**5. Calibration of the model using data of full scale test**

264 Earthquake Engineering

the whole bridge.

Z

Mass

X

Y

Bridge [e.g., 14,15].

**4. Modelling of the bridge** 


The structural system of the bridge allows the development of a model of a selected segment of the bridge rather than modelling the entire bridge. Because of the repetitiveness of the units of the structural system (i.e., portal frames and drop-in girders) along the bridge, a proper model of a selected segment would be quite representative of

**Figure 5.** Model of two portal frames and one drop-in span using 3-D beam elements.

P31

weight of each drop-in girder were applied at the ends of the overhangs.

segment is quite representative of the main bridge.

P32 -29.3 m

+39.24 m

Figure 5 shows the model used in this study. It is a three-span frame model consisting of 3-D beam elements. The modelling was conducted using the computer program SAP 2000 [13]. The model represents the bridge segment between piers P29 and P32 (Fig. 1), which consists of two rigid portal frames (P29-P30 and P31-P32), and one drop-in span (P30-P31). This segment was modelled since it is the instrumented portion of the bridge, and recorded data is available for use in the calibration of the model. Also, the height of the piers of this

 -33.6 m P29

Mass

Bearings

95 m 250 m 250 m 250 m 95 m

 -28.4 m P30

0.0 Water level

Drop-in girder (60 m)

The model consists of 179 beam elements and 180 joints. The bridge girder is modelled by 123 elements, and each pier is modelled by 14 elements. The interaction with the adjacent drop-in girders (left of P32, and right of P29) was modelled by adding masses at the ends of the overhangs, as shown in Fig. 5. A half the mass of each drop-in girder was added at the end of the supporting overhang in transverse and vertical directions, full mass was added in the longitudinal direction for a hinge connection, and no mass was added in the longitudinal direction for a sliding connection. Similarly, vertical forces from a half the

In addition to the three-span model (Fig. 5), a single-span model consisting of a single portal frame (P31-P32), and a five-span model with three portal frames and two spans with drop-in girders (between P29 and P34; Fig. 1) were also considered. While the natural periods and mode shapes of these three models were quite comparable, the three-span model was chosen for the analysis in this study because it provides results for both the portal frame spans and the spans with drop-in girders, and requires an acceptable computation time for the analysis. The single-span model does not provide results for the drop-in girder, and the five-span model requires an excessive computation time. Note that the segment shown in Fig. 5 is normally used as a typical segment in studies on the behaviour of the Confederation 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.

**Figure 6.** Locations of accelerometers: (a) instrumented sections of the bridge girder and piers, and (b) locations of accelerometers in the girder.

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.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 267

Measured Computed

Measured Computed

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

**Figure 8.** Fourier amplitude spectra of measured and computed acceleration time histories of vibrations

0 1 2 3 4 5 6 7 8 9 10 Frequency (Hz)

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

Mode No. Period (s) Mode type 1 3.13 Transverse 2 2.99 Transverse 3 2.72 Transverse 4 2.48 Transverse 5 2.22 Transverse 6 2.13 Longitudinal 7 2.08 Transverse 8 2.01 Longitudinal 9 1.54 Vertical 10 1.43 Vertical

**Table 2.** Natural periods of the first 10 modes of the bridge model.

**6. Seismic excitations for time-history analysis** 

at midspan between piers P31 and P32.

0

20

40

60

Amplitude (mm/s)

Amplitude (mm/s)

80

100

120

140

considered.

described above is considered appropriate for the seismic evaluation of the bridge.

**Figure 7.** Acceleration time histories of transverse vibrations at midspan between piers P31 and P32 (a) measured, (b) computed.

It was found that the model with a rotational stiffness of 3.35x109 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.

266 Earthquake Engineering

(a) measured, (b) computed.


Acceleration (mm/s 2

)

(b)


Acceleration (mm/s 2

)

(a)

respectively to the 7th and the 18th modes of the model.

very close to those of the model developed in this study.

**Figure 7.** Acceleration time histories of transverse vibrations at midspan between piers P31 and P32

It was found that the model with a rotational stiffness of 3.35x109 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

0 5 10 15 20 25 30 35 40 Time (s)

0 5 10 15 20 25 30 35 40 Time (s)

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

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

**Figure 8.** Fourier amplitude spectra of measured and computed acceleration time histories of vibrations at midspan between piers P31 and P32.


**Table 2.** Natural periods of the first 10 modes of the bridge model.

#### **6. Seismic excitations for time-history analysis**

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.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 269

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

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

**Figure 10.** Design spectrum and scaled response spectra of high A/V excitations; 5% damping.

location determined from the seismic hazard analysis (see Section 3.3).

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

0 0.5 1 1.5 2 2.5 3 3.5 4 Period (s)

**6.1. High A/V excitations** 

in Section 3.3.

than 0.5 s.

**6.2. Low A/V excitations** 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Spectral acceleration (g)

**Figure 9.** Mode shapes of the bridge model.

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.

#### **6.1. High A/V excitations**

268 Earthquake Engineering

**Figure 9.** Mode shapes of the bridge model.

were used.

frequencies lower than 2 Hz (i.e.,periods longer than 0.5 s).

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

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 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.

**Figure 10.** Design spectrum and scaled response spectra of high A/V excitations; 5% damping.

#### **6.2. 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).

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 271

Design spectrum No.1 No.2 No.3

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

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

**Figure 13.** Design spectrum and scaled response spectra of Miramichi earthquake 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

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Period (s)

approximately 5.

5% damping.

**6.5. Simulated excitations** 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spectral acceleration (g)

exceedance of 0.0004).

**6.4. Miramichi earthquake excitations** 

larger than the value of the design spectrum.

**Figure 11.** Design spectrum and scaled response spectra of low A/V excitations; 5% damping.

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.

#### **6.3. 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.

**Figure 12.** Design spectrum and scaled response spectra of Saguenay earthquake excitations; 5% damping.

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.

#### **6.4. Miramichi earthquake excitations**

270 Earthquake Engineering

**Figure 11.** Design spectrum and scaled response spectra of low A/V excitations; 5% damping.

**6.3. Saguenay earthquake excitations** 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Spectral acceleration (g)

with the design spectrum are shown in Fig. 12.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Spectral acceleration (g)

5% damping.

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.

0 0.5 1 1.5 2 2.5 3 3.5 4 Period (s)

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

**Figure 12.** Design spectrum and scaled response spectra of Saguenay earthquake excitations;

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Period (s)

Design No.1 No.2 No.3 No.4 No.5

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.

**Figure 13.** Design spectrum and scaled response spectra of Miramichi earthquake excitations; 5% damping.

#### **6.5. 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.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 273

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

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 response-

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

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

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 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

the time-history analysis.

**Response-spectrum analyses** 

combination (CQC) rule.

**Time-history analyses** 

applied at the bases of the piers.

**7. Dynamic analysis and results** 

spectrum analyses and time-history analyses.

vertical design spectra relative to horizontal spectra [9].

**Figure 14.** Design spectrum and scaled response spectra of simulated excitations; 5% damping (a) short-period hazard motions, (b) long-period hazard motions.

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.
