## Energy Based Seismic Design and Evaluation Procedures for Reinforced Concrete Bridge Columns |

## Abstract

Objective and Approach

Accomplishments (Full Text)

Conclusion

Personnel and Institutions

Collaboration

Technical References

Publications

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- Mander, J.,
*Energy Based Seismic Design and Evaluation Procedures for Reinforced Concrete Bridge* *Columns .*in Research Accomplishments, 1986-1994: The National Center for Earthquake Engineering Research, pages 207-216. (Buffalo : National Center for Earthquake Engineering Research, September 1994)

This project is concerned with the experimental determination and computational
micromodeling of energy absorption or cyclic fatigue *capacity* of reinforced
concrete bridge piers. The results are used with a new smooth hysteretic rule to generate
seismic energy *demand* spectra. By comparing the ratio of energy capacity to demand,
inferences of column damageability can be made.

This seismic capacity analysis of bridge piers is developed starting from the basic principles of micromechanics. Constitutive models that predict the hysteretic behavior of mild and high strength steel reinforcing bars are dealt with in detail; stability, degradation and consistency of cyclic behavior is explained and an energy based low cycle fatigue model is proposed. A hysteretic model for confined and unconfined concrete subjected to either cyclic tension and/or compression is advanced.

A column analysis program, UB-COLA, is developed to predict the behavior of columns when subjected to large inelastic cyclic deformation. The axial, flexure and shear deformations are modeled and all of the various failure modes such as longitudinal bar or transverse hoop fracture, or concrete crushing and bar buckling are captured. Flexural deformations are modeled using a fiber element routine. Shear deformations are modeled by developing a new Cyclic-Inelastic-Strut and Tie (CIST) model. This computational model was validated through experiments on bridge piers typical of construction in the eastern and central United States. These experimental studies included cyclic loading tests on models of entire piers (at reduced scales of 25 to 33%) as well as full size subassemblage tests on column-to-cap connections retrieved from prototype bridge structures.

A smooth rule-based hysteretic model was developed to simulate bridge pier behavior.
Using this model, nonlinear dynamic analyses were conducted to assess seismic energy *demand*
and the associated inelastic energy based fatigue spectra. Seismic analysis and design
recommendations regarding the assessment of fatigue energy are made based on the nonlinear
dynamic analysis. A methodology for the evaluation of existing bridge structures is
proposed; this incorporates traditional strength and ductility aspects and fatigue energy
demand. The relevance of fatigue aspects for the seismic design of new bridge structures
is also demonstrated. It is shown that the present code use of force reduction factors
that are independent of natural period, are unconservative for short period stiff
structures. Recommendations are made for force reduction factors to be used in fatigue
resistant seismic design.

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This research is being performed to develop seismic evaluation procedures for bridge
columns using energy based analyses that implicitly account for the duration effects of
earthquakes. The evaluation first assesses the hysteretic energy absorption *capacity*
of bridge columns and then compares this with the *demand* imposed by a critical
earthquake.

A dual experimental-theoretical approach is adopted whereby the energy absorption *capacity*
of typical bridge columns is determined by laboratory testing. The test results are used
to validate computational models that are based on the hysteretic micromechanical behavior
of confined and unconfined concrete and reinforcing steel. From hysteretic macro models
that are validated by the experiments as well as the associated analytical micromodeling
predictions, the hysteretic energy and cyclic loading *demand* is determined for
historically recorded earthquakes.

This research task is part of NCEER's **Highway Project**. Task numbers are 91-3412
and 10693-E-5.2.

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Traditional (ATC-6-2, 1983) and more recent (Chai, Priestly and Seible, 1991 and NCEER,
1993) seismic evaluation procedures compare displacement ductility capacity with demand.
If for a given peak ground acceleration the capacity exceeds the demand, the structure is
considered to be able to survive the entire earthquake; however, no recognition is made in
these analyses regarding the length or energy content of earthquake ground motions. This
research has focused on using energy as the principal means of determining the damage
potential of bridge columns. The proposed energy-based damage evaluation procedure is a
three-step process as follows: (a) evaluate the hysteretic energy and cyclic loading *capacity,*
(b) evaluate the seismic energy *demand,* and (c) compare the energy capacity/demand
ratio, and if this is less than unity, incipient failure is expected and the bridge pier
should ideally be retrofitted.

In what follows in this paper are the results of research associated with the determination of hysteretic energy capacity and demand with a particular emphasis on non-ductile bridges in the eastern and central United States.

This phase of the research has used a dual experimental-analytical approach for the determination of hysteretic energy capacity. Several reduced scale model bridge piers, as well as full scale subassemblages, have been tested in the laboratory under quasistatic reversed cyclic loading. These experimental studies have been used to validate computer programs that have been developed to derive the hysteretic energy capacity using the principles of micromechanics.

A 25% scale model of a shear-critical bridge pier with twin 36 inch
square columns was constructed and tested under cyclic loading. The model was based on the
Jewett-Holmwood Road bridge crossing of the east branch of Cazenovia Creek at East Aurora,
New York. This specimen had 1.0% longitudinal steel and only nominal hoops (#3 @ 12 inch *crs*
in the prototype). The gravity axial load on the columns was P = *0.05 f' _{c}A_{g}.*
The prototype bridge piers were demolished as part of an Erie County bridge rehabilitation
scheme. The opportunity was therefore taken to retrieve a column to cap beam connection
and test this full-size specimen under reversed cyclic lateral load in the University at
Buffalo seismic laboratory. Figure 1 presents the
experimental specimens together with the normalized test results. It is evident that the
experimental results demonstrate reasonably good ductile behavior despite poor transverse
steel detailing.

A second set of model and prototype pier studies were undertaken on a
bridge that had a typical three circular column frame pier bent. The prototype bridge,
located at Niagara Falls, New York, was a two-span overpass. The central pier had three 33
inch diameter columns 20 feet long. Each column possessed a longitudinal steel volume of
0.019 with #4

circular hoops at 12 inch centers and carried an average gravity axial load of *0.03 f' _{c}A_{g}.*
Prototype and model specimen details are presented along with the experimental results in figure 2. Again, test results show that in spite of
poor (non-ductile) detailing, there is a fair degree of ductile response. Damage was
mostly located in the connections (beam column joints) of these two specimens.

These prototype test results provide added confidence to the above-mentioned reinforced concrete model studies and basically confirm that well-conducted experiments on reduced scale physical models down to 25% in size show little difference when compared to their full-size companions.

The seismic capacity of the aforementioned piers was evaluated using existing (ATC-6-2,1983; Chai, Priestley and Seible, 1991; NCEER, 1993) recommendations. The first of these approaches, ATC 6-2, dates back to research work done in the 1970's following the 1971 San Fernando earthquake (ATCW1,1983).The focus of that approach is on the flexural and shear ductility of columns, with no recognition of possible column-to-cap beam joint vulnerability. Due to the very conservative assumptions made based on the paucity of test results at the time, shear brittle columns are generally predicted. Thus, by using these recommendations engineers may be tempted to either demolish or retrofit a bridge pier for the wrong reasons

The second recommended seismic evaluation procedure is based on more recent work by Priestley and his coworkers at the University of California, San Diego (Chai, Priestly and Seible, 1991). Recommendations have now been made for assessing joint strength and ductility capacity. These tend to agree quite well with the aforementioned experiments. New shear recommendations have also been developed, but these are still based on displacement ductility amplitude.

This research project has returned to the fundamentals of micromechanics in an attempt to predict the energy absorption capacity of bridge columns. Bridge pier failure is defined as that state in which the columns are unable to sustain the gravity load of the superstructure, that is, the onset of collapse. Incipient pier collapse may occur when: (a) the longitudinal bars fracture due to low cycle fatigue; (b) the transverse hoops fracture, thus leaving the column unconfined; (c) the lateral capacity is reduced to zero due to either shear strength deterioration, P-delta effects, or both. For columns with a moderate-to-high axial load intensity, failure modes (b) and (c) generally prevail. Most bridge columns, however, have low levels of axial load, thus either failure modes (a) or (c) occur depending on the reinforcing steel detailing.

The analytical portion of this study is concerned with modeling the energy absorption
(fatigue) *capacity* of reinforced concrete bridge columns using a cyclic dynamic
Fiber Element computational model. The complete analysis methodology for bridge column
capacity is developed starting from the basic principles of micromechanics. The hysteretic
behavior of ordinary mild steel, as well as high strength threadbar prestressing
reinforcement, was dealt with in detail by modeling cyclic stress-strain behavior and
accounting for stability, degradation and consistency of cyclic behavior. An energy-based,
universally-applicable low cycle fatigue model for such reinforcing steels is proposed.
This new damage modeling approach using energy obviates the need for cycle counting and
its use is therefore attractive for random loading situations.

A hysteretic model for confined and unconfined concrete subjected to both tension or
compression cyclic loading was advanced. Such sophisticated modeling was found necessary
to enable the assessment of inelastic shear deformations under *cyclic* loading. This
concrete stress-strain model is an enhanced version of the well-known model of Mander, et
al (Mander, Priestley and Park, 1988). The model has been enhanced to predict the behavior
of high strength concrete, and is also capable of simulating gradual
crack closure under cyclic loading. A fiber element based column analysis computer
program, UB-COLA, was developed for the purpose of accurately predicting the behavior of
reinforcing concrete columns subjected to inelastic cyclic deformations. The axial,
flexural and shear cyclic behavior are modeled, as well as the low cycle fatigue
properties of reinforcing and high strength prestressing steel bars. Fracture of
transverse confining steel is modeled using the energy balance theory of Mander, et al
(1988). For assessing inelastic shear deformations under reversed cyclic loading, a Cyclic
Inelastic Strut-Tie (CIST) model was developed which uses the new concrete model. Figure 3 shows the essence of how shear and flexural
deformations are captured in the analysis. First, the column is divided into cracked and
uncracked zones, figure 3(a). Next, for shear
computations, the cracked zone is modeled as with equivalent strut and tie elements, figure 3(b). Using energy methods and the cyclic
constitutive relations for concrete and steel, the truss deformations (figure 3c) are computed on an incremental step-by-step shear force
control basis. The resulting total shear deformations are added to the inelastic plus
elastic flexural deformations, which are computed using the fiber element analysis and
moment area theory (figure 3(d)).

The program proved to be reliable in predicting the failure mode of either low axial load (low cycle fatigue of longitudinal reinforcement) or high axial load columns (fracture of confining reinforcement and crushing of concrete). For shear critical columns, the cyclic inelastic behavior is accurately simulated through the CIST modeling technique. An example of the predictive capabilities of the program UB-COLA is presented in figure 4 in which the prototype specimen previously shown in figure 1 is analytically modeled. Careful instrumentation of the laboratory experiments enabled a decomposition to be made of the flexure and shear components of total column displacements. It is evident that the modeling procedure is capable of capturing well both of these inelastic components of behavior.

In order to assess the hysteretic energy and cyclic loading demand of reinforced concrete bridge piers, reliable hysteretic models that are representative of real bridge behavior are necessary. Therefore, a rule-based smooth hysteretic model was developed that is capable of capturing the behavior of bridge piers. The model parameters are determined automatically by using a system identification routine in conjunction with either (a) real experimental data from large scale laboratory tests, or (b) results generated from the reversed cyclic loading Fiber Element analysis computer program UB-COLA.

A SDOF inelastic dynamic time-history analysis program was developed
for using the new rule-based smooth model as well as more traditional hysteretic models
such as the piece-wise linear Takeda model. Spectral results were produced by using the
smooth model and an example of all the spectra generated for one earthquake are shown in figure 5. The smooth model was calibrated with the
full-size bridge column experimental data to determine global parameters to simulate
structural force-deformation behavior. The calibration is summarized in figure 6. The cyclic loading demand results from several analyses
are summarized in figure 7, and the effective
dynamic magnification of displacement response depicted in figure 8.

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A complete methodology of seismic evaluation of existing bridge structures is proposed which incorporated the traditional strength and ductility aspects plus the fatigue energy demand. The relevance of fatigue aspects for the seismic design of new bridge structures is also demonstrated. Theoretical predictions using the new CIST-Fiber Element modeling techniques were validated by a combination of reduced scale and full size experiments on the reversed cyclic loading behavior of bridge piers.

It is shown that the present code use of force reduction factors that are independent
of natural period are unconservative for short period stiff structures. Recommendations
are made for force reduction factors to be used in fatigue resistant seismic design.

*Back to table of contents for this report *

This work has been undertaken by Professor John Mander, of the University at Buffalo, and his graduate students:

F.D. Panthaki, M.T. Chaudhary,and

S.M. Waheed

G.A. Chang.

The following people have also collaborated on this project:

Dr. S.S. Chen, University at Buffalo, with associated field work and the retrieval of the prototype specimens;

Dr. P. Gergely, Cornell University, in critiquing the work; Dr. A.M.>

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damage modeling of concrete elements;

Dr. M. Saiidi, University of Nevada, Reno on experimental testing;

Dr.J. Kulickiof Modjeski and Masters, Inc. on providing data on typical bridge piers in the eastern and central U.S.;

Erie Country Department of Public Workson field testing and retrieval of prototype specimens; and

Region 5, NYSDOT, on field testing and retrieval of prototype specimens.

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Stuart Chen

Andrei Reinhorn

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ATC 6-2, "**Seismic Retrofitting Guidelines for Highway Bridges "**,
Applied Technology Council, 1983.

Chai, Y.H., Priestley, M.J.N. and Seible, E., "**Seismic Retrofit of Circular
Bridge Columns for Enhanced Flexural Performance**", ACI Structural Journal, Vol.
88, No. 5, Sept.-Oct. 1991, pp. 572-585.

Mander, J.B., Priestley, M.J.N., and Park, R., "**Theoretical Stress-Strain Model
For Confined Concrete**", Journal of Structural Engineering, ASCE, Vol. 114, No. 8,
1988, pp 1804-1826.

NCEER Report to FHWA and U.S. Congress, "**Seismic Retrofitting Manual for
Highway Bridges**", prepared by the National Center for Earthquake Engineering
Research, State University of New York at Buffalo, New York, Nov. 1993;

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Chang, G.A. and Mander, J.B., (1994) "**Seismic Energy Based Fatigue Damage
Analysis of Bridge Columns: Part I, Evaluation of Capacity**", Technical Report
NCEER-94-0006, National Center for Earthquake Engineering Research, Buffalo, New York,
March 14, 1994

Chang, G.A. and Mander, J.B., (1994) "**Seismic Energy Based Fatigue Damage
Analysis of Bridge Columns: Part II, Evaluation of Demand**", Technical Report
NCEER-94-0013, National Center for Earthquake Engineering Research, Buffalo, New York,
June 1, 1994.

Mander, J.B., Panthaki, ED., and Chaudhary, M.T. (1992) "**Evaluation of Seismic
Vulnerability of Highway Bridges in the Eastern United States**", Lifeline
Earthquake Engineering in the Central and Eastern U.S., ASCE Technical Council on Lifeline
Earthquake Engineering, No. 5. pp 72-86.

Mander, J.B., Waheed, S.M., Chaudhary, M.T.A., and Chen, S.S. (1993) "**Seismic
Performance of Shear-Critical Reinforced Concrete Bridge Piers,**" Technical Report
NCEER-93-0010, National Center for Earthquake Engineering Research, Buffalo, New York, May
12, 1993.