directional effect of the strong ground motion on the seismic...

ABSTRACT: One of the main issues on seismic design of bridges is the determination of strong ground motion application direction in order to capture the most unfavorable situation. The most common approach to this problem is known as 30% combination rule. In this approach, one of the two horizontal components of the strong ground motion record is applied in one principal direction of the bridge whereas the remaining horizontal component is applied to the other direction. Then, the resultant response is calculated by simply adding the results of the first case to the 30% of the results of the second case. In order to get the envelope, the reverse condition is also investigated. However, 30% combination rule is applicable only for the structural elements having an elastic behavior under seismic loads. Thus, for bridge elements such as columns and cap beams which can go beyond the elastic range, 30% combination rule may not provide reliable results. On the other hand, choice of the horizontal component of strong ground motion to be applied in which principal direction of the bridge is another problem to deal with while performing nonlinear response history analysis. Furthermore, in nonlinear response history analysis, deciding the angle of attack of ground motion in which the most unfavorable situation can be captured is a distinctive property depending on the rigidity and skewness of bridges. In this study, two types of bridges are investigated one of which is characterized to be rigid and the other is flexible. Both types of bridges are modelled for 7 different skew angles starting from 0° up to 60° in an increment of 10°. Therefore, 14 models are created for variable geometrical properties. A series of nonlinear response history analysis are performed for each of them at 12 particular angles of attack starting from 0° with an increment of 15° at each step up to an angle of 120°. Moreover, these analyses are repeated for 7 different strong ground motion records and sensitivity analyses are accomplished. Change in column moments and curvatures in strong and weak axis are examined as seismic demand parameters. At the end of the study, strong dependence of critical angle of attack on the skewness and rigidity properties of the bridges is emphasized.

KEY WORDS: Earthquake direction; Earthquake angle of attack; Seismic analysis of bridges; Skewness.

1 INTRODUCTION

In seismically active regions, one of the main concerns in the design of bridges is to consider the most unfavorable seismic actions that may affect during their service life. Generally, nonlinear response history analyses are conducted in the design stage of bridges for seismic actions. While performing those analyses on the bridge models, two horizontal components of strong ground motion records are used. The challenge lies in deciding for the correct directions through which the bridge should be excited by the selected ground motion pairs. As shown in Figure 1, two horizontal components of the earthquake records can be applied to the bridge models randomly at an angle θ with respect to the bridge orthogonal directions.

Acc.-NS

Acc.-EW

Longitudinal-Dir.

Transverse-Dir.

(X)(Y)

(1)

(2)

Figure 1 Ground motion excitation angle.

The most unfavorable response can be obtained when the

analyses are repeated for adequate number of angles of attack. However, the critical excitation direction changes with respect to the response parameter under consideration which results in the fact that a single critical angle cannot be selected for a bridge to govern the seismic design for all of its components.

According to Caltrans (2010), seismic response analyses of bridges are performed by using either of the following methods; the first method is the application of well-known 30% combination rule. One of the horizontal components of strong ground motion is applied in the longitudinal direction of the bridge, and the remaining component is assigned along the transverse direction of the bridge. Results of the first analyses are superimposed with 30% of the results of second analyses. The opposite case is also checked as a second trial. Moreover, the analyses are repeated after switching the horizontal components between the two orthogonal directions. Finally, maximum of the four trials are selected to be used in the design. In the second method suggested in Caltrans (2010), bridge is excited by the two horizontal components of the ground motion at sufficient number of different angles of attack to capture the most unfavorable condition for each of the parameters of all bridge members [3]. According to Priestley et al., as well as the other combination rules, 30%

Directional Effect of the Strong Ground Motion on the Seismic Behavior of Skewed Bridges

B Atak1, Ö. Avşar2, A. Yakut3

1Department of Civil Eng., Faculty of Engineering, Anadolu University, Res. Assist. Bengi Atak, Eskişehir, Turkey 2Department of Civil Eng., Faculty of Engineering, Anadolu University, Assist Prof. Dr. Özgür Avşar, Eskişehir, Turkey

3Department of Civil Eng., Faculty of Engineering, Middle East Technical University, Prof. Dr. Ahmet Yakut, Ankara, Turkey

email: [email protected], [email protected], [email protected]

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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4

combination rule can reliably be applied to the structural members that have a linearly elastic behavior [7]. Especially for the bridge members that go beyond the inelastic range such as columns and cap beams, utilizing the first method can be inappropriate. Moreover, reliability of this method is questionable for irregular bridges that are located on curves or that have high skew angles or that consist of varying column heights. Therefore, in this study, second method is selected to be followed in the sensitivity analyses.

In order to seek for the uncertainty of directional effects of excitation on bridges that have altering geometrical properties, 2 bridge types having 7 different skew angles are modelled. Type 1 and type 2 bridges represent rigid and flexible structural systems, respectively. They are formed such that they serve as an example of two extreme cases of the existing highway bridges in Turkey. All of the 14 models are excited with 7 different strong ground motion records in 12 different angles of attack. Skew angles start from 0 degrees, increase in 10° up to 60° that is the largest skew angle that is likely to be applied in practice. Twelve angles of attack are arranged in 15 degree of increment from 0° to 165°. To sum up, 1176 nonlinear response history analyses are performed in OpenSees [6] and directional effects are investigated on two engineering demand parameters; column moments and curvatures in both strong and weak directions of their cross sections.

To carry out analyses in OpenSees, the excitation can only be applied to the models through the orthogonal directions of the bridge that are represented by ‘X’ and ‘Y’ in Figure 1. In order to assign the loads in ‘1’ and ‘2’ directions, the acceleration time series should be transformed utilizing Equation 1 given below [5].

)(

)(

cossin

sincos

)(

)(

2

1

ta

ta

ta

ta

y

x

(1)

2 STRUCTURAL MODELS OF BRIDGES

In Turkey, bridges with two or more spans having a composite superstructure of prestressed I-beams and reinforced concrete decks, resting on a rectangular cap beam via elastomeric bearings and connected to the foundation with oblong-shaped columns have been widely used especially in recent 25 years [2]. This type of bridges can be classified as ‘Ordinary standard bridges’ according to Caltrans (2010) [3]. In this study, this type of bridges are investigated by use of the two extreme rigidity conditions to represent bridges with comparatively rigid structural systems and bridges with more flexible systems according to their natural periods.

In Figure 2 below, general characteristics and structural elements of ordinary standard bridges are demonstrated. In the transverse direction, a single column pier and a framed column system are both presented. Foundation systems are indicated to have piles in order to imply fixed base conditions.

SKEW ANGLE

SPAN-n

Longitudinal Dir.

Column

Bent Elevation(Transverse Dir.)

Cap Beam

L

H

Deck Plan

#N GIRDER

#2 GIRDER

#1 GIRDER

SPAN-1L1

SPAN-...L...

C GIRDERSL

Ln

Prestressed Girders

Cast-in-place RC Deck

Superstructure (Deck + Girders)

BentAbutment

Pile Cap

Piles

Shear Keys Shear Keys

Column

Superstructure (Deck + Girders)

Cap Beam

H

Single-Column Bent

Multi-Column BentB B

AA

Column Section A-A or B-B

D

Bc

Widely Spaced Prestressed Girders

Closely Spaced Prestressed Girders

Figure 2 General characteristics of ordinary standard bridges

2.1 Description of Bridges

As it is mentioned before, two types of bridges are investigated in the analyses to represent two extreme rigidity conditions in order to observe change in directional effects according to the stiffness of the structure. Both of them have the same 12m-width superstructure consisting of 8 prestressed I-beams. C25 and S420 materials are used for concrete elements and reinforcing bars, respectively. Longitudinal reinforcement in columns is 1% as a minimum requirement. Cap beams have 1.2mx1.1m rectangular sections. The differences in two types of bridges are their number of spans and the span lengths, column clear heights, column cross sections and transverse arrangements of piers. First type of bridge is a comparatively rigid one with a natural period of 0.5s. It has two spans in 15m of length. Four meter height columns have 1mx2m oblong sections and 3 of them are framed in the transverse direction. On the other hand, second bridge type is a more flexible one having a natural period of 0.95s. Each of the four spans of this type has 35m length. One single column in 8.7m clear height is used transversely in each of the piers. Column cross section is decided to be 1.2mx4m in oblong shape. Recall that each of these two types of bridges is modelled in 7 different skew angles from 0 to 60 degrees.

2.2 Construction of the Analytical Models

Each of the fourteen bridge models are analyzed through nonlinear response history analysis under seven earthquake ground motions using OpenSees. Elements of bridge analytical models are represented in Figure 3 below. The details of each of the members in the models are explained in Avşar et al. (2011) and the identical analytical models are used in this study as well [2].

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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

Vertical (V)

LL

Abutment/Soil Spring

T

Transverse Dir.

Spring for Elastomeric Bearing

Rigid Element

Superstructure- Abutment PoundingL

Longitudinal Dir.

Shear Key Transverse Pounding

T

Rigid Element

T

LCap Beam

Transverse Dir.

L


Rigid Element

Longitudinal Dir.

T

Shear Key Transverse Pounding

Pounding Element

Abutment/Soil Spring


Rigid Elements

Superstructure

Transverse (T)

Longitudinal (L)

Lumped Masses

Superstructure Elements

Inelastic Elements

Figure 3 Elements of the bridge analytical models

Since the superstructures of the bridges are expected to

remain in the elastic range under seismic loads, elastic frame elements are used to model them. At the joints where the superstructure is connected with the substructure, elastomeric bearings are modelled such that they transmit lateral loads to the substructure until the frictional force between the bearing and concrete element is exceeded. Bridge members that are expected to go beyond the inelastic range such as columns and cap beams are modelled by utilizing fiber-based nonlinear elements. Nonlinear spring elements are employed at the abutments to represent soil structure interaction. In transverse direction, contact elements are assigned into the models to consider the impact effects due to the shear key arrangements. The same impact occurrence is valid at the expansion joints between the abutments and the superstructure. Hence, similar contact elements are applied there as well [2].

3 PROPERTIES OF SELECTED STRONG GROUND MOTION RECORDS

In this study, seven strong ground motion acceleration time series are used in the nonlinear response history analysis. They are selected from past events that belong to a strike slip fault mechanism which is the most common fault type in Turkey. They are listed in Table 1 below with their intensity measures that are peak ground acceleration (PGA), peak ground velocity (PGV), ratio of PGA/PGV and another quantity ASI (Intensity of Acceleration Spectrum) which is explained in detail in the study of Avşar et al [2]. Initial period for ASI measure is 0.4s and final period is 1.1s. Two horizontal components of the seven ground motion acceleration time series are used in the analyses.

First event and last four events are downloaded from PEER’s database [8]. Denizli earthquake is obtained from European Strong Motion Database and source of Bingöl event is General Directorate of Disaster Affairs/ERD.

Table 1 Selected strong ground motion records

No Event /Date Station ASI (g*s)

PGA (g)

PGV (cm/s)

PGA /PGV

1 Duzce, 1999

375 Lamont 375

0.249 0.706 27.15 25.51

2 Denizli,

1976

Denizli Directorate of Public Works

and Settlement

0.283 0.300 19.3 15.23

3 Bingöl, 2003

Bingöl Directorate of Public Works

and Settlement

0.284 0.396 28.37 13.67

4 Coyote

Lake, 1979 57383 Gilroy

Array #6 0.346 0.370 34.72 10.46

5 Morgan

Hill, 1984

1652 Anderson

Dam (Downstream)

0.364 0.350 26.42 12.98

6 Landers,

1992 22170 Joshua

Tree 0.425 0.279 34.47 7.94

7 Superstition Hills, 1987

286 Superstition

Mtn. 0.528 0.781 37.03 20.68

4 RESULTS OF THE ANALYSES

In order to evaluate the effect of angle of attack on the seismic response of different types of bridges, a series of nonlinear response history analysis are conducted in OpenSees. Selected engineering demand parameters are column bending moments and curvatures in both their strong and weak axes. Strong axes of the cross sections are denoted by 3 and the weak ones by 2. For instance, M3 and K3 stand for column strong axis bending moment and curvature respectively.

For each of the two types of bridges, 7 models are created for different skewness conditions. Each model is excited by seven ground motion acceleration components that are given in Table 1 at 12 particular angles of attack. As a result, 1176 nonlinear response history analyses are performed. Resultant column moments in strong and weak axes are gathered from these analyses and they are presented in Figure 4 after normalizing with respect to the maximum value obtained for each excitation direction.

Figure 4 Distribution of maximum normalized column moments

In Figure 4, all of the results are visualized in terms of their randomness with respect to changing angle of attack.

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However, in order to investigate the effects depending on the types of bridges and their skewness, the graphs are redrawn separately in Figure 5 for the type of bridge that represents the bridges with rigid structural systems and in Figure 6 for flexible ones.

Figure 5 Mean of maximum normalized column moments for rigid bridge type with varying skewness

Figure 6 Mean of maximum normalized column moments for flexible bridge type with varying skewness

When Figures 5 and 6 are examined, it is seen that the effect of angle of attack can cause 35% variation in the column

strong axis moments and this variation remains beneath 10% for column weak axis moments. Therefore, it can be concluded that in both of the bridge types, directional effect is more pronounced in strong axis column moments. Critical angle varies both according to the rigidity condition of the bridge and its skewness. Hence, a single critical angle cannot be selected for their seismic design. In Figure 5, for bridges with rigid structural systems, it is observed that for all skew angles critical angle of attack that results in maximum strong axis column moment (M3) is between 45° and 90°. On the other hand, critical angle for weak axis column moments (M2) is amongst 90° and 120° for highly skewed bridges and it occurs in smaller angles for bridges with smaller skew angles. When Figures 5 and 6 are compared it can be observed that effect of angle of attack is more apparent for bridges with rigid structural systems. According to the analyses results, it should be emphasized that selecting a single critical excitation angle is not possible for all types of bridges in varying geometries. Moreover, the most unfavorable excitation direction even depends on the response parameter itself. For the same bridge, the critical angle for bending moment of a column may be totally different than the one that is determined for curvature of the same column.

Change in column moments, which is a force based parameter, has been investigated in Figures 5 and 6. As a displacement based parameter, column curvatures will be discussed in the following part. First of all, column curvature resultants obtained from 1176 nonlinear response history analysis are presented in Figure 7 below.

Figure 7 Distribution of maximum normalized column curvatures

In Figure 7, the effects of angle of attack cannot be visualized separately with respect to the type or skewness of the bridge, as it is seen in Figure 4 as well. One conclusion related with the scatter of mean value is that in strong axis, change in mean value of column curvatures is more pronounced than one in the weak axis. It has an increasing portion between angles of attack between 40° and 100°; however, increasing portion for weak axis results appears within 100° and 140°.

In order to investigate how different excitation directions affect response of bridges in terms of column curvatures according to changing skewness and rigidity conditions of bridge structural systems, the results are classified and demonstrated accordingly in Figures 8 and 9 below.

0.5

0.6

0.7

0.8

0.9

1.0

-15 0 15 30 45 60 75 90 105 120 135 150 165 180

Excitation Dir. (o)

Max

. No

rmal

ized

Co

lum

n M

3

Skew_00

Skew_10

Skew_20

Skew_30

Skew_40

Skew_50

Skew_60

0.5

0.6

0.7

0.8

0.9

1.0

-15 0 15 30 45 60 75 90 105 120 135 150 165 180

Excitation Dir. (o)

Max

. No

rmal

ized

Co

lum

n M

2

Skew_00

Skew_10

Skew_20

Skew_30

Skew_40

Skew_50

Skew_60

0.5

0.6

0.7

0.8

0.9

1.0

-15 0 15 30 45 60 75 90 105 120 135 150 165 180

Excitation Dir. (o)

Max

. No

rmal

ized

Co

lum

n M

2

Skew_00

Skew_10

Skew_20

Skew_30

Skew_40

Skew_50

Skew_60

0.5

0.6

0.7

0.8

0.9

1.0

-15 0 15 30 45 60 75 90 105 120 135 150 165 180

Excitation Dir. (o)

Max

. No

rmal

ized

Co

lum

n M

3

Skew_00

Skew_10

Skew_20

Skew_30

Skew_40

Skew_50

Skew_60

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Figure 8 Mean of maximum normalized column curvatures for rigid bridge type with varying skewness

Figure 9 Mean of maximum normalized column curvatures for flexible bridge type with varying skewness

When Figures 8 and 9 are investigated, it is realized that larger column curvatures occur at bridges with higher skew

angles. Similar with the results of column moments, randomness of column curvatures depending on the excitation direction are different with respect to the rigidity conditions of the bridges. For instance, when the scatters of less skewed bridges are compared in Figures 8 and 9, effects of excitation direction falls beneath 10% in flexible bridge types, whereas it is beyond 20% in the rigid type.

Main purpose of this study is to determine the critical angles of excitation for bridges that causes the most unfavorable results in seismic response. As a general idea, it is realized that the most critical response has occurred when the bridge is excited at its two principal directions. However, it is still a contradiction that which horizontal component of the strong motion should be applied at which principal direction of the bridge. In order to get rid of this question, both alternatives are tried in this study and the most unfavorable case is selected to be used in the implementations as seen in Figure 10 below.

Case 2:

Case 1:

Transv

erse-D

ir.Longitudinal-Dir.

Longitudinal-Dir.Transv

erse-D

ir.

Acc.-NSAcc.-EW

Acc.-NS Acc.-EW

Figure 10 Ground motion excitation angle for maximum bridge response

5 CONCLUSION

In this study, a series of nonlinear response history analysis are performed on different bridge models to visualize the effects of changing excitation directions on the seismic response of bridges with different characteristics. Bridge models are created such that they represent the most widely used bridge types in Turkey. They are formed by using different skew angles and rigidity properties. Two extreme stiffness conditions are modeled for 7 different skewnesses. Two horizontal components of seven selected strong ground motion records are applied at the models at 12 different directions. Change in column moments and curvatures are reported as engineering demand parameters. Directional effects of earthquake loads on seismic response of bridges are investigated in terms of their stiffness conditions and skewness properties separately.

It is a clear conclusion that critical angle of attack changes depending on the type and geometrical properties of the bridge, its skew angle and the demand parameter which is under consideration. Therefore, a single certain critical angle

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cannot be selected for the seismic design of all components of the bridge.

According to the analyses results of this study, the column moments in the strong axis reach to the maximum values at 45-60 degrees of angle of attack for less skewed and rigid bridges; however, they occur around 90-120 degrees for bridges with flexible structural systems for similar skew angles. Moreover, the consequences differ significantly when column moments in weak axis are under consideration. For any skew angles, change in weak axis column moments has remained in 10% range.

On the other hand, the results vary absolutely when the column curvatures are investigated. For small skew angles in stiff bridges, column curvatures have shown a change in 20%, whereas in flexible ones the change is almost negligible.

Finally, for seismic design of bridges, it is emphasized that critical angle of attack differs according to the rigidity and skewness of the bridges. It changes depending on the response component and its direction as well. Thus, a single critical angle cannot be addressed accurately and precisely for all of the design parameters.

REFERENCES [1] AASHTO, 1996. AASHTO Guide Specifications for LRFD Seismic

Bridge Design, American Association of State Highway and Transportation Officials 16th Ed. with 2001 Interims, Washington D.C.

[2] Avşar, Ö., Yakut, A. and Caner, A. (2011). Analytical fragility curves for ordinary highway bridges in Turkey. Earthquake Spectra 27:4, 971-996.

[3] Caltrans, 2010 Seismic Design Criteria Version 1.6., California Department of Transportation, Sacramento, CA.

[4] Turkish Earthquake Code, 2007 (TEC-2007), Ministry of Public Works and Settlement.

[5] Khaled A., Tremblay R. and Massicotte B. Assessing the Adequacy of the 30% Combination Rule in Estimating the Critical Response of Bridge Piers under Multi-Directional Earthquake Components”, 7th International Conference on Short&Meduim Span Bridges, Paper No. SD-014-1, Montreal, Canada, 2006.

[6] OpenSees, (2005). Open System for Earthquake Engineering Simulation, Version 1.7.3, Pacific Earthquake Engineering Research Center, http://opensees.berkeley.edu.

[7] Priestley M.J.N., Seible F. and Calvi G.M., “Seismic Design and Retrofit of Bridges”, John Wiley & Sons, Inc., New York, NY, 1996.

[8] Pacific Earthquake Engineering Research Center, http://peer.berkeley.edu/

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directional effect of the strong ground motion on the seismic...

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