CONCRETE LIBRARY OF JSCE NO. 29, JUNE 1997
EFQERIMENTAL STUDY ON REVERSED LOAD-DISPLACEMENT BEHAVIOR OF
RC PIERS USING LARGE-SCALE MODEL
(Translation from Proceeding of JSCE, No. 538/V-31, May 1996)
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The sectional area of elevated reinforced concrete (RC) bridge piers is generally made small in
urban areas because of space constraints. The main reinforcement is then usually multi-layered. In
order to evaluate the influence of this multi-layering on the load-displacement behavior of bridge
piers, reversed cyclic loading tests were conducted on a large-scale model (1/3 scale) constructed
with the same reinforcement details with actual piers as well as on a small-scale model (1/l0
scale) for comparison. According to the experimental results, there was no serious decline in
ductility in the large-scale model as compared with the small-scale model. However, pull-out of
reinforcement from the footings of the large model was three times more serious than in the case
of the small model due to the multi-layered arrangement of reinforcement. This suggests that
reinforcement pull-out may have a significant influence on the behavior of actual bridges under
earthquake loading. On the basis of the bending moment-rotation relationship derived from an
analysis of reinforcement pull-out, fiber model based nonlinear RC analysis was conducted on the
large scale model with reinforcement pull-out taken into account as rotational spring. It was found
that the analytical result was in good agreement with the experimental result.
Keywords: ductility, load-deflection hysteresis, nonlinear analysis, pull-out of reinforcement
Kenji Kosa, a member of the JSCE and ASCE, is a senior highway engineer at the Hanshin
Expressway Public Corporation, Osaka, Japan. He obtained his Ph.D. from the University of
Michigan, Ann Arbor in 1988. His main research interests are the analysis and design of concrete
structures.
Kazuo Kobayashi is a professor in the department of Civil Engineering at the Osaka Institute of
Technology. He received his Dr. Eng. from Kyoto University in 1973. He has authored several
books and a number of technical papers in the analysis and design of reinforced and prestressed
concrete structures. He is a member of the JSCE.
Yasuo Murayama is a senior manager at the Technical Research Institute in Kajima Corporation.
He obtained his Dr. Eng. from Kyushu University in 1995. He is a registered engineer and a
member of the JSCE and JCI. His main research interest is the seismic design of concrete
structures.
Yoshio Yoshizawa is a chief at CTI Engineering C0., Ltd. He obtained his BS in civil engineering
from Saitama University in 1986. His research interest is the design of concrete structures. He is a
registered consulting engineer and a member of the JSCE.
—121—
1. INTRODUCTION
In earthquake-prone countries like Japan, the reinforcement details of RC bridge piers are
predominantly determined by the seismic load because seismic resistance is of such importance.
To date, a number of reversed loading tests have been carried out on the behavior of RC piers
under seismic loading by investigators such as Akimotoi), Kawashima «, Ishibashi 3), Osaka4), and
Machidas). These tests have clarified the failure pattern of piers with a conventional reinforcement
arrangement. Flexural cracks start to appear near the column end and they gradually spread over
the entire cross section subject to reversed loadings by the time yielding displacement ( 6 y) is
reached. Thereafter, when the displacement exceeds 2 d y, diagonal cracks begin to occur and
slowly form an x-shaped crack pattern as loading continues. With further advance, the cover
concrete starts to spall off, and the main reinforcement begins to buckle, leading to ultimate
failure. Clearly, the ultimate displacement of a pier is a complex function of such factors as the
strengths of materials, the main reinforcement ratio, and the shear reinforcement ratio.
Despite this complexity, the specimens used in past experiments have been to 1/6 scale at most, as
shown in Table 1, due to various restrictions associated with the experiments, typically cost and
experimental complexity. They are roughly 50 cm in width and simulate the cross section of real
piers only by the reinforcement ratio.
However, given the failure process mentioned above, it is clear that the arrangement of
reinforcement plays a crucial role in the behavior of RC piers in the ultimate state. For example, it
has been pointed out that if a small specimen, 10 x 10 cm, with only one reinforcing bar in each
corner is used in an experiment, a significant decline in load bearing capacity occurs as soon as
core concrete has been damaged, and thus the derived results do in fact differ from the behavior
of an actual bridge in its ultimate state). Also, the degree of influence of reinforcement pull-out
from the footing on the overall horizontal deformation, which is approximately
50% in small
specimens, is generally considered substantially
less in the case of real piers, because the
reinforcement diameter in real piers is typically
small compared with the cross-sectional size of
the column.
However,few studies have attempted to consider this issue on the real bridge level. Further, in the
case of elevated bridge piers in urban areas, it is feared that the ultimate bearing capacity may be
further decreased and reinforcement pull-out further increased under loading because they contain
a large amount of reinforcement to compensate for their slim configuration compared with
ordinary piers. To summarize, the reinforcement details of ordinary small specimens differ from
those in urban elevated bridge piers in the following points:
Table 1 Reverse-loading
inves ti gators
dimensions (cm) and the
number of specimens
K aw ashim a et al. 40 x 80X 240
:25
50 x 50x 240-250 :15
testes in the literature
mam
parameters
m am reinforcem entratio,loading
type,hoop tie ratio,concrete strength,
bending m om ent/shearforce ratio
35 X 150 x 100-200 :12
60 x 60x 130
40 x 60x 95- 155
:5
0 65 x 165-230
:6
bending m om ent/shearforce ratio,
tension reinforcem entratio,
axialstress,shearreinforcem entratio
O saka cta .
40 x 40x 140
: 12
m ain reinforcem entratio,
hoop tie ratio,axialstress
M achida ctal.
20 x 15 x 85
:33
bending m om ent/shearforce ratio,
tension reinforcem entratio,
axialstress,hoop tie r
a tio,concrete
strength
Ishibashietal.
40x 40 x 150
40x 50 x l15
60x 40 x 150
:27
:15
Y am am olo cta .
tension reinforcem entratio.
hoop tie ratio,axialstress,
concrete strength
122
0 The diameter of the reinforcement in small specimens is relatively large compared with the
column dimensions.
(2) The main reinforcement is single-layered
in small specimens, whereas in real piers it is multilayered.
(D The main reinforcement is not cut off at the midheight of the column, whereas in real piers it
is cut off at the midheight.
© Hoop ties are closed in the cross section of small specimens, but they are not closed in real
piers.
These disparities may cause a difference in the ultimate displacement and ductility between small
test specimens and real piers. Hence, in our experiment aimed at reproducing the behavior of real
piers as closely as possible, a large size model (1/3 scale of column-end flexural failure type) was
constructed with reinforcement details identical to those of elevated bridge piers used in urban
areas. Cyclic loading was applied at the column top in the horizontal direction and the test results
were compared with those obtained with a small specimen (1/10 scale). Next, in order to
quantitatively
evaluate the reinforcement pull-out due to the effect of the multi-layered
reinforcement arrangement, reinforcement stress-pull out analysis was conducted using a bond-slip
hysteresis model proposed by Suzuki et al. 6) as well as a stress-strain model. Then, to evaluate
the overall behavior of the specimen subjected to loading, a P- S simulation analysis was carried
out based on the nonlinear RC analysis method using a fiber model and taking into account
reinforcement pull-out from the footing as a nonlinear rotation spring. Through this procedure, a
modeling method for successfully predicting the load-deformation behavior of real bridge piers
under seismic loading is proposed.
2
. EXPERIMENTAL
2
.1
PROCEDURE
Specimen preparation
a) Configuration and reinforcement details
Two specimens were prepared: one small and the other large. The dimensions of the large
specimen and the test set-up are shown in Fig. 1. The cross-sectional reinforcement details of the
unit
iiuu
PP ctool
Kor
y
reaction wall
^
5500
PC steel
bar
hydraulic
jack
loading
block for fixing
loading flame
PC steel bar
jack
specimen
ajack
/
hydraulic
I
I
I
I
I
I
I
I
I
I
I
I
( North)
plan view
side view
Fig. 1 Dimensions
flame
of the specimen and loading method (Large size model)
-123-
two specimens are shown in Fig. 2. The shear span ratio of the column (a/d, a: shear span length,
d: cross sectional size in the direction of applied loading) was 4.3, the main reinforcement ratio
(the ratio of cross sectional areas of main reinforcement and column) was 2.2% and the hoop tie
ratio was 0.3% at the column end in both specimens.
The small specimen (1/10 scale), manufactured with a similar shape and the same reinforcement
ratio as the large specimen, was used for comparisons with the large specimen. Relatively large
diameter reinforcing bars compared with the column cross section were used in the small
specimen: D19 bars as the main reinforcement and D6 as the hoop ties.
The large specimen was a 1/3 scale model manufactured to model the reinforcement details of a
real pier. In a real pier, D35 and D19 bars are commonly used as the main reinforcement and
hoop ties, respectively.
In this large model, D13 and D6 bars were used, respectively, in
accordance with the reduced scale of the specimen as compared with a real pier. The main
reinforcing bars were arranged in three layers in the lower section of the column, and the innermost layer was extended up to a point 2.16 m above the upper face of the footings. This position
was determined by adding the effective depth of the column cross section to the point at which
such cut-off is allowed by calculation according to the Japanese Specifications for Highway
Bridges.
Main reinforcement was extended down to the bottom face of the footing and anchored there. The
spacing of the main reinforcement was 7.6 $ ( <£> : reinforcement
diameter)
in the small
specimen, whereas in the large specimen the spacing between bars was 3.6 $ and the spacing
between layers was 2.6 <£. As to the shape of the hoop ties, a closed type with hooks at both
ends was used in the small specimen, whereas in the large specimen hoop ties bent into a U shape
in compliance with those used in real piers were inserted from both sides and closed with lap
splices. As shown in Fig. 2, intermediate hoops were placed in a proportion of 0.1% in terms of
hoop tie ratio.
b) Materials
The mechanical properties of the reinforcement such as yield point, tensile strength, and strain
hardening point were identical in both specimens, as seen in Table 2. High-early-strength
Portland cement was used for concrete. In the small specimen, ready-mixed concrete with a
maximumaggregate size Gmaxof 20mm was used, whereas in the large specimen, " micro
concrete " with Gmax
=10 mmwasused in consideration of the reduced scale of the specimen
compared with a real pier. The mix proportion of the concrete and its strength at the time of
loading tests are shown in Tables 3 and 4, respectively.
l
small size model
arge size model
1167
37 68
m m
Br ｻr
ra
VO
4
VD
X
r CO
16 x 5 0 = 8 0 0
ra
350
8 37
ti a m
la
Q
lo i i n s d ir e :tio n
3 0
145
14 5
3 0
H
Q v
u p p e r se c tio n
o f th e c o lu m n
lo w e r s ec tio n
o f th e c o lu m n
D6
Q
o
CN
o
(N
D 6
fl
lo a d i n g d ir e c t io n
Hm n
s p a c i n go f h o o pt i e s
D13IE I
s p a c i n go f h o o pt i e s
u p p e rs e c t i o no f t h e c o l u m n1 0 . 0( c m )
l o w e rs e c t i o no f t h e c o l u m n5 . 0 ( c m )
n
DT N1i9rv
u p p e rs e c t i o no f t h e c o l u m n1 1 . 4 ( c m )
l o w e rs e c t i o no f t h e c o l u m 5n . 7( c m )
Fig. 2 C r o s s s e c t i o n a l size a n d r e i n f o r c e m e ndte t a i l s
124 -
2
.2 Loading and measurements
Loading was applied to the column top in a horizontal direction while the column was subject to
an axial force from the top so that the axial stress acting on a real pier was taken into account.
The loading set-up is shown in Fig. 1. An axial force equivalent to a stress of 15kgf/cm 2 was
applied using a jack fitted to the column top via a prestressing steel bar through the center of the
specimen and anchored at the footings. This steel bar was encased in a sheath of such size that
the bar did not touch it even when the specimen was deformed.
In both specimens, incremental reverse loading was applied by load control method up to the
yield load Py determined by calculation. This Py is the load at which the outer-most main
reinforcement around the column end reaches the yield point. After the yield load was reached, 10
cycles of reversed loading with the same displacement amplitude were applied successively at
multiples of d y. Loading was continued by the displacement control method until the load fell to
the yield value after reaching the maximum load. The yield load Py and the corresponding
displacement
3 y were 8.5 tf and 10.5 mmin the small specimen, and 92 tf and 26 mmin the
large specimen.
Table 2 Properties
main reinforcements
of large specimen
main reinforcements
of small specimen
hoop ties
of reinforcements
diameter
yield point
(kgf/mm2}
tensile strength
(kgf/mm*)
D13
38.3
57.
D19
39.1
32.6
D6
used
strain hardening
(%)
elongation
(%)
contraction
(%)
1 .7
26
48
57.7
1 .5
23
42
44.2
3 .0
16
57
1
T
able 3 Mix proportion of concrete
water/cement
ratio of fine
unit content (kg/m3)
slump air content
fi ne
coarse
water
cement
ratio (w/c)
aggregates S/a
coarse aggregates
aggregates
aggregates
(cm)
(%)
(%)
S
G
(mm)
max.size of
w
admixture
l
arge model
small model
10
18
62.0
46.0
200
3 23
20
15
57.5
44.8
175
305
785
T
able 4 Concrete strength at the time of experiment
compressive strength tensile strength
Y oung's modulus
( kgf/cm2)
l
arge model
small model
(kgf/cm2)
( x l06 kgf/cm2)
283
24
0 .22
278
26
0 .29
-125
951
1015
0
.808
0 .762
Measurements included displacement
at the loading point, the distribution
of horizontal
displacement in the longitudinal
direction, the relative vertical displacement of the footings and
the column, and the strain of main reinforcement in the footings, as shown in Fig. 3.
3. EXPERIMENTALRESULTS AND DISCUSSION
3.1
Results for small specimen
Load-displacement hysteresis loops for the two specimens obtained at multiples of d y are shown
in Fig. 4. The distribution
of horizontal displacement
in the longitudinal
direction
at each
displacement step is given in Fig. 5, and the crack and failure conditions are shown in Fig. 6. As
seen from Fig. 4, the load-displacement
envelope (P - 8 ) indicates that a maximumload of ll.2
tf was reached at a displacement of 4 8 y, and that the capacity did not visibly decrease even
when a displacement of 5 d y was reached. The yield ratio, which is the ratio of yield load to
maximumload, was approximately 0.75.
Regarding the displacement
ductility
factor, several definitions have been proposed: one, for
example, takes the ductility factor at the point when the load falls to the yield load after reaching
the maximumload; another takes the ductility factor at the point when the load falls to 80% of
the maximumload. In our experiment, however, since the yield ratio was 0.75, the ductility
factor was roughly identical
whichever definition
was adopted. The resulting displacement
ductility
factor, slightly smaller than 6, is 1.2 times bigger than the value calculated using the
equation proposed by Machida et al. (based on the latter definition)
5). Nevertheless, given the
20% scatter in their experimental results, it can be considered that our test on the small specimen
basically differs little from past experiments by other investigators.
3.2 Results for large specimen
The shape of the load-displacement
envelope (P - 8 ) for the large specimen is roughly identical
to that of the small specimen, as seen in Fig. 4. The maximumload of the large specimen was
122 tf, whereas that of the small specimen was ll.2 tf. This difference is approximately the
second power of the size difference between the two specimens. The ductility factor was roughly
5.5, slightly smaller than but broadly similar to the ductility factor of the small specimen.
Though diagonal cracks appeared from the early loading stage around the point where the main
reinforcement was cut off, this section did not undergo yielding or indicate damage progress even
when the maximumload was reached. As a result, the distribution of displacement at over 3 8 y
was roughly linear, as seen in Fig. 5, implying that the main cause of deformation is concentrated
in the area around the fixed end of the column. This was also the case with the small specimen.
However, looking at the yielding displacement (1 8 y) , it is somewhat smaller than the value
obtained by scaling up in accordance with the size difference between the two specimens. Also,
several portions of the main reinforcement ruptured while cyclic loading was being applied with a
displacement of 5 8 y , a behavior not observed in the small specimen test.
3.3 Discussion
As described above, the deformation behavior was roughly the same for both specimens, but there
were minor differences. The following discussion focuses on the potentially
influential
factors
mentioned earlier.
a) Effect of main reinforcement cut-off
In the large specimen, the yield ratio was 0.75, whereas the ratio of the distance between loading
point and cut-off point vs. shear span length was about 0.5. Hence, the specimen had been given a
considerably
large safety factor, approximately
1.5 by calculation,
and so no yielding was
observed in the area of the main reinforcement cut-off. Since the displacement observed at the
column top in the large deformation stage was mostly a result of plastic deformation at the
-126-
o
[=>
>o
r-I
<N
surface of
footing
jRj
unit:
mm "tff
A :LVDT
I : concrete strain gauge
à": main reinforcement strain gauge
* : hoop tie strain gauge
Fig. 3 Measuring
2
l
<5y
points
3£y:.4<Sy
arge model
E>
small model
-6Sy
/
B^f^xfX
arge model
-iay
-2Sy
>U-
V
-5*y.AS^-3Sy
l
H
<\
"A
*yg^?
i
aa
(ton)
-3Sy-4Sy-
^d
&
n
,21
£1
Fig. 4 Load-displacement
at loading points
hysteresis
loops
Fig. 6 Crack and failure
-127-
-,(
v
conditions
I
-\
column end as well as by deformation associated with pull-out of the main reinforcement at the
footing, it can be concluded that the effect of main reinforcement cut-off on the overall
deformation of real piers will remain very minor if the cut-off point is determined as in this case.
b) Effect of multi-layered arrangement of reinforcement
The distribution of the main reinforcement strain in the longitudinal
direction in the area below
the cut-off point was roughly similar in both large and small specimens. However, in the large
size specimen, the reinforcement showed a longer yield extension in the footing as illustrated
in
Fig. 7 and the reinforcement stress was transferred deep into the footings. As a result, as shown
in Fig. 8, the amount of main reinforcement pull-out from the footing is consistently
greater in the
large specimen made of D13 bars than in the small specimen containing D19 bars when compared
at the same ductility ratio.
When reinforcement pull-out is compared at 4 8 y, close to the ultimate displacement, in terms of
a non-dimensional reinforcement diameter, it is 0.4 $ in the large specimen, approximately three
times bigger than the 0.13 $ of the small specimen. This is because the spacing of the main
reinforcement in the large specimen (3.8 $ , 2.6 <f> ) is closer than that of the small specimen
(7.8 $ ). The value (0.4 <£ ) is, however, considerably larger than the 0.2 $ derived by Ishibashi
et al. 3). This is probably because the bond strength between each bar and concrete decreases due
to the multi-layered arrangement of the reinforcement.
The ratio of column top displacement caused by column end rotation to overall displacement was
small in the large specimen compared with that of the small specimen, as shown in Fig. 9. The
loops shown in Fig. 9 are similar to the results of existing studies by others. However,given that
our data shows about 25% of the ultimate displacement at the column top being attributed to
rotation at the column end, the effect of reinforcement pull-out in actual piers cannot necessarily
be assumed to remain minor.
c) Effects of reinforcement diameter and the shape of hoop ties
In the small specimen, fracture occurred in the column in the range 0.8d from the column end,
which is roughly similar to the results by other investigators. In contrast, in the large specimen, it
occurred in the range 0.4d from the column end (Fig. 6). According to visual observations, the
length of the fracture region in both specimens' roughly corresponded with the region in which the
main reinforcement buckled. The difference in the fracture range (0.8d vs. 0.4d) is considered
attributable
to differences in main reinforcement diameter and the shape and size of the hoop ties
used. The cause of main reinforcement rupture in the large specimen is possibly that fracturing
was concentrated excessively in a narrow range around the column end. In the large specimen, the
lap-spliced
hoop ties were reinforced by intermediate hoops amounting to 0.1% in terms of hoop
tie ratio in the same way as done in real piers.
small model
(experiment)
l
arge model
(experi ment)
large model (analysis)
HI
(4.3d)
120
80
South direction
40
0
40
80
120
(mm)
< I > North direction
Fig. 5 Distribution
160
120
80
40
South direction
0
40
(mm)
< I >à"North direction
of horizontal displacement
-128-
I
120
80
40
South direction
in the longitudinal
direction
0
40
80
120
(mm)
< I >à"North direction
The strain of the intermediate hoop measured on the plane perpendicular to the loaded plane was
quantitatively
similar to the hoop tie strain. Accordingly, it is concluded that intermediate hoops
performed as expected as shear reinforcement. Also, in the case of the large specimen, it is
inferred that the presence of the intermediate hoops restrains the decrease of confinement due to
the enlargement of hoop ties, and that a deformation capacity no different from that of the small
specimen was achieved as a result.
4. ANALYTICAL
4.1
INVESTIGATION
OF MAIN REINFORCEMENT
PULL-OUT
Outline
Conventionally, it has been accepted that the influence of rotation at the column end due to main
reinforcement pull-out on displacement at the column top, and consequently on the overall
deformation capacity, is large in small specimens, but that it is comparatively small in real piers.
However,our experiment on the large specimen indicates that this influence is not necessarily
small, because the bond strength between concrete and reinforcement degrades in elevated bridge
piers designed for urban use due to the close arrangement of main reinforcement. To evaluate this
effect analytically,
a numerical investigation was carried out on the amount of reinforcement pullout from the footing in the large specimen.
large model
compress!ve strain
tensile
-5,oqp__
o
l
arge model : <£>=13mm
small model : 0=19mm
strain (x 10"6)
10,000
20,000
fl-q
0
.4 <f>
0.3
l
arge
'(rei nforcement strain gauge)
0
l
0.20
0.10
arge (LVDT)
small (LVDT) i
small
strain gauge)
0
( reinforcement
0
Itfy2Sv3£v4Sy
5Sy
displacement at the columntop
Fig. 8 The relationship
between pull-out of main
reinforcement and displacement
small model
compressive strain
-5,000
tensile
0
strain (x 10"6)
10,000
-n-q
I
.J
I
2w~
3Sy,4Sy,
large : l £y =26.0mm
small l(Sy =10.5mm
small (LVDT)
20,000
5<?y
>>
-°
«à"
à"aa
<U Q>
i§
2a
g&
I^
§3
43
small
0 .4
( reinforcement
strain gauge)
0 .3
U2
32
0 .2
à"8§
0 .1
^
l arge
(LVDT)
l arge
-^(reinforcement
strain gauge)
^- --A
l
arge (analysis)
à"2 '|
a 2
t-4
i-C
0
I
ISy2dy3§y4dy5Sy
displacement at the column top
Fig. 9 Ratio of displacement caused by rotation
to total displacement at the column top
Fig. 7 Distribution of main reinforcement
strain in the footing
-129-
4
.2 Method of analysis
Analysis associated
with reinforcement pull-out is often conducted using a stress-strain
relationship
for the reinforcement ( a - E model) and a bond-slip relationship
between the
reinforcement and concrete ( T - s model). This procedure was employed in our analysis. The
Menegotto-Pinto model 12) was used as the a - E relationship. This model is characterized by
the explicit derivation of stress level from reinforcement strain. As the T - s model, the model
shown in Fig. 10 as proposed by Suzuki et al. 6) for the analysis of main reinforcement pull-out
wasused.
4.3
Results of analysis
Analysis was conducted on the reinforcement pull-out from the footing. The strain distribution
of
main reinforcement in the footing was calculated
under conditions that the analytical
reinforcement stress was in conformity with the measured stress up to yielding and, after that the
analytical
reinforcement pull-out expressed by an integral of reinforcement strain was in
conformity with the measured stress. The calculated strain distribution
is compared with the
experimental result in Fig. 1 1.
The calculation agrees well with the experimental result in the case of the small specimen. With
regard to development length (the distance from the upper face of the footing to the position
where the reinforcement strain reaches almost zero), the calculation is roughly in agreement with
the experimental result. In particular, the calculation fairly successfully expresses the yielding
range of reinforcement near the face of the footing at a displacement of 2 S y. In contrast, in the
case of the large specimen, the calculation failed to estimate the experimental result as good as in
the case of the small specimen. Although both calculation and experimental results are similar in
terms of the pattern of yielding zone, they deviate quantitatively.
Also, strain of the elastic zone
are in a ' shallow' range in the calculation, a different tendency from the experiment. It can be
said that this is because the bond strength is lower in the large specimen due to the dense
arrangement of bars, whereas the proposed T - s model is intended for columns with relatively
large reinforcement spacing.
4.4 Modification
of analytical
bond-slip
model
The T - s model shown in Fig. 10 was modified so as to reflect the influence
reinforcement spacing in the large specimen. The modifications are outlined below.
of the closer
© Change the amount of yielding slip (Sy) of 0.014 <f> derived from the T - s model by Suzuki
et al. to 0.08 $ based on the experimental result.
(D Reduce the bond strength, or change the scale of the T axis, to take into account the
influence of reinforcement spacing as suggested by Ishibashi et al. 3)
(D As a reduction coefficient for the bond strength influenced by the reinforcement spacing, adopt
the product of the reduction coefficient due to the spacing between layers and the reduction
coefficient
due to the spacing between main reinforcement bars. The reduction coefficient
calculated in this way is approximately 30% for the large specimen.
(D Adjust the residual constant bond strength ( i R ) after yielding to match the calculated pullout after yielding with the experiment.
The modified T- s model thus established
is shown in Fig. 12. Indicated in Fig. 13 are the
calculated strain distribution
corresponding to the measured reinforcement pull-out derived using
the modified x -s model. From this figure, it is clear that the strain distribution
in the large
specimen associated with pull-out of the main reinforcement is well predicted when the modified
T -s model is adopted.
4.5
Analysis
ofM- 6 hysteresis
Using the modified
loop at the column end
T -s model, the bending
moment-pull out hysteresis
130-
loop was calculated.
Next, using this result, the hysteresis loop for the bending moment-rotation angle (M- 9 ) at the
fixed end due to pull-out was calculated. To derive the 9 value, hysteresis
values for
reinforcement stress and position of the neutral axis are needed. For this purpose, the relationships
between bending momentand reinforcement stress, and between bending moment and the neural
axis at the column end were calculated in advance by the fiber model based analysis. The
analytical M-6 hysteresis loop is compared in Fig. 14 with the measured result. The measured
hysteresis loop was obtained from the relative vertical displacement between footings and column
taken on the two opposite sides. As seen from the figure, the measured M-6 hysteresis loop
shows a pattern similar to that of the P- 8 curve, which indicates that analytical result is able to
predict the measured M-6 loop up to roughly a displacement of 3 b y.
M AX
MAXj
s ta n d a r d
/ I
/ I
I
r A f
rAJ
!
§
.£>
-^
S A
A=0.003
<£
Fig.10
s
Fig.
T-s
--e
>
S v
0.014$
Sv=0.0190
slip
-
r c
O
JD
S
c o m p a r e d w i th n o r m a l v a l u e s
i
T3
T3
T is re d u c e d b y 3 0 %
a n d s l ip b y 0 .0 8 <｣
12
0.080(about
slips
Modified
T -s
1 mm)
model
model
strain of reinforcement
1.0
o
strain of reinforcement
1.0
2.0
2.0
x
4 .0X
à"3
|4(H
U
C
£ 2
experiment
experiment
experiment
analysis
analysis
analysis
S L'«H
s 20H
*
à"£3
large model
experiment ! Py
experiment : 2d y
-*40\
analysis
analysis
X3
HH
60J
1.0
80 -1
100J
',Py
I23y
Fig. 13
10
! Py
: 2Sy
!3 dy
;Py
;2Sy
.'3$y
Reinforcement strain in the axial
direction (Large model)
600 1
1.5
4CXH
2 .0X10
Oi
-e-
-Q-
à"s
a.
strain of reinforcement
0.5
.0x
20-
10
x
II
4
à"e-
3.0
-e-
CD
3.0
-
^
200-1
x
,s sioi
o H
£2
<u
!!
à"Q-20 -1
à"s
Ou
<u
à"o
small model
experi ment
experi ment
analysis
anal ysi s
£
Py
28y
Py
28y
"S
-200-1
-400^
-600
J
-8.0
30J
-6.0
-4.0
-2.0
0
fixed-end rotation
Fig. 1 1 Distribution
of reinforcement strain
in the axial direction
-131-
Fig. 14
2.0
4.0
: 6 (rad)
M- 6 hysteresisloop
6.0
8.0Xl(T
5
. ANALYTICAL INVESTIGATION OF THE P- 8 CURVE OF THE COLUMN
5.1 Outline
One effective method of estimating the ultimate resistivity
of bridges against strong earthquake
loading is to carry out nonlinear seismic response analysis. In doing so, it is important that the
nonlinear hysteresis characteristics
of the structural members constituting the bridge should be
reflected accurately in the analysis. This is particularly
important in a pier where the design is
governed by seismic loading. Accordingly, in our study, analytical investigation
was conducted on
the large model that simulated the influence of rotation at the column end due to pull out of main
rei nforcem ent.
The fiber model based analysis was employed for the analysis. This method assumes that the
column comprises multiple bar members and that the column cross section is constituted
of
elements of concrete and reinforcement. It also presumes that the cross section remains plane after
deformation and that the material properties are those under the uniaxial stress state. This method
is advantageous in that it is applicable
to a wide range of cross sectional features, material
properties, and loading conditions compared with a method using empirical load-displacement
hysteresis models. Also, the labor and time needed for calculation are significantly
less than for
FEM analysis.
5.2 Modeling
of the column member
a) Material models
As the material models, those used by Yamada et al. 1 0) were employed. Namely, the concrete is
modeled using the ac -E c hysteresis loop based on the rule by Muguruma et al. :n.
As for
the reinforcement, the a s - e s hysteresis loop proposed by Menegotto-Pinto 12) was utilized.
The concrete model and the reinforcement model are shown in Fig. 15 and Fig. 16, respectively.
The physical properties of the materials used are given in Table 5.
b) Modeling of the member and cross section
As shown in Fig. 17, the column member was divided into a total of 19 elements in the
longitudinal
direction. Elements in the possible plastic region in the range up to 1.0 m from the
column end were made small. The cross section was divided into 50 fibers and reinforcement
elements were taken into account according to the arrangement of bars at each position along the
column.
5.3
Model for the rotation spring at the column end
Arotation spring was installed at the column end, in which a series model of the linear spring and
nonlinear hysteresis spring was taken into account. The linear spring and the nonlinear hysteresis
spring take into account elastic deformation of the footing and the pull-out of the main
reinforcement, respectively. By placing these springs in series, the displacement is determined as
the sum of the displacements of each spring when a bending momentacts on the column end.
a) Linear spring
The linear spring was established
by taking into consideration the difference between Young's
modulus of the concrete model and that of the micro concrete, the shear deformation of the
column, and the deformation of the footings.
b) Nonlinear hysteresis spring
The trilinear model shown in Fig. 18, as proposed by Muto, was used as the' nonlinear rotation
spring at the column end. The characteristics of the skeleton curve were determined with reference
to measured and analytical results of the M- 6 hysteresis loop: 4.7 X 10 5 tfm/rad for the first
gradient; 2.1 X 10 5 tfm/rad for the second gradient; and 1.8 X 10 4 tfm/rad for the third
gradient. The rotation angles at the two inflection points were made 6 X 10 ~4 rad and 1.5 X 10
~3rad.
-132-
Table 5 Physical
unloading
A P0"ll
V
/
/ SIVCHUIl
unloading
/ point
properties
(unit : kgf/cm2)
Y o u n g 's m o d u lu s o f c o n c r e t e
2 .2 x I f f
c o m p r e s s iv e s tr e n g th
2 83
2 .1 x lO -
Y o u n g 's m o d u l u s o f r e in f o r c e m e n t
y i e ld s t re n g th
3 83 0
4 .2 x 1 0 "
s e c o n d g r a d ie n t
600
strain
Y ule
Fig. 15
cT" reloadin8
Point
Model for the stress-strain
relationship
of concrete
600
-0. 006
0
.006
fixed end rotation (rad)
E
( eM2)),
(
Fig. 18
(4V ')
i
Relationship
of bending
moment-
rotation at the column end
eW)
Fig. 16 Model for the stress-strain
relationship
of reinforcement
-0. 15
0 .15
displacement
( a)
(b) cross section
of the column
element of the column
axial force
Fig. 19 Relationship
of load-displacement
at loading points
f
1
orced
displacement
li n e a r e l e m e n t
( 9 e le m e n ts )
(m)
1 .1 6 7 m
I B
l l .0 m
4. m
nonlinear rotational spring
+ linear rotational spring
Fig. 17
Analytical
reinforcement
r ^ ^ S ^ rc
element
n l
-150
-0. 15
displacement
(m)
0 .15
model for the column
Fig. 20 Comparison of experimental and analytical
results on load-displacement relationship
-133-
A
nalytical results of the P - 5 hysteresis loop at the column top are shown in Fig. 19. Two cases
are compared: one ignores the rotation spring at the column end and the other takes it into
account. The analytical result for the case where the rotation spring is considered is compared in
Fig. 20 with the experimental result. The analytical M-6 loop at the column end due to pull-out
is compared in Fig. 18 with the experimental result. The proportion of the displacement at the
column top attributed to rotation at the column end induced by the reinforcement pull-out as a
ratio of overall displacement at the column top is given in Fig. 9. The distribution
of horizontal
displacement along the column in the longitudinal
direction is shown in Fig. 5.
From these figures, it is found that a larger load is given by calculations with the same plastic
factor when the rotation spring is ignored (which means that the column end is fixed) compared
with when it is taken into consideration;
this is because the rigidity of the member as a whole is
increased in the former case. This tendency is particularly
conspicuous at the time of 1 8 y (Fig.
19). In contrast, if the rotation spring is taken into account, it is possible to estimate the skeleton
of the P - 8 curve and the hysteresis loop with better accuracy (Fig. 20).
The analytical M-6 loop is in relatively
good agreement with the experimental result, which
suggests that the Muto model is adequate for the analysis of the rotation spring at the column end
in relation to reinforcement pull-out (Fig. 18). In the analytical
result, the proportion of
displacement at the column top attributed to rotation at the column end is approximately 20% at 1
8 y and 30% at 2 8 y. These values are close to those obtained in the experiment (Fig. 9). In the
analysis, the proportion of displacement at the column top attributable to rotation of the column
end decreased near the ultimate state compared with the proportion at 2 d y or 3 8 y. For
example, it was 15% at the displacement of4 8 y (Fig. 9).
The distribution of horizontal displacement in the longitudinal
direction was roughly linear in the
analytical result, except in the area around the column end, and this is in good agreement with the
experimental result, which showed that the bulk of displacement at the column top is governed by
deformation around the column end (Fig. 5).
6. CONCLUSIONS
Experimental and analytical investigations
were conducted using a large model (1/3 scale)
constructed with the reinforcement arrangement of a real pier as well as with a small model (1/10
scale). The type of RC bridge piers used in urban areas was adopted as the prototype. The
following conclusions can be drawn from the results:
© The P- 8 envelope obtained in the experiment on the large model was roughly identical to
that obtained from the small model. The displacement ductility factor of the large model was 5.5,
which was slightly smaller than that of the small model, which was 6.0.
(D The amount of reinforcement pull-out in the large model was greater than that in the small
model. For example, the reinforcement pull-out with a displacement of 4 8 y, which was close to
the ultimate displacement was 0.4 $ in the large model, three times greater than that of the small
model (0.13 $ ) when converted into a non-dimensional reinforcement diameter. This is considered
attributable to a decrease in bond strength between reinforcement and concrete due to the close
spacing of reinforcement and its multi-layered arrangement in the large model.
(3) Analysis was conducted on the large model with multi-layered
reinforcement details to
investigate the main reinforcement pull-out induced by reversed cyclic loading using the T - s
model proposed by Suzuki et al. It was found that the model was not quite satisfactorily
able to
predict the behavior of the large model. Therefore, instead of this model, a modified T - s model
reflecting the influence of the close reinforcement spacing was developed and used for the same
analysis. And then, the result revealed that the modified T - s model is able to simulate relatively
satisfactorily
the measured amount of reinforcement pull-out and distribution
of reinforcement
strain inside the footings.
134-
© As a simulation, nonlinear RC analysis taking into account reinforcement pull-out using a
nonlinear rotation spring was carried out on the experimental results utilizing a fiber model. The
results verify that the load-displacement
relationship
obtained in the experiment was predicted well
by this analytical method.
Acknowl edgements
The authors greatly appreciate the valuable
'Technical Research Group for Investigating
advice from members of the Hanshin Expressway's
the Ductility of RC Piers' in completing this paper.
References
[I] Akimoto and Osaka
"Study on the Deformation
Capacity
of RC Piers under Seismic
Loading,"
Proc. of the Colloquium on the Ductility
of Concrete Structures and its Evaluation,
pp. n-241-252,
1988.3 (in Japanese)
[2] Kawashima, K., Unjoh, S., Sugita, and Nakajima
"Study on Main Reinforcement Cut-Off of
the RC Bridge Piers under Seismic Loading, Evaluation of Seismic Resistivity
and Reinforcing
Methods," Technical Report of PWRI of the Ministry of Construction, Vol. 189, p. 96, 1993.9 (in
Japanese)
[3]
Ishibashi,
T., and Yoshino, S. "Study on Deformation Capacity of Reinforced
Concrete
Bridge Piers Under Earthquake,"
Proc. of JSCE No. 390, V-8, pp. 57-66, 1988.2 (in Japanese)
[4] Ozaka, Y., Suzuki, M., Kuwasawa,S., and Ishibashi,
T. "Load-Deflection
Characteristics
of
Reinforced Concrete Columns Under Static Alternating Cyclic Loads," Proc. of JSCE No. 372, V
-5, pp. 45-54, 1986.8 (in Japanese)
[5]
Machida, A., Mutuyoshi, H., and Toyoda, K. "Evaluation of the Ductility
of Reinforced
Concrete Members," Proc. ofJSCE
No.378, V-6, pp.203-212,
1987. 2 (in Japanese)
[6] Suzuki, M., Jang, I, Watanuki, M., and Ozaka, Y. "Study on the Pullout Property of Axial
Bars from Footings,"
Proc. of Concrete Research and Technology, JCI, Vol.3, No.l, pp. 33-44,
1992 (in Japanese)
[7] Design Procedures for Reinforced Concrete Structures,
Hanshin Expressway Public
Corporation, 1991.4 (in Japanese)
[8] Murayama, Y., Suda, K., and Mimura. "Effect of Column Reinforcement Pull Out on the
Deformation Capacity
of RC Piers,"
Proc. of the Colloquium
on the Ductility
of Concrete
Structures and its Evaluation,
1988.3 (in Japanese)
[9] Yamamoto, T., Ishibashi,
T, Otsubo, M., and Kobayashi,
S. "Experimental
Studies on
Seismic Resistance of a Pier with Reinforcement Terminated in a Tension Zone," Proc. of JSCE,
No. 348, V-l,
[10]
Yamada,
pp. 61-70,
1984.8
(in Japanese)
Y., lemura, H., Matumoto, T., Riestic,
D., and Ukon, H.
"Stress-Strain
Based Inelastic Earthquake Response Analysis of Reinforced Concrete Frame
Structures,"
Proc. of IABSE International Symposium, Delft, 1987
[I I] Muguruma, H., Watanabe, F., Iwashimizu, T., and Mitueda, R. "Ductility Improvement of
High-Strength
Concrete by Lateral Confinement," Transactions of Japan Concrete Institute, Vol.
5, pp.
403-410,
1988
[12]
Menengotto, M., and Pinto, P. "Method of Analysis for Cyclically
Loaded Reinforced
Concrete Plane Frames Including Changes in Geometry and Nonelastic Behavior of Elements
under Combined Normal Force and Bending,"
IABSE Symposium on Resistance and Ultimate
Deformability
of Structures Acted on by Well-Defmed Repeated Loads, Final Report, Lisbon,
1973
-135