/V ratios [19, 20]. As discussed above, an ensemble of records with high A/V ratios from strong earthquakes around the world [19] was adopted for the analysis. The ensemble consisted of 13 pairs of horizontal and vertical records. The magnitudes of the earthquakes are between 5.25 to 6.9, the distances are between 4 km to 26 km. The average A/V ratio of the records is 2.06. It is necessary to mention that the magnitudes of these earthquakes cover the magnitude range of 6.0 to 6.75 of the scenario earthquakes for the short period ground motion hazard for the bridge location as discussed in Section 3.3.
    The excitation motions for the time-history analysis were obtained by scaling the records to the peak ground velocity of 7.1 cm/s computed by GSC for an annual probability of exceedance of 0.00027. These excitations are referred to as high A/V excitations. Figure 10 shows the acceleration response spectra of the scaled horizontal records of the ensemble. For comparison, the design spectrum is superimposed on the figure. It can be seen that the spectra of the records exceed significantly the design spectrum for periods shorter than approximately 0.5 s, and the spectra are well below the design spectrum for periods longer than 0.5 s.

    Low A/V excitations

    The low A/V ensemble consisted of 15 pairs of horizontal and vertical records of seismic ground motions [18]. The records were taken during strong earthquakes around the world with magnitudes ranging from 6.3 to 8.1. The distances at which the records were taken were within the range from 38 km to 469 km. The average A/V ratio of the records is 0.48. Both the magnitudes and the distances cover the magnitude and distance ranges of the scenario earthquakes for short and long period ground motion hazards for the bridge location determined from the seismic hazard analysis (see Section 3.3).

    Figure 11 shows the acceleration response spectra of the horizontal records of the low A/V ensemble scaled to the peak ground velocity of 7.1 cm/s. The design spectrum is also included in the figure. It can be seen that the spectra for the low A/V records are all enveloped by the design spectrum. Given this, no time-history analyses were conducted for this ensemble.

    Saguenay earthquake excitations

    It was of special importance for this study to investigate the performance of the bridge when subjected to seismic motions from earthquakes in eastern Canada. On November 25, 1988, an earthquake of magnitude of 5.7 occurred in the Saguenay region of the province of Quebec. This was the most significant earthquake in the past 50 years in eastern North America. Ground motion records were obtained at 16 sites at distances ranging from 43 km to 525 km [21, 22]. The response spectra for all horizontal records were scaled to the peak ground velocity for the bridge location of 7.1 cm/s and were compared with the design spectrum. Based on the comparison, 5 horizontal records and the companion vertical records were selected for the analysis. The scaled spectra of the horizontal records together with the design spectrum are shown in Fig. 12.

    It can be seen in the figure that the scaled spectra of the Saguenay earthquake motions are significantly higher than the design spectrum for periods below 0.25 s. The highest spectra (i.e., spectra of records No. 2 and No. 3) exceed the design spectrum by a factor of approximately 5.

    Miramichi earthquake excitations

    In 1982, several earthquakes occurred in the Miramichi region of the province of New Brunswick [23]. The epicentres of earthquakes were approximately 150 km from the bridge site. By considering the response spectra, three records representing the strongest motions during the earthquakes were selected for this study. It was found that the A/V ratios of the records are very high (about 11). Consequently, the ground motions from the Miramichi earthquakes are dominated by very short period (i.e., very high frequency) motions. The selected records were scaled to the peak ground velocity of 7.1 cm/s for the bridge location, and the scaled response spectra of the horizontal records are shown in Fig. 13. It can be seen clearly in Fig. 13 that the ground motions of the Miramich earthquakes are dominated by very short period (i.e., about 0.04 s). Figure 13 also shows that for the period of 0.04 s, the spectral acceleration for the strongest motion (i.e., record. No. 1) is approximately 9 times larger than the value of the design spectrum.

    Simulated excitations

    In addition to the “real” records of seismic ground motions discussed above, “simulated”¬†acceleration time histories (i.e., accelerograms) were also used as excitation motions. As¬†reported by [11] seismic hazard for eastern Canadian sites can be approximated using a¬†magnitude M=6.0 event to represent the short-period hazard, and M=7.0 event to represent¬†the long-period hazard. They simulated ground motion accelerograms for eastern Canada¬†for M=6.0 and M=7.0, and for different distances. For each distance, four accelerograms were¬†simulated for a probability of exceedance of 2% in 50 years (i.e., annual probability of¬†exceedance of 0.0004).

    Since the seismic hazard based on the service life and the importance of the bridge corresponds to an annual probability of exceedance of 0.00027, it was necessary to scale the simulated accelerograms to be consistent with the uniform hazard spectrum (UHS) for a probability of exceedance of 0.00027 (Fig. 3). To determine the short-period hazard motions for the bridge, the simulated accelerograms for the M=6.0 event were scaled to have the same spectral values at the period of 0.2 s as that of the UHS for the bridge location. Similarly, the long-period hazard motions were obtained by scaling the simulated accelerograms for the M=7.0 event to have the same spectral values as that of the UHS at the period of 2.0 s.

    Trial time-history analyses showed that the largest responses of the bridge model are associated with the scaled accelerograms corresponding to the epicentral distances of R=50 km for the M=6.0 event and R=100 km for the M=7.0 event, and therefore, only these accelerograms were considered. The response spectra of the scaled short-period hazard accelerograms (R=50 km, M=6.0) and long-period hazard accelerograms (R=100 km, M=7.0) are shown in Figs. 14(a) and 14(b) respectively. It can be seen in Fig. 14(a) that the spectra of the short-period hazard accelerograms exceed the design spectrum by a factor of approximately 2.5 for periods below 0.2 s. On the other hand, the spectra of the long-period hazard accelerograms (Fig. 14(b)) are only about 20% higher than the design spectrum for periods below 0.3 s. Given these observations, only the short-period hazard accelerograms were used as excitation motions in the time-history analysis.

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  • The model shown in Fig. 5 was calibrated using records of vibrations and tilts of the bridge¬†obtained during a full scale tests of the bridge were conducted on April 14, 1997, about two¬†months before the official opening of the bridge. The objectives of the tests were: (i) to¬†measure the deflection of the bridge pier under static loads, and (ii) to measure the free¬†vibrations of the pier due to a sudden release of the static load. The instrumentation of the¬†bridge (Fig. 6) was used to measure the bridge response during the pull tests. It consists of¬†76 accelerometers and 2 tiltmeters. The accelerometers were used to measure acceleration¬†time histories of the response of the bridge. The two tiltmeters installed at locations 3 and 4¬†of pier P31 were used to measure the tilts of the pier.

    The first pull test was a static test. Using a steel cable, a powerful ship pulled pier P31 in the transverse direction of the bridge. The pulling was at the top of the ice shield, approximately 6 m above the mean sea level. The force was increased steadily up to 1.43 MN, and then released slowly.
    The second pull test was a dynamic test. In this test, the load was applied at a slow rate up to 1.40 MN and then suddenly released. This triggered free vibrations of the bridge, which were recorded by several accelerometers. The acceleration time history of the transverse vibrations recorded at the middle of span P31-P32 (location 9 in Fig. 6) along with the recorded tilts at locations 3 and 4 were used in the calibration of the model.

    The parameter that was varied in the calibration process was the foundation stiffness.
    Rotational springs in the longitudinal and transverse directions were introduced in the model, at the bases of the piers, to represent the foundation stiffness. A trial value of the stiffness of the springs was initially selected, and a number of iterations of static and dynamic elastic analyses were performed in order to determine the stiffness that provides a close match between the computed and the measured tilts and free vibrations of the bridge.
    In each iteration, the tilts and the response were computed by using a load function closely representing the actual loading during the test. A modulus of elasticity of the concrete of 40,000 MPa was used in the analyses. This value was based on experimental data for the bridge [14], and is representative of the modulus of elasticity at the time when the test was conducted.

    It was found that the model with a rotational stiffness of 3.35◊109 kN¬∑m/rad provides the¬†best matching of the computed and measured responses. Figure 7 shows the measured and¬†the computed acceleration time histories of the transverse vibrations of the bridge girder at¬†the mid-span between piers P31 and P32, and Fig. 8 shows the Fourier amplitude spectra of¬†these time histories. It can be seen in Fig. 7 that the computed response of the bridge is very¬†similar to the measured response. Also, Fig. 8 shows that the Fourier amplitude spectra of¬†the computed and the measured responses are quite close. Note that the first two¬†predominant frequencies of the computed response of 0.51 Hz and 1.28 Hz correspond¬†respectively to the 7th and the 18th modes of the model.
    Table 2 shows the natural periods of the first ten modes obtained from dynamic analysis of the model. For illustration, the vibrations of the first five modes are presented in Fig. 9. It is necessary to mention that a similar model was developed by Lau et al. [15] using the computer program COSMOS [16]. The natural periods and mode shapes of that model are very close to those of the model developed in this study.
    It is useful to mention that certain variations of the dynamic properties of the model are expected due to different effects. For example, the modulus of elasticity increases with the age of concrete and varies due to temperature changes. Also, the responses used in the calibration of the model are substantially smaller than those from expected seismic motions at the bridge location. A comprehensive investigation of the possible variations of the dynamic properties due to the foregoing effects conducted by [17] showed that these variations are insignificant from practical point of view, therefore, the model developed as described above is considered appropriate for the seismic evaluation of the bridge.

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