Bidirectional Seismic Response of Reinforced Concrete Bridges

Recent earthquake-induced damage to bridges and other structures located within a few kilometers of a fault rupture has raised questions regarding the adequacy of current seismic design procedures for structures situated in near-fault regions. The intense motions associated with near-fault sites or large earthquakes can impose special demands that require careful consideration in site evaluation and bridge design.

In recent years considerable attention has focused on explicitly estimating and accounting for the special characteristics of near-fault motions in the development of seismic design criteria for major projects (Somerville 1997). Provided that appropriate design ground motions are selected, properly applied linear and nonlinear time history analysis methods can be used to accurately predict and evaluate response in both the elastic and inelastic ranges. However, the ability of simplified design methods to adequately estimate response under multiple components of excitation has been questioned, especially for near-field, pulse-like ground motions.

Research is under way at the Pacific Earthquake Engineering Research Center, University of California, Berkeley, to study the effects of near-fault and other intense ground motions on bridge systems. The main research objectives are to investigate

  1. the effects of bidirectional loading on the response of bridge columns,
  2. the effects of short-duration near-fault ground motions as opposed to long-duration motions, and
  3. the effectiveness of linear and nonlinear analysis techniques.

Some preliminary observations from these investigations are presented in this article.

Effects of Multiple Components of Motion

Early studies comparing the demands on reinforced concrete columns subjected to one or two components of motion (Pecknold 1975) suggested that the peak dynamic displacement response can be greater under bidirectional excitation. In the few studies done on the capacity of bridge columns under bidirectional excitation (Wong et al. 1993; Zayati et al. 1996, among others), the results have generally indicated small to moderate reductions in strength and deformation capacity. The limited number of bidirectional shaking table tests conducted to date (e.g., Kitajima et al. 1994) have used either very small-scale specimens or details unrepresentative of U.S. bridge design practice.

The series of analytical and experimental investigations initiated at PEER is assessing the dynamic behavior of reinforced concrete bridge columns and simple bridge systems. Shaking table tests are simulating the dynamic response of models of bridges and columns subjected to one and two components of motion.

Two types of columns are being investigated: one type having a circular cross section, the other an elongated octagonal section with transverse reinforcement consisting of pairs of interlocking spirals. A specimen representing a segment of a single column viaduct structure is also planned. The results presented in this paper focus on the initial set of four spirally reinforced cantilever columns.

Fig. 1. Reinforced concrete column prepared for testing on PEER shaking table.


Based on the results of preliminary dynamic analyses, a set of four identical cantilever columns were designed and constructed. The height-to-width ratio chosen for the columns was 6 (measured from the base of the column to the centroid of the reactive mass); the length scale factor for the column was reduced by a factor of 4.5 compared to the prototype structure. The resulting column, shown in figure 1, has a diameter of 400 mm. The column was designed to have a supported weight equal to 0.1Agf'cassuming a design concrete strength of 22.4 MPa. In order to realistically simulate P-delta effects, a large concrete block was attached directly to the top of the column to simulate gravity loads and the inertial mass (fig.2).

Fig. 2. Shaking table test specimen

Longitudinal reinforcement was selected to satisfy the Bridge Design Specifications for lateral loading (Caltrans 1990), using a Ductility and Importance factor of 4. The resulting longitudinal reinforcement consisted of 12 no. 4 (12-mm) rebars (a longitudinal reinforcement ratio of 1.2%),with 13-mm cover.


The columns were divided into two pairs. One column from each pair was subjected to unidirectional excitation, and the other was subjected to both components of a record. The first pair was subjected to a near-fault motion recorded at the Olive View Hospital during the 1994 Northridge, California, M 6.7 earthquake. Several bridges that were damaged are near this site. The second pair was subjected to the Llolleo record from the 1985 Chile M 7.8 earthquake, which is nearly 120 seconds in duration. The time scale for the Olive View motion was shortened by a factor of 1/(4.5)1/2, while the duration of the Llolleo record was scaled by a factor of 1/(2)1/2.

The testing program consisted of (1) a series of small amplitude snap-back tests to characterize frequencies and damping ratios; (2) a single test within the elastic range to characterize the response of the specimens under small amplitude earthquakes; (3) a single excitation at the design-level earthquake amplitude; (4) a larger amplitude event to simulate a reasonable maximum credible event; followed by (5) a repetition of the design-basis event to assess the deterioration in the response characteristics due to accumulating damage (and possible response characteristics in a significant aftershock). Specimens within each pair were then subjected to the same series of repetitions of the maximum credible and design-basis events to study damage accumulation and deterioration in performance with additional excitations.


Some representative results for the Northridge records are presented here. Figure 3 presents the displacement orbits for the first application of one or two components of the maximum credible earthquake based on the near-fault Olive View record.

Fig. 3. Plane displacement for specimen A2, run 3

The measured table accelerations were 0.88g and zero, and
0.93 g and 1.02 g in the fault-normal and -parallel directions, respectively. In spite of intense fault-parallel motions, the response is dominated by the fault-normal component. The peak displacement is about 10% more during the unidirectional test.

Time histories of the absolute and relative column displacement in the fault-normal direction are shown in figure 4. The response is dominated by a single large displacement cycle.

Fig. 4. Absolute and relative displacement histories for bidirectional Olive View record, run 3, fault-normal direction (1 in. = 25.4 mm)

The damage at this stage consisted of crushing of the concrete cover near the base over a height of about 200mm. Considerable flexural (horizontal) cracking also occurred all around the section, up to a height of 300 mm. The displacement ductility developed by the column at this stage was about 4.5. The observed damage was similar to that in the specimen subjected to only the more dominant fault-normal component. While spalling extended over about the same amount of the section as when only one component of excitation was used, the location of the spalling rotated about 30° away from the axis of the fault-normal excitation for the bidirectional input. No rebar buckling was observed at this stage. Damage was similar but less severe under the design-level event. A displacement ductility of about 4.1 was achieved for the column subjected to its design-basis event.

Figure 5 shows the increase in displacement during the various biaxial excitations imposed.

Fig. 5. Peak fault-normal and -parallel displacements for Olive View record (1 in. = 25.4 mm) respectively.

Throughout these tests the column exhibited nearly constant maximum flexural capacity, and this did not vary significantly for the unidirectional or bidirectional tests. Repetition of the maximum credible earthquake gradually increased the displacements in the structure. Following the sixth application of the maximum credible event, the displacements were nearly 100% larger than during the first application.

It is interesting to note that the displacements attained in the three repetitions of the design-basis earthquake were nearly constant, suggesting that reasonably good behavior might be expected during aftershocks. Residual displacements started to become significant toward the end of the test, and a longitudinal rebar buckled at the base during run 8, accompanied by increased concrete crushing. During run 9, another rebar buckled, and the rebar that buckled during run 8 fractured in tension. This damage was similar to, but less severe (or occurred later) than, that observed during the unidirectional test, during which the same bars on the extreme tension and compression sides of the member appeared to be consistently and severely loaded. During the bidirectional tests, the orientation of the displacement excursions varied, distributing the damage among various perimeter bars.

Interestingly, both columns subjected to the near-fault motion began to develop flexural cracks near their tops during early cycles, and to lightly spall during the later runs.

These observations are attributed to the significant higher mode effects introduced by the near-fault motions. The higher mode effects are associated with the rotational mass moment of inertia of the weight used to represent the deck. During the initial large displacement excursion for the near-fault motions, the top of the cantilever column does not immediately translate or rotate, resulting in significant moments at the top of the column, and higher shears (fig. 6).

Fig. 6. Force-displacement plots for longitudinal direction under two components of the Olive View record: (a) shear forces and (b) normalized overturning moment

These generally fluctuate with a relatively high frequency (corresponding to the second mode of the structure). However, they do influence the distribution of damage and the maximum shears experienced by the column, and make the hysteretic behavior more complex for shear than for base moment.

The results for the Llolleo record were similar in character to those observed for the near-fault motion. Damage consisted of moderate spalling during the design-basis event. Because of the shape of the spectrum and lower peak-ground velocity, the displacements did not increase as much during a considerably larger maximum credible event, and did not increase during repetitions of this event. Owing to the large number of cycles of loading, rebar buckled and fractured (fig. 7) more than for the near-field record considered.

Fig. 7. Specimen B1 at the end of the test

An extensive series of analyses is being carried out to assess various analysis methods appropriate for design and more refined evaluation, and to study the accumulation of damage during the tests. Figure 8 shows a plot of a fiber model representation of the specimen, subjected to bidirectional response.

Fig. 8. Computed and recorded fault normal Very good correlation was obtained for the initial near-field pulse portion of the record. The response at the end of the record, where the response should be essentially elastic, is not as good. This result is attributed to the lack of a model for rebar pullout at the foundation of the column.


Analyses are continuing to validate finite element models as well as design idealizations. Parametric investigations will be undertaken to assess the effects of various ground motion and structural characteristics on performance. In the near future, additional tests will be conducted using noncircular columns with interlocking spirals. As part of this new phase of the experimental investigation, two columns will be connected to forma portion of a single column viaduct structure. In this case, the periods will be different in the longitudinal and transverse directions of the roadway, and the columns will develop plastic hinges at the top and bottom under longitudinal frame action, and at their bottom under transverse cantilever action.

The results of the parametric studies, shaking table tests, and verification analyses are being used to assess the adequacy of existing linear and nonlinear analysis procedures for bridge columns, and the reliability of design methods for near-fault and multicomponent excitations. The results suggest that elastic methods can predict peak displacement demands relatively well so long as the period of the structure is long compared to the duration of the pulse or predominant period of the structure, and that the bidirectional response has relatively small effects. Additional investigations are needed to fully explore these preliminary observations.


The work reported herein is largely funded by the California Department of Transportation, with Kelly Holden acting as Project Manager. The UC Nishkian Chair and the Pacific Earthquake Engineering Research Center have provided additional funding. The findings and conclusions in this paper are preliminary and do not represent the views or policies of the sponsors.

Mahmoud Hachem, Graduate Student Researcher


Stephen Mahin, Professor
Department of Civil and Environmental Engineering
Structural Engineering Mechanics and Materials
University of California, Berkeley


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