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 977 ICOSSAR 2005, G. Augusti, G.I. Schuëller, M. Ciampoli (eds) © 2005 Millpress, Rotterdam, ISBN 90 5966 040 4