SeismicAnalysis-QuitoBridge

Seismic Analysis and Parametric Study for a Continuous Seven

Spans Post-tensioned Bridge in Quito, Ecuador

Authors:

Sameh Salib, M.Sc., Ph.D., P.Eng, BDS, Senior Project Engineer, Marshall Macklin Monaghan

Ltd (MMM Group Ltd), Thornhill, Ontario, Canada

Maged Ibrahim, M.A.Sc., P.Eng, Senior Project Manager, Marshall Macklin Monaghan Ltd

(MMM Group Ltd), Thornhill, Ontario, Canada

ABSTRACT

A continuous post-tensioned bridge over seven spans, 27m each, was recently designed and is

currently under construction in Quito, Ecuador. Located in one of the most active

seismic/volcanic regions of South America, several challenges were faced during the bridge

design. In addition to the limits on the deck horizontal displacement because of the adjacent

buildings, a substructure system of circular columns without pier-caps or framing connections

into the deck was adopted to satisfy the required vertical clearance. Consequently, the post-yield

behaviour of pier reinforcement could not be allowed as a hysteretic energy dissipation system

since the formation of plastic hinges at such piers impairs not only the control over deck

displacement but also the stability of the bridge deck. A response spectrum analysis was first

conducted on a three dimensional finite element model (3D-FEM) in order to study the

relationship between superstructure, bearings, substructure and foundations as well as to obtain a

preliminary design of bridge components. Thereafter, a non-linear time history analysis

accompanied by a parametric study was carried out considering different types of base isolation

bearings. The study emphasized that the interaction between the superstructure and substructure

through the bearings is a major key to achieve the target level of energy dissipation, base shear,

and deformations. Herein, the FEM, seismic analysis, as well as the part of the conducted

parametric study for a flat sliding friction/spring type of bearings are presented.

INTRODUCTION

The subject bridge is a part of the departure level at the New Quito International Airport (NQIA).

A preliminary design of the bridge using conventional bearings resulted in too high seismic

forces as well as very large columns and foundations. Due to the considerable mass of the deck

and the adopted substructure/foundations system, which has neither pier caps nor deep

foundations, a base isolation type of bearings was essential. The main concept behind such

bearings is to lengthen the fundamental period of the bridge, which reduces the acceleration of

the deck during an earthquake event and consequently lowers its inertial/seismic forces [1,2,3].

Some types of base isolation bearings dissipate seismic energy through viscous damping or

internal friction or by other means for further reduction of seismic forces. Therefore, a

comprehensive study was carried out in order to evaluate the effectiveness of different types of

base isolation bearings prior to finalizing the bridge design. The part of this study covering a flat

2008 ASCEStructures 2008: Crossing Borders

sliding friction/spring type of bearings is presented herein. The following paragraphs discuss in

details the development of the FEM as well as the conducted parametric study.

BRIDGE DESCRIPTION The subject bridge consists of a continuous 7 spans (27m each), 1.0m depth, solid concrete deck

supported by two circular columns/shallow combined footing at each pier and abutment. The

columns diameter is 1.2m at abutments and 1.5m at piers. A pedestal of 2.0m diameter is

provided from about 0.5m under grade level to footings for each column at the south abutment

and piers 1, 2 and 3.

Figure 1 BRIDGE ELEVATION

SEISMIC DATA

Due to the seismic sensitivity of the project site, e.g. being relatively close to an active fault with

a history of frequent strong/long period earthquakes and having a thick fill layer to support the

bridge footings, a specific seismic analysis was carried out. The study accounted for the site

geology, soil conditions, shear wave propagation characteristics, and regional seismic activities.

The response spectrum and time history data were provided by the study as well.

FINITE ELEMENT ANALYSIS

Model Geometry

A three-dimensional Finite Element Model (3D-FEM) of the bridge was developed using the

software SAP2000 [4]. This software has been used recently for several research programs

addressing seismic analysis of bridges [5,6]. Shell elements were used to model the deck and

footings while the columns were modeled by frame elements. A combination of Joint constraints

and link members represented the bearings. Spring elements were used to model the soil-

structure interaction at footings and deck back walls. See Figure 2.


FIGURE 2 AN ISOMETRIC VIEW OF THE BRIDGE FINITE ELEMENT MODEL

Analysis, Phase 1

This phase was considered a preliminary analysis to obtain approximate values of the forces and

displacements associated with seismic loading as well as to check the proposed sizes for columns

and footings. The seismic loads were applied through the response spectrum curve where the

bearings were assumed to lock the tip of columns to the deck with respect to the displacement in

the three global directions (i.e. column is hinged at deck). The maximum horizontal force applied

at the bearings elevation as obtained from the analysis were in the order of 9000 kN and 8000 kN

in the longitudinal and transverse directions respectively while the maximum horizontal

displacement of the deck was about 200 mm in each direction. It should be mentioned that these

values did not take place simultaneously but each value for a specific direction was obtained due

to the seismic excitation of the bridge in that direction. Based on the results of this phase of the

analysis, not only the obtained displacement exceeded the design limit but also the forces and

their associated moments were far beyond the capacity of the proposed substructure and

foundations. Therefore, it was essential to use special bearings that can dissipate some of the

seismic energy before it is transferred to the substructure and foundations. Consequently, a more

sophisticated seismic analysis had to be performed as detailed below.

Analysis, Phase 2

Through this phase, a non-linear time history analysis was performed. A flat sliding

friction/spring type of bearings was studied where the investigated parameters were as follows:

Bearing Gap; the maximum relative horizontal displacement allowed between top of column and soffit of deck at bearing location (in each direction; longitudinal and

transverse). This feature can be achieved through stopper plates anchored to deck and

column at each side of the bearing in both directions. Gap values of 0mm, 50mm,

75mm, 100mm and infinity were investigated. It should be noted that zero gap

represents the case when top of columns are hinged to deck while infinity gap

represents the elimination of the stopper plates.

Bearing friction coefficient; the dynamic friction coefficient of the plates sliding inside the bearing during bridge movement. Friction coefficients of 0.1, 0.2, 0.3 and

0.4 were considered in the study.


Bearing spring stiffness; a component required to restore the bridge original position after the earthquake event [2] as well as to absorb most of the impact force when the

stopper plates start to get in contact. Also, such springs prevent the bridge from

experiencing excessive displacements during service loads, e.g. braking forces and

thermal effects.

The maximum horizontal force induced at a bearing and the maximum horizontal deck

displacement in both longitudinal and transverse directions for different values of gap and

friction coefficient are shown in Figures 3, 4, 5 and 6. The bearing spring stiffness was taken as

the minimum value required for restoring the bridge original position [2]. The friction coefficient

of the abutments bearings was half of that proposed for the piers bearings. Based on the values

shown on Figures 3 to 6, the following observations can be made:

For a zero gap, the maximum displacements and forces obtained from the time history analysis were about 1.15 those obtained by the response spectrum analysis conducted

in phase 1. The difference might be attributed to the type of analysis (linear versus

non-linear) and input data (response spectrum curve versus time history curve).

For a 50mm, 75mm and 100mm gap, the increase of the friction, in general, coefficient reduced the induced forces. This behaviour is consistent with the concept

that introducing a gap between the top of column and soffit of deck where the bearing

plates, with a friction coefficient, can slide and dissipate part of the seismic energy

(prior to locking the column with the deck through the stopper plates) has a useful

effect on the reduction of the induced forces. However, for a 100mm gap, increasing

the friction coefficient above 0.2 increased the forces slightly. This reflects the

complexity of the interaction behaviour between the bearings parameters and the

overall bridge characteristics. While increasing the friction coefficient and gap is

expected to reduce the forces at the bearings, the increase of friction coefficient adds

to the the rigidity of the bridge, reduces the fundamental time period and magnifies

the bridge acceleration/inertial force during the earthquake event. In addition, the

horizontal forces at the bearings are proportional to their friction coefficient (through

the vertical reaction) and gap (through the spring stiffness). Therefore, increasing the

friction coefficient/gap does not always reduces the seismic forces at the bearings.

For an infinite gap, comparing the results with those for a 100mm gap, both deck displacement and bearing force became higher, especially for friction coefficients 0.1

and 0.2. The reason behind that is without stopper plates, the bridge becomes more

flexible, the fundamental time period is larger, and the maximum bridge acceleration

during the earthquake event is less. However, as the deck is allowed to experience

larger movements, the associated spring force at bearings is magnified as well.

The maximum displacement of the deck obtained for the transverse direction was at the south abutment and, in general, higher than that of the longitudinal direction. This

is because of the deck twist in the plan under the seismic excitation in the transverse

direction. See Figure 7. This twist resulted from the height difference of the bridge

columns where the southern half of the bridge has higher columns (i.e. less rigid) for

both abutment and piers than those for its northern half. See Figure 1. In addition, the

abutments columns and footings were smaller in size than those for the piers.


0500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.1 0.2 0.3 0.4

Coefficient of Friction

Force (kN)

50mm Gap

75mm Gap

100mm Gap

Infinite Gap

FIGURE 3 LONGITUDINAL BEARING FORCE VS. COEFFICIENT OF FRICTION

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.1 0.2 0.3 0.4


Force (kN)

50mm Gap

75mm Gap

100mm Gap

Infinite Gap

FIGURE 4 TRANSVERSE BEARING FORCE VS. COEFFICIENT OF FRICTION

0

50

100

150

200

250

300

0.1 0.2 0.3 0.4


Displacement (mm)

50mm Gap75mm Gap100mm GapInfinite Gap

FIGURE 5 LONGITUDINAL DECK DISPLACEMENT VS. COEFFICIENT OF FRICTION

0

50

100

150

200

250

300

350

400

0.1 0.2 0.3 0.4


Displacement (mm)

50mm Gap

75mm Gap

100mm Gap

Infinite Gap

FIGURE 6 TRANSVERSE DECK DISPLACEMENT VS. COEFFICIENT OF FRICTION


FIGURE 7 DISPLACED DECK PLAN UNDER TRANSVERSE SEISMIC ACTION

CONCLUSIONS

Based on the conducted seismic study for the subject bridge, the following conclusions can be

made:

Performing a non-linear time history analysis on a 3D-FEM helps to understand the behaviour of bridges especially those located in critical seismic zones and provided

with sophisticated types of bearings

Providing the bridge with flat sliding friction/spring seismic isolation bearings rather than conventional hinge bearings between bridge deck and columns reduces the

maximum horizontal forces but not necessarily the maximum horizontal

displacements

Providing flat sliding friction/spring bearings with devices that lock the bridge columns with deck when a specific horizontal gap is reached can help controlling

both horizontal forces and displacements

Increasing the bearing friction and/or the gap prior to the deck-column locking takes place may not always reduce the forces and displacements. A parametric analysis

should be carried out to obtain the optimum bearing design

The deck displacement at a bearing should not be considered a direct indication to the expected corresponding force at that bearing since the relative displacement between

deck and top of column (i.e. the displacement magnitude and direction of deck and

top of column at every moment during the seismic excitation) governs the magnitude

and direction of such forces

REFERENCES

[1] Chopra, A, K, "Theory and Applications to Earthquake Engineering", Prentice-Hall, NJ, 1995

[2] AASHTO Guide Specifications for Seismic Isolation Design, 1999 and Successive Interims, Washington, DC

[3] AASHTO-LRFD Bridge Design Specifications, 3rd Edition, 2004 and Successive Interims, Washington, DC

[4] Computers and Structures Inc., "SAP2000-Version11", Integrated Analysis and Design Software, Berkeley,

CA, 2007

[5] Maleki, S, "Seismic design force for single-span slab-girder skewed bridges", Electronic Journal of Structural

Engineering (EJSE), Vol, No # 2, 2001, 135-142 pp.

[6] Dehne, Y, and Hassiotis, S, "Seismic Analysis of Integral Abutment Bridge: Scotch Road I-95 Project", 16th

Annual ASCE Engineering Mechanics Conference, University of Washington, DC, 2003


SeismicAnalysis-QuitoBridge

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