**3. Seismic design parameters and seismic hazard for the bridge**

#### **3.1. Seismic design parameters**

The design life of 100 years and the safety index of 4.0 were the basic design requirements for the Confederation Bridge. These requirements were much higher than those prescribed in the highway bridge design codes available at the time when the bridge was designed. The specified design life and safety index for the Confederation Bridge required special studies in order to determine the seismic ground motion parameters at the bridge location.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 261

Design spectrum Uniform hazard spectrum

period range (T > 3.0 s), which is a common approach for constructing design spectra based on peak ground motions and spectral amplification factors [8]. The vertical design spectrum was taken as 2/3 of the horizontal spectrum [5], which is also a common practice for defining

Period, T(s) Governing parameter Spectral acceleration (g) < 0.5 Acceleration = 0.326 g 0.326 0.5 – 3.0 Velocity = 24.8 cm/s 0.1589 / T > 3.0 Displacement = 11.8 cm 0.48 / T 2

Figure 3 shows the horizontal seismic design spectrum. The other spectrum in the figure,

Since the development of the design parameters for the Confederation Bridge in early 1990s, there have been significant advances in the understanding of the seismic hazard in Canada. New source models, and most updated software have been used for the assessment of the seismic hazard. It should be mentioned, however, that there are still significant uncertainties in the estimation of seismic hazard. As pointed out by [10], the ground motion attenuation relations for eastern Canada are the major source of uncertainty in the seismic hazard estimations. This is because of lack of recordings of ground motions from strong earthquakes in eastern Canada for use in the calibration of the attenuation relations. It is noted that the ground motion attenuation relations for eastern Canada may change

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

The seismic hazard in Canada is currently represented by uniform hazard spectra rather than by peak ground motions. A uniform hazard spectrum represents an acceleration

**Table 1.** Parameters of the design spectrum for horizontal seismic motion; 5% damping [5].

vertical design spectra, based on the findings reported in [9].

designated "uniform hazard spectrum" is discussed below.

**Figure 3.** Design and uniform hazard spectra; 5% damping.

significantly as new events are recorded as reported in [10].

**3.2. Seismic hazard for the bridge location** 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Spectral acceleration (g)

The seismic ground motion parameters used in the design of the bridge were given in the design criteria specified by J. Muller International – Stanley Joint Venture Inc. [5]. These included the peak ground acceleration, the peak ground velocity, the peak ground displacement, and the seismic design spectrum for the bridge location. The methods for determining these parameters were described by [6]. Two methods were used for the estimation of the peak ground acceleration of the expected seismic motions at the bridge location. The first method was based entirely on probabilistic considerations. According to this method, the peak ground acceleration for the design service life of 100 years and the design safety index of 4.0 corresponded to an annual probability of exceedance of 0.00027. The value of the peak ground acceleration for this probability of exceedance was found to be A=0.136 g.

The second method was primarily based on engineering considerations. In this method, first, the peak ground acceleration was determined for a probability of exceedance of 10% during the design service life of 100 years. The background for this was to keep the same probability of exceedance during the service life as that required by the 1990 edition of the National Building Code of Canada (NBCC) [7]. Then, the acceleration value corresponding to 10% in 100 years probability of exceedance was increased by applying a factor of 1.43 representing the product of the commonly used importance factor of 1.3, and an additional importance factor of 1.1 because of the unusual importance of the bridge. The resulting peak ground acceleration was 0.12 g, and this value was adopted for the design. Using the same approach, the peak ground velocity was found to be 10.8 cm/s. Having the values for the peak ground acceleration (A) and the peak ground velocity (V), a value for the peak ground displacement (D) of 5.9 cm was obtained using the relationship between A, V, and D, proposed by [8].

The 5% damped elastic seismic design spectrum for horizontal seismic motions was developed using the foregoing values for the peak ground acceleration, velocity and displacement, and applying the corresponding spectral amplification factors proposed by [8] for the mean plus one standard deviation level. This level corresponds to a probability of 84% that the spectral amplification factors will not be exceeded. The parameters for the construction of the horizontal design spectrum are given in Table 1, adopted from the design criteria. It can be seen that the spectrum was defined assuming a constant spectral acceleration in the short period range (T<0.5 s), a constant spectral velocity in the intermediate period range (0.5 s < T< 3.0 s), and a constant spectral displacement in the long period range (T > 3.0 s), which is a common approach for constructing design spectra based on peak ground motions and spectral amplification factors [8]. The vertical design spectrum was taken as 2/3 of the horizontal spectrum [5], which is also a common practice for defining vertical design spectra, based on the findings reported in [9].


**Table 1.** Parameters of the design spectrum for horizontal seismic motion; 5% damping [5].

Figure 3 shows the horizontal seismic design spectrum. The other spectrum in the figure, designated "uniform hazard spectrum" is discussed below.

**Figure 3.** Design and uniform hazard spectra; 5% damping.

#### **3.2. Seismic hazard for the bridge location**

260 Earthquake Engineering

A=0.136 g.

proposed by [8].

**3.1. Seismic design parameters** 

**3. Seismic design parameters and seismic hazard for the bridge** 

in order to determine the seismic ground motion parameters at the bridge location.

The design life of 100 years and the safety index of 4.0 were the basic design requirements for the Confederation Bridge. These requirements were much higher than those prescribed in the highway bridge design codes available at the time when the bridge was designed. The specified design life and safety index for the Confederation Bridge required special studies

The seismic ground motion parameters used in the design of the bridge were given in the design criteria specified by J. Muller International – Stanley Joint Venture Inc. [5]. These included the peak ground acceleration, the peak ground velocity, the peak ground displacement, and the seismic design spectrum for the bridge location. The methods for determining these parameters were described by [6]. Two methods were used for the estimation of the peak ground acceleration of the expected seismic motions at the bridge location. The first method was based entirely on probabilistic considerations. According to this method, the peak ground acceleration for the design service life of 100 years and the design safety index of 4.0 corresponded to an annual probability of exceedance of 0.00027. The value of the peak ground acceleration for this probability of exceedance was found to be

The second method was primarily based on engineering considerations. In this method, first, the peak ground acceleration was determined for a probability of exceedance of 10% during the design service life of 100 years. The background for this was to keep the same probability of exceedance during the service life as that required by the 1990 edition of the National Building Code of Canada (NBCC) [7]. Then, the acceleration value corresponding to 10% in 100 years probability of exceedance was increased by applying a factor of 1.43 representing the product of the commonly used importance factor of 1.3, and an additional importance factor of 1.1 because of the unusual importance of the bridge. The resulting peak ground acceleration was 0.12 g, and this value was adopted for the design. Using the same approach, the peak ground velocity was found to be 10.8 cm/s. Having the values for the peak ground acceleration (A) and the peak ground velocity (V), a value for the peak ground displacement (D) of 5.9 cm was obtained using the relationship between A, V, and D,

The 5% damped elastic seismic design spectrum for horizontal seismic motions was developed using the foregoing values for the peak ground acceleration, velocity and displacement, and applying the corresponding spectral amplification factors proposed by [8] for the mean plus one standard deviation level. This level corresponds to a probability of 84% that the spectral amplification factors will not be exceeded. The parameters for the construction of the horizontal design spectrum are given in Table 1, adopted from the design criteria. It can be seen that the spectrum was defined assuming a constant spectral acceleration in the short period range (T<0.5 s), a constant spectral velocity in the intermediate period range (0.5 s < T< 3.0 s), and a constant spectral displacement in the long Since the development of the design parameters for the Confederation Bridge in early 1990s, there have been significant advances in the understanding of the seismic hazard in Canada. New source models, and most updated software have been used for the assessment of the seismic hazard. It should be mentioned, however, that there are still significant uncertainties in the estimation of seismic hazard. As pointed out by [10], the ground motion attenuation relations for eastern Canada are the major source of uncertainty in the seismic hazard estimations. This is because of lack of recordings of ground motions from strong earthquakes in eastern Canada for use in the calibration of the attenuation relations. It is noted that the ground motion attenuation relations for eastern Canada may change significantly as new events are recorded as reported in [10].

The seismic hazard in Canada is currently represented by uniform hazard spectra rather than by peak ground motions. A uniform hazard spectrum represents an acceleration

spectrum with spectral ordinates that have the same probability of exceedance. Uniform hazard spectra can be computed for different probabilities and different confidence levels. Confidence levels of 50% (median) and 84% are typically used for uniform hazard spectra. These levels represent the confidence (in %) that the spectral values will not be exceeded for the specified probability.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 263

**Figure 4.** Magnitude-distance contributions to the seismic hazard of the Confederation Bridge, (a) for

Figure 4(a) shows the contributions to the seismic hazard for period of 0.2 s, representing the short period ground motion hazard, while Fig. 4(b) shows the contributions for period of 2.0 s, representing the long period ground motion hazard. The contributions are computed for magnitude increments of 0.25, and distance increments of 20 km. It can be seen in Fig. 4(a) that the scenario earthquakes that have predominant contributions to the short period ground motion hazard are with magnitude ranging from 6 to 6.75 at distances of 60 km to 80 km. Similarly, Fig. 4(b) shows that the scenario earthquakes that have predominant contributions to the long period ground motion hazard are with magnitudes ranging from

spectral acceleration at period of 0.2 s, and (b)for spectral acceleration at period of 2.0 s.

7.25 to 7.5 at distances of approximately 500 km.

For the purpose of this study, Geological Survey of Canada (GSC) computed the uniform hazard spectrum for the bridge location for an annual probability of exceedance of 0.00027 and confidence levels of 50% and 84%. Among the two confidence levels, the uniform hazard spectrum at the 84% confidence level was used in this study. The 84% (rather than 50%) level was chosen since the spectral amplification factors used in the development of the design spectrum are for that level. The 84% level uniform hazard spectrum (UHS) is shown in Fig. 3. The spectral values for periods below 2.0 s were provided by GSC. For periods between 2.0 s and 4.0 s, the spectrum was extended assuming a constant spectral velocity with the same value as that at 2.0 s. This is the same as assumed in the defining of the spectral values in the intermediate period range of the design spectrum.

It can be seen in Fig. 3 that the uniform hazard spectrum is somewhat higher than the design spectrum for periods below 1.5 s. As will be discussed later, this difference does not have significant effects on the seismic response of the bridge.

#### **3.3. Scenario earthquakes for the bridge location**

The seismic hazard at a given site represents the sum of the hazard contributions of different earthquakes at different distances from the site. For each site, however, there are a few earthquakes that have dominant contributions to the hazard. These earthquakes are normally referred to as scenario or predominant earthquakes. The shape of the uniform hazard spectrum for a given site, representing the seismic hazard for the site, depends on the magnitudes of the scenario earthquakes and the distances of these earthquakes from the site. In general, the dominant contribution to the short period ground motion hazard is from small to moderate earthquakes at small distances, whereas larger earthquakes at greater distance contribute most strongly to the long period ground motion hazard.

For the purpose of the selection of earthquake ground motions for use in the seismic analyses, it is necessary to determine the scenario earthquakes for the Confederation Bridge. This can be done by computing the seismic hazard contributions of selected magnitudedistance ranges that cover all possible magnitude-distance combinations. Figure 4, provided by Geological Survey of Canada, shows the magnitude-distance contributions for the Confederation Bridge for annual probability of exceedance of 0.000404 (i.e., 2% in 50 years). Such graph could not be produced for a probability of exceedance of 0.00027 because of the uncertainties in the hazard analysis due to the extrapolations relative to the current hazard models. However, it was reported by [11] that the predominant magnitude increases very slowly as probability decreases. Also, results reported in [12] indicated that the lowering of the probability has small effects on the predominant magnitude and distance values. Given this, the magnitude-distance contributions shown in Fig. 4 were considered to be representative of those for probability of exceedance of 0.00027.

the specified probability.

spectrum with spectral ordinates that have the same probability of exceedance. Uniform hazard spectra can be computed for different probabilities and different confidence levels. Confidence levels of 50% (median) and 84% are typically used for uniform hazard spectra. These levels represent the confidence (in %) that the spectral values will not be exceeded for

For the purpose of this study, Geological Survey of Canada (GSC) computed the uniform hazard spectrum for the bridge location for an annual probability of exceedance of 0.00027 and confidence levels of 50% and 84%. Among the two confidence levels, the uniform hazard spectrum at the 84% confidence level was used in this study. The 84% (rather than 50%) level was chosen since the spectral amplification factors used in the development of the design spectrum are for that level. The 84% level uniform hazard spectrum (UHS) is shown in Fig. 3. The spectral values for periods below 2.0 s were provided by GSC. For periods between 2.0 s and 4.0 s, the spectrum was extended assuming a constant spectral velocity with the same value as that at 2.0 s. This is the same as assumed in the defining of

It can be seen in Fig. 3 that the uniform hazard spectrum is somewhat higher than the design spectrum for periods below 1.5 s. As will be discussed later, this difference does not

The seismic hazard at a given site represents the sum of the hazard contributions of different earthquakes at different distances from the site. For each site, however, there are a few earthquakes that have dominant contributions to the hazard. These earthquakes are normally referred to as scenario or predominant earthquakes. The shape of the uniform hazard spectrum for a given site, representing the seismic hazard for the site, depends on the magnitudes of the scenario earthquakes and the distances of these earthquakes from the site. In general, the dominant contribution to the short period ground motion hazard is from small to moderate earthquakes at small distances, whereas larger earthquakes at greater

For the purpose of the selection of earthquake ground motions for use in the seismic analyses, it is necessary to determine the scenario earthquakes for the Confederation Bridge. This can be done by computing the seismic hazard contributions of selected magnitudedistance ranges that cover all possible magnitude-distance combinations. Figure 4, provided by Geological Survey of Canada, shows the magnitude-distance contributions for the Confederation Bridge for annual probability of exceedance of 0.000404 (i.e., 2% in 50 years). Such graph could not be produced for a probability of exceedance of 0.00027 because of the uncertainties in the hazard analysis due to the extrapolations relative to the current hazard models. However, it was reported by [11] that the predominant magnitude increases very slowly as probability decreases. Also, results reported in [12] indicated that the lowering of the probability has small effects on the predominant magnitude and distance values. Given this, the magnitude-distance contributions shown in Fig. 4 were considered to be

the spectral values in the intermediate period range of the design spectrum.

distance contribute most strongly to the long period ground motion hazard.

representative of those for probability of exceedance of 0.00027.

have significant effects on the seismic response of the bridge.

**3.3. Scenario earthquakes for the bridge location** 

**Figure 4.** Magnitude-distance contributions to the seismic hazard of the Confederation Bridge, (a) for spectral acceleration at period of 0.2 s, and (b)for spectral acceleration at period of 2.0 s.

Figure 4(a) shows the contributions to the seismic hazard for period of 0.2 s, representing the short period ground motion hazard, while Fig. 4(b) shows the contributions for period of 2.0 s, representing the long period ground motion hazard. The contributions are computed for magnitude increments of 0.25, and distance increments of 20 km. It can be seen in Fig. 4(a) that the scenario earthquakes that have predominant contributions to the short period ground motion hazard are with magnitude ranging from 6 to 6.75 at distances of 60 km to 80 km. Similarly, Fig. 4(b) shows that the scenario earthquakes that have predominant contributions to the long period ground motion hazard are with magnitudes ranging from 7.25 to 7.5 at distances of approximately 500 km.

### **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 the whole bridge.

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

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 segment is quite representative of the main bridge.

Dynamic Behaviour of the Confederation Bridge Under Seismic Loads 265

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

of pier P31 were used to measure the tilts of the pier.

locations of accelerometers in the girder.

released slowly.

conducted.

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

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

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

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

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

recorded tilts at locations 3 and 4 were used in the calibration of the model.

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

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