ENGINEERING NONLINEAR STRUCTURAL RESPONSE IN RC PIERS:
A COMPARISON BETWEEN FULL SCALE EXPERIMENTS AND FIBER ELEMENT MODEL ANALYSIS
Y. Kai, H. Aoto, H. Matsuyama and H. Yoshikawa

Introduction

The 1995 Hyogoken Nanbu Earthquake caused a great deal of damage to bridge structures. As a result, the Japan
Road Association’ s Specifications for Highway Bridges was modified the following year. Modifications included the introduction of the stress-strain relationship in concrete and changes to the calculation method for the horizontal forcedisplacement relationship in RC piers. At the same time, the stress-strain relationship of concrete was introduced in consideration of the confinement effects of tie reinforcements. Moreover, in order to improve ductile properties, the details
oreinforcement arrangement were coded and the shear resistance was revaluated to take dimensional effects into consideration.
Even though several experiments were carried out on small-scaled models, the large-scaled model's experimental data
was necessary to make safety judgments on the bridge design
E-Defense, the world's largest shake table experiment facility, is owned by the NIED, a non-profit organization, and wasconstructed to help clarify damage mechanisms of structures affected by the Hyogoken Nanbu Earthquake. Since manyof the damage phenomena have not been understood, several experiments were performed.
This paper reviews the completed C1-2 experiments and introduces a results comparison of the analysis model and theexperiment in the anticipation of blind analysis contest. The modeling tool and model validity is also verifiedExperimental Summary
Shape and Materials

Figure 1 shows the C1-2 experiment set and Figure 2 shows the dimension and reinforcement arrangement of the pier.
The C1-2 height from the pier base to the cap beam upper position is 7.5m and its diameter is 1.8m. All main reinforcements are D32, and their arrangments are 2.5 layers from the pier base to 1.87m, 2 layers from 1.87m to 3.87m, and 1layer from 3.87m to the pier top. The tie reinforcements are D13 with 300mm intervals for the internal, middle, and outside layers. But the outer layer tie at the part from the base to 0.95m and from 4.85 to the top is condensed with interval

Forecast the damage behavior corresponding to the seismic
ground motion (target waves) input to the shake table.

The hysteresis of the reinforcement employed is a bilinear type in the bone frame; its inner loop is the modified Menegotto-Pinto model.

Stage 2) Analysis after experiments:
Forecast the damage behavior with the same model as Stage
1 and analyze methods corresponding to the seismic groundmotion (observed waves) input to the shake table.
This paper describes the results of Stage 2. The contest washeld in the following two sections:

εce = 5310μ(εce = 4840μ)Concrete hysteresis is defined differently forcover concrete and core concrete.
The numerical value in Figures 6(a), (b) and (d)is concrete of pier base parts and the value inbrackets is a parameter for the upper part concrete.

Section A) FEM model analysis section:
Use the finite element method to analyze reinforcement concrete by solid elements.

Three kinds of springs that modeled bearings
were defined as shown in the Figure 7. Fixedbearings (represented as circles) were set up at
the top of the pier, and falling-prevention bearings(represented as triangles) were set on both sidesof the circles in the transverse direction. Movablebearings (represented as rectangles) by spring elements were set to consider the friction on thesides in the longitudal direction.

Section B) Fiber model analysis section:
Use the fiber model to analyze reinforcement concrete bybeam elements.
We employed an analytical tool, UC-win/FRAME(3D), which isan all-purpose analysis program for the spatial frames. The
program was used to create a fiber model simulation to predict
the Section B contest.
Among the materials for the analysis, the following five items
were opened to the contest participants. They weredownloadable from the NIED server.

The damping matrix was taken as the proportion
type depending on elements. The viscous damping constant of each element was set as follows.

▲Figure 3(1) Shape of structure: Details such as plane drawing, spatial drawing, member sections and bearings(2) Weight distribution: Details of each member, parts and spindles, and bearing conditions

Edes = 10000N/mm2

Ec = 28900N/mm2(Ec = 25300N/mm2)

σcc = 33.1N/mm2(σcc = 28.4N/mm2)

σcc = 33.1N/mm2(σcc = 28.4N/mm2)(a) Cover Concr(b) Core Concretete

Stress (N/mm2)e

σy = 372.67N/mm

2E2 =E1/100 = 1923N/mm2

TRLG

E1 = 192333N/mm2

Strain (μ)(c) Section cell divisio(d) Reinforce

nment

0m2mLGTR4m▲Figure 6▲Figure 12

Concrete Ultimate of Cut-off Part (T=10.895 Second)

It is the step that the ultimate state occurred, the curvature and strain at the H=3.9m experienced the maximum. As shown inFigure 13, it can be concluded that the damage at the cut-off part had occurred in the experiment.

PF = μ*RDδδ1 = 0.1mm

Analysis Conditions･ Analysis tool: UC-win/FRAME(3D) Ver.3.00.02 developed by FORUM8 Co., Ltd.
･ Integration method: Newmark β Method (β=1/4)･ Integration interval of time: ΔT=0.005 second･ Input acceleration: Two horizontal directions and vertical direction input simultaneously, observed wave (acceleration) to shake table･ Geometrical consideration: Large displacement analysis (Compatibility Condition: Nonlinear)

Analysis ModelFigure 4 shows an analytical model with 585 nodes, 735 elastic elements, 8 spring elements, and 6 fiber elements forthe pier column. As for the bearing conditions, only the bearing on the top of the pier is fixed, and the side ones aremovable. However, the friction of slipping is considered.
The pier where the fiber element is used is described in detail. The cap beam and the footing are assumed to be elastic.
As described before, concrete was casted in three phases that included (a) footing, (b) column base part, and (c) column
upper part and cap beam. The strength of those materials was published and reproduced. The length of fiber elements isset to the half of section diameter, D=1.8m.The fiber element sections are finely divided and the stress-strain relationshipof each cell is defined respectively. Figure 6(c) shows the division chart of the section. Because large stress occurs at aposition away from a neutral axis, the cover concrete is divided
more finely than the core concrete. As a result, the number of cells
in the section becomes 1400.

δTouching :effectivenessTR▲Figure 7▲Figure 8LG▲Figure 9

Comparison of Analysis and Experiment

0m2m

Displacement Histories of Pier TopLGTR4m

Figure 10 shows the displacement history of the top of the pier. It can be concluded that both amplitudes and the periodof the experiment could be reproduced well.
The relation between the load and the displacement generated at the fixed bearing position on a central pier is shown in
Figure11. The outcome of the experiment and the analytical results correspond within about 200mm as does thecomparison of displacements.

Conclusions▲Figure 13･ Response analysis of time history was executed for the real large experiment body which has a cut-off reinforcement.
A comparison between the experiment and analysis was conducted.
･ The displacements and forces in the experiment were reproduced very well in macro level of the model analysis.
･ A verification on the micro level is planned. This will examine more detailed results between the experiment and analysis
according to the materials available from the NIED.

Acknowledgments▲Figure 2

Elastic Element
1 Layer Reinf.

The input acceleration was the observed waves at JR Takatori station in the Hyogoken Nanbu Earthquake as shown inFigure 3. The three direction components (two horizontal directions and one vertical direction) are input simultaneously.
Because of the interaction between the soil and structures, the used acceleration is 80% of the original recorded ones.

Fiber Element

2 Layer Reinf.
2.5 Layer Reinf.

Blind Analysis

In order to improve the numerical analysis technology to forecast the response and damage behavior of RC structuresduring earthquakes, the NIED executed a blind analysis contest against the experimental C1-2 pier. The analysis wasperformed in the following two stages:
Stage 1) Analysis before experiments:

Ec = 28900N/mm2(Ec = 25300N/mm2)
Edes = 10000N/mm2

Distribution of Curvature and Strain Reinforcement Yield of Base Part
(T=9.305 Second)

Detaching :no-effectiveness

Analysis Methods

Moreover, superstructure girder weight with the bearings
totaled 307t. Additionally, if the two side frame piers andprotecting frame are summed together, the weight on thevibration table for loading was about 1030t.

Strain(μ)σce = 6.62N/mm2(σce = 5.68N/mm2)

http://www.forum8.co.jp

Figure 12 shows the strain distribution and the curvature distribution at 9.305 seconds, the time of main reinforcement
yielding. The curvature of cut-off part at the upper part of the column (H=3.9m) becomes somewhat larger but themaximum curvature appears at the base of the pier because of locating in the elastic range.

Stress (N/mm2)

Strain(μ)P(5) Photographs of experimental sample

The experimental body of the RC pier is about 310t.

εcc = 2000μMoreover, the viscous damping constant for the fiber element used for the pier column was assumed as zero so thathysteresis damping only was considered automatically.

(4) Input earthquake waves

Loads

εce = 4648μ(εce = 4272μ)εcc = 2000μ Stress (N/mm2)･ Girder: 2%･ Concrete (elastic): 5%･ Rigid member and bearing: 0%(3) Material: basic properties and strain-stress relationship of used materials, and concrete composition▲Figure1150mm. The reinforcement material is SD345 and its tension strength based test is 372MPa. Test points were also
set on the concrete surface at a position 3.0m from thepier base. The concrete strength on the test day according to tabular tests was 33.1MPa for the lower part and28.4MPa for the upper part.

FORUM8 Co., Ltd.

▲Figure 4Upper part of Column(Including cap)
E = 25300N/mm2
σ = 28.4N/mm2References

Technical Note of the National Research Institute for Earth Science and Disaster Prevention, No. 331, 2009.1, Large-scale Shake Table Experimenton a Component Model (C1-1model) Using E-Defense –Experiment on a RC Column Build in 1970’ s which Fails in Flexure - (in Japanese)
Tomohiro SASAKI, 2009, On the Damage Characteristics of RC Piers with Cut-off Reinforcement in E-defense, Proc. of the 12th Symposium on
Ductility Design Method for Bridges, pp.199-206, JSCE (in Japanese)
Japan Road Association, 1996.12, Specifications for Highway Bridges, Part 5 Seismic Design, (in Japanese)
Japan Road Association, 2002.12, Specifications for Highway Bridges, Part 5 Seismic Design, (in Japanese)

Base of Column
E = 28900N/mm2
σ = 33.1N/mm2
Footing
E = 27900N/mm2
σ = 34.3N/mm2

Elastic Element

We very much appreciate the NIED’ s permission to publish materials related to the C1-2 experiment.

▲Figure 5

FORUM8 Co., Ltd.

▲Figure 10▲Figure 11