1456
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Figure 1. Seismic hazard curves in Taiwan (after Cheng, 2002)
These PGAs are the design target PGA (PGAt), one can use
these PGAs to calibrate the possible seismic records in hand.
The calibrated seismic records can be regarded as scenarios for
numerical studies. For any specific pile foundation located in
Taipei metropolitan, the vertical load (V), horizontal load (H),
pile diameter (D), pile length (L) and the area ratio of steer bar
(Ar) are known from the regular design. The site conditions are
also acknowledged from the previous work of site investigation.
A simplified ground conditions can be thus assumed.
Notwithstanding, the soil parameters in use must be calibrated
carefully. For example, the solution of EQWEAP adopts
empirical formulations suggested for soils in Taipei. The shear
wave velocities (Vs) of the soils can be correlated to the in-situ
SPT-N values. Moreover, all the model parameters used in the
stress analysis must be calibrated with cautions. The nonlinear
soil model used in EQWEAP are those suggested by Finn et al.
(1977), Seed and Idriss (1982) and Skempton (1986). One can
use such analysis to compute the pile responses under the
scenarios. The maximum pile displacement occurred during the
quake will be taken as the EDP index, and the maximum
internal bending moments occurred along the pile will be used
as the DM index. Using the schemes suggested by Kramer
(2008), one can find the annual rates of exceedance to both
EDPs and DMs under different PGAt. Nonlinearities of the
piles can be modeled through a tri-linear relationship of the
bending moment and curvature of the pile (see Figure 2). An
approximate Bouc-Wen model suggested by Kunnath and
Reinhorn (1989) was considered. The model parameters
and
Z were solved easily by interpreting the moment capacities and
the associated curvatures obtained from LPILE analysis (Sung,
2012).
Figure 2. Approximation of the tri-linear moment-curvature relationships
for concrete pile
Table 1 presents the information and model parameters of a
numerical study using EQWEAP for bridge pile foundations of
an expressway in Hsinchuang District, New Taipei City.
Figures 3a,b shows the results of the maximum pile
displacements versus PGAt and the corresponding annual rates
of exceedance versus maximum pile displacements. Figures
4a,b shows the ones of the maximum pile bending moments
versus the maximum pile displacements and the corresponding
annual rates of exceedance versus maximum bending moments.
It can found that the maximum pile displacements of the
numerical model under the seismic levels are 19, 45 and 79 cm,
respectively. The corresponding maximum pile moments found
at the pile head are 7347, 22148 and 28679 kN-m. Comparing
to the moment capacities (i.e., Mcr, My and Mult) obtained
from the LPILE analysis, the numerical piles will have
concrete cracks occurred under the moderate earthquakes
(however most of the pile shaft still remains elastic). For
design earthquake, the piles are found to be within the yield
limit of the bar. As to the maximum consideration earthquake,
the plastic hinge will not be generated in this case. A
corresponding design scheme is suggested in Figure 5 whereas
the zone of the dash lines is an option in which one can
determine the allowable pile displacements according to the
moment capacities for different seismic concerns.
Table 1 Geotechnical information of numerical model in this study
Depth
(m)
Layers
Soil
γ
(kN/m
3
)
SPT
-N
C
(kN/m
2
)
(
˚)
Vs
(m/s)
0~4 Surface
fill
Sand
18
3
9.8 30 115
4~10 SS form.
VI
CM 19
5
9.8 28 171
10~20 SS form.
V SM 20
14
0
33 192
20~40 SS form.
IV CM 20
11
20
28 222
40~50 SS form.
III
SM 20
21
0
34 221
50~60 SS form.
II
CM 20
14
20
35 241
60~70 SS form.
I
SM 20
30
0
30 248
Table 2 Material parameters and structural dimensions in use
Parameters and dimensions of piles
Bridge pile foundation 3×3 piles
Pile diameter: 2m, Pile length: 60m
Design vertical loads: Ordinary 9000 kN, Seismic 18000 kN,
Horizontal load = 10~15% vertical load
、
Maximum steel bar Ar = 2%
E=30 MN/m
2
、
= 0.1
5
、
=24 kN/m
3
Model parameters used for soils
Approach
Method/model parameter
Spring and damper
EPWP
Finn’s EPWP model
where C
1
=0.8, C
2
=0.79,
C
3
=0.45, C
4
=0.73; R =
0.00031(100-Dr)
2
+
0.0062; m=0.43, n = 0.62,
k
2
= 0.0028; Seed and
Idriss’s model of G/G
max
where K
2,max
=
f
(Dr);
and Skempton’s equation
where Dr (%) =
f
(N
1,60
)
Spring:
K
s
=
n
h
x ;
empirical relationships
of SPT-N and
n
h
could
be found in Johnson
and Kavanagh (1968)
Damper: Transformed
damping (Chang and
Yeh, 1999)
NOTE:
V
s
=80N^1/3 for sand,
V
s
=100N^1/3 for clayey soils
.
Figure 3 (a) EDP and IM relationship (b)
and EDP relationships
0.0
0.2
0.4
0.6
PGA, IM (g)
0
40
80
120
Displacement, EDP (cm)
PGA=0.12g
PGA=0.29g
PGA=0.51g
0
40
80
120
Displacement, EDP (cm)
1E-4
1E-3
1E-2
1E-1
1E+0
Annual Probability of Exceedance (1/year)
