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Comparative Study on EQWEAP Analysis with 2D/3D FE Solutions
Étude comparative sur l'analyse EQWEAP avec des solutions 2D/3D FE
Chang D.-W., Wang Y.-C.
Tamkang University, Taipei, Taiwan
Wu W.-L.
CECI Engineering Consultant Inc., Taipei, Taiwan
Chin C.-T.
Star Energy Corporation, Taipei, Taiwan
ABSTRACT: The seismic responses of the piles using one-dimensional wave equation analysis EQWEAP are compared to the ones
from 2D and 3D finite element analyses based on PLAXIS and MIDAS GTS programs. It is found that the solutions of 1D wave
equation analysis are compatible to those from finite element analyses providing that the site conditions and structural geometry are
relatively simple. Moreover, pile deformations are found mainly governed by the ground motions at the same direction. The effects of
ground motions at different directions are rarely important to the pile displacements. These observations suggest that the
one-dimensional EQWEAP analysis is an applicable tool in estimating the seismic responses of piles under the earthquake.
RÉSUMÉ: Les réponses sismiques des pieux en utilisant une analyse EQWEAP d’onde d’équation unidimensionnelle sont comparées
à celles des analyses 2D et 3D par éléments finis basés sur des programmes PLAXIS et MIDAS GTS. On retrouve que les solutions
des analyses d’équations d’ondes 1D sont compatibles avec celles des analyses par éléments finis pour autant que les conditions du
site et la géométrie structurelle soient relativement simples. De plus, des déformations de pieux se retrouvent principalement régies
par des mouvements du sol dans la même direction. Les effets de mouvements de sol dans des directions différentes ne sont que
rarement importants pour les déplacements de pieux. Ces observations suggèrent que l’analyse unidimensionnelle EQWEAP est un
outil utilisable dans l’estimation des réponses sismiques des pieux sous le tremblement de terre.
KEYWORDS:
seismic analysis, pile, wave equation analysis, finite element analysis
1 INTRODUCTION
One-dimensional wave equation analysis can be used to monitor
the time-dependent dynamic responses of piles under earthquake.
An uncoupled analysis termed as EQWEAP models the seismic
ground motions from lumped mass analysis, and superimposing
the ground motions to the piles via the discrete wave analysis
has been proposed (Chang
et al.,
2006, 2008, 2009a and 2012).
Alternative models can be used for soils with liquefaction
potential. The available ones including the use of soil
parameter reduction coefficient (SPRC), the excess pore water
pressure (EPWP) and the pseudo dynamic earth pressures
obtained by modifying the permanent/cyclic displacement
profiles (Tokimatsu and Asaka, 1998) or the maximum earth
pressures (Japan Road Association, 1990).
Such modeling is
rather convenient for massive computations required in
performance based design of piles. The authors have
demonstrated a couple of case studies on bridge pile foundations
using such analysis with probability analysis (Chang
et al
, 2010
2013a,b). This study intends to verify the 1D wave equation
analysis with the 2D/3D FE analyses. The comparative studies
were conducted using PLAXIS and MIDAS GTS programs.
2 1D WAVE EQUATION ANALYSIS EQWEAP
To model the seismic responses of the piles, the EQWEAP
analysis has been suggested for years (Chang
et al
., 2001, 2008
and 2009). To obtain the solutions, free-field ground responses
due to the earthquake was calculated first. A simple lumped mass
analysis on horizontal layered soils was adopted to obtain the
ground responses due the earthquake. The soil displacements
were then applied to the discrete wave equations with the
expressions of finite difference schemes. Figure 1 illustrates the
discrete pile segments and the equilibrium to derive the wave
equations. For large earthquake excitations whereas the ground
soils are liquefiable, the so-called soil parameter reduction
coefficient (JRA, 1996) could be used. Alternatively, more
rigorous solutions were achieved using the excess pore water
pressure (EPWP) model. The generations and dissipations of the
excess pore water pressures can be simulated by using proper
soil models. Once the ground responses were resolved, one could
choose the
P-y
and
t-z
soil models and other types of empirical
formulations to model the soil stiffness and strength parameters
for the wave equation analysis. Some people use the cylindrical
wave propagation theory to calculate for the elastic/inelastic soil
stiffness. The model parameters must be calibrated carefully in
order to obtain rational results of the simulations. In addition, a
transformed radiation damping model (Chang
et al
, 2000) was
used to compute time-dependent damping of the soils. In such
analysis, a good control of the superstructural loads is important.
The structural loads and inertia force of the pile cap as well as
the lateral earth pressures on the cap were analyzed properly, and
then applied to the piles. The seismic responses of a single pile
can be predicted using the time-dependent ground motions. In
the seismic impacts, the pile-to-pile interaction effects could be
ignored (Chang
et al
., 2009b). Such analysis can serve as a fast
and rational design tool for the seismic performance of piles
(Chang
et al
, 2010).
3 2D AND 3D FE ANALYSES FOR COMPARISONS
Finite element (FE) analysis has been extensively used to model
