Fragility Curves for Tall Structure on Stochastically Variable Soil
R. Popescu & P. Chakrabortty
School of Engineering and Applied Science, Memorial University, St. John’s, Newfoundland and Labrador, Canada
J.H. Prevost
School of Engineering and Applied Science, Princeton University, Princeton, NJ, USA
Keywords: soil liquefaction, spatial variability, non-Gaussian, Monte Carlo, seismic motion
ABSTRACT: A tall structure placed on a “stochastically heterogeneous” saturated soil deposit is subjected to
random seismic excitation. The acceleration time histories are digitally generated as non-stationary stochastic
processes compatible with two different seismic design spectra. A Monte Carlo simulation approach involv-
ing generation of sample functions of 2D non-Gaussian vector fields and nonlinear dynamic finite element
analyses is used to investigate the effects of soil heterogeneity and of the seismic loading rate. The finite ele-
ment analyses are performed using fully coupled solid-fluid equations and a multi-yield plasticity soil consti-
tutive model. The calculations are performed for a range of seismic acceleration intensities, and the results,
incorporating effects from (1) random soil spatial variability, (2) seismic loading rate, and (3) uncertainties
related to the actual realizations of the seismic motion, are presented in terms of fragility curves expressing
the probability of exceeding a certain degree of damage as a function of earthquake intensity.
1 INTRODUCTION
Natural soil properties vary from one point to an-
other, even within so called “uniform” soil layers. In
addition to inducing uncertainty in the computed re-
sponse, natural spatial variability of soil properties
within geologically distinct layers affects the me-
chanical behavior of geotechnical structures. For ex-
ample, for phenomena involving the presence of a
failure surface (such as encountered in landslides or
in bearing capacity failures) the actual failure sur-
face can deviate from its theoretical position to pass
selectively through weaker soil zones and thus the
average mobilized strength is reduced when com-
pared to that of a corresponding uniform soil (e.g.
Focht and Focht 2001, Popescu et al., in review). For
the case of seismically induced soil liquefaction, it
was proven both experimentally (e.g. Budiman et al.
1995, Konrad and Dubeau 2002), and by numerical
analyses (e.g. Popescu et al. 1997, Chakrabortty et
al. 2004a) that a larger amount of excess pore water
pressure (EPWP) is generated in a heterogeneous
soil than in the corresponding uniform soil having
geomechanical properties equal to the average prop-
erties of the variable soil.
It was also demonstrated (Popescu et al., in re-
view) that the spatial variability (i.e. actual variation
of soil properties from one point to another) and the
uncertainty in the actual value of soil strength (de-
pending only on the degree of knowledge about the
soil at the site) have different effects on the pre-
dicted structural behavior. Spatial variability induces
both mechanical effects (e.g. reduction in average
mobilized strength) and statistical effects (variability
in the computed response), while the uncertainty in
the value of soil strength has only statistical effects.
Therefore, those two factors have to be accounted
for separately in analysis.
A soil-structure system has its own characteristic
frequency, which depends on material properties,
geometry, and degree of saturation of the soil. This
characteristic frequency may decrease during dy-
namic excitation, due to degradation of the soil ef-
fective deformation moduli as a result of pore pres-
sure build-up and/or large shear strains. Any
mechanical system is more sensitive to dynamic
loading as its characteristic frequency becomes
closer to the frequency range corresponding to the
maximum spectral values of the excitation. Conse-
quently, both the frequency content of seismic exci-
tation and the evolution of structural frequency char-
acteristics can make a significant difference in the
dynamic response of geotechnical structures.
This study, focusing on the two aspects discussed
before, analyzes the behavior of a tall (7-story)
structure sitting on a liquefiable soil deposit and sub-
jected to horizontal seismic motion. The effects of
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