r - The Hong Kong Polytechnic University

columns were reinforced with three types of design details. One with 12-D19 main reinforcements was
transversely reinforced with D13 perimeter hoops spaced 9 cm (volumetric confinement ratio ρ s = 0.012),
corresponding to a case with sufficient transverse reinforcements. The other two with 18-D19 main
reinforcements were transversely reinforced with D13 perimeter hoops spaced 9 cm and 18 cm, respectively. The
one with the transverse reinforcements spaced 18 cm was designed to represents a column with an insufficient
volumetric confinement ratio (ρ s = 0.006) in order to investigate the ductility demand for a column allow to rock.
The nominated material properties for these specimens are as follows: concrete compressive strength f c ’ =280
kg/cm 2 ; yield strength of main reinforcements F y = 4200 kg/cm 2 ; yield strength of transverse reinforcements
F yh =2800 kg/cm 2 . The test schedule is listed in Table 5, which also includes pseudo-dynamic loading test and
quasi-static cyclic loading test.
Test Results and Conclusions
As mentioned previously, both series of rocking experiments include pseudo-dynamic test and cyclic loading
test. However, only part of the cyclic loading test results will be presented in this paper due to the page limit of
the paper. The test results of the first series of experiment are given Fig. 4. In this figure, (a) shows the lateral
load versus the total lateral displacement curves and (b) shows the moment versus rotation curves at the column
base. From these figures, it is evident that the hysteretic response for specimen B show a pattern of response
behavior that is similar to that of specimen A, including exhibiting a sudden and significant loss of lateral
resistance with low ductility under reversed cyclic deformation. However, the pinching effect in specimen B is
not as serious as that in specimen A. If we further compare specimen A with specimen B at the same drift ratio
of 5%, we can find that the rocking mechanism of specimen B resulted in an increase of lateral load resistance
and a decrease of plastic deformation in the plastic hinge zone. This observation confirms the isolation effect of
a rocking foundation. For the retrofitted specimen C, it demonstrates a nonlinear rocking behavior in Fig. (a)
and that the seismic force that the pier sustained was limited to an almost constant value of 25 tonf. This means
that specimen C was able to sustain large lateral displacement without significant strength degradation. The
plastic deformation of specimen C shown in the moment-rotation curve is also smaller than that of specimen B.
30
20
Drift (%)
-8 -6 -4 -2 0 2 4 6 8
Specimen A
(cyclic loading test)
Drift (%)
-8 -6 -4 -2 0 2 4 6 8
30
Specimen B
20 (cyclic loading test)
30
20
Drift (%)
-8 -6 -4 -2 0 2 4 6 8
Specimen C
(cyclic loading test)
Lateral force (tonf)
10
0
-10
Pull
Push
Lateral force (tonf)
10
0
-10
Pull
Push
Lateral force (tonf)
10
0
-10
Pull
Push
-20
-20
-20
Moment (tonf-m)
-30
-30 -20 -10 0 10 20 30
Lateral displacement (cm)
100
80
60
40
20
0
-20
-40
-60
-80
Specimen A
(cyclic loading test)
Pull
Push
-100
-0.08 -0.04 0 0.04 0.08
Rotation (radians)
Moment (tonf-m)
-30
-30 -20 -10 0 10 20 30
Lateraldisplacement (cm)
100
80
60
40
20
0
-20
-40
-60
-80
(a) Lateral force-displacement curves
Specimen B
(cyclic loading test)
Pull
Push
-100
-0.08 -0.04 0 0.04 0.08
Rotation (radians)
Moment (tonf-m)
-30
-30 -20 -10 0 10 20 30
Lateral displacement (cm)
100
80
60
40
20
0
-20
-40
-60
-80
Specimen C
(cyclic loading test)
Pull
Push
-100
-0.08 -0.04 0 0.04 0.08
Rotation (radians)
(b) Moment-rotation curves
Figure 4 Experimental results for the cyclic loading test of specimens A, B and C
In theory, if the foundation of a pier is allowed to rock with the uplift, the foundation lifts off the ground once its
moment of resistance provided by gravity is overcome. Thus, the base moment can be limited to the value
required to produce uplift against the restraining forces due to gravity. The base moment limitation will then
possibly reduce the inelastic deformation of the pier at the plastic hinge zone. These experiments showed that
there was a decrease of plastic deformation at the plastic hinge of a column as a result of the energy dissipation
of the inelastic rocking mechanism of the footing. However, this effect is not very significant for the
un-retrofitted case of specimen B. This is because before the base moment of the foundation could reach its limit
value, the column yielded and the strength degraded earlier due to its inadequate lap-splicing of the main
reinforcements and poor transverse confinement. Because the column yielded before the isolation effect of
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