seismicanalysis-quitobridge
DESCRIPTION
Seismic Analysis and Parametric Study for a Continuous SevenSpans Post-tensioned BridgeTRANSCRIPT
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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
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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.
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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.
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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.
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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
Coefficient of Friction
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
Coefficient of Friction
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
Coefficient of Friction
Displacement (mm)
50mm Gap
75mm Gap
100mm Gap
Infinite Gap
FIGURE 6 TRANSVERSE DECK DISPLACEMENT VS. COEFFICIENT OF FRICTION
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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
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