Keywords: seismic response, heterogeneity, shear modulus, lognormal distribution, fraction of critical damping, beta distribution, Monte Carlo simulation, finite element method.

Geotechnical earthquake engineering deals with many kinds of uncertainties which should be considered in the computation of site earthquake response. These uncertainties are related mainly to earthquake input which is caused by earthquake source mechanism, transmission path and others, and also to, soil properties which vary from place to place within deposits. Unlike structural or mechanical engineering in which design geometries and material properties are specified by the engineer, geotechnical engineering deals with natural processes and material properties of geological formations which must be interpreted from limited observations and data availability. Consequently, the reliable behaviour of an heterogeneous soil profile under seismic environment can not proceed from deterministic approach. The resort to probabilistic techniques enables modelling of such uncertainties by analysing their dispersion effects.

The scope of this paper is to analyse the behaviour of heterogeneous soil profile under uniform seismic excitation. Soil properties of interest are shear modulus, and fraction of critical damping modelled herein as spatially random fields [1] by considering the spatial Gaussian correlation. Shear modulus is modelled using the lognormal distribution. This choice is motivated by the fact that this parameter is positive, and the lognormal distribution enables analysing its large variability. Because fraction of critical damping is bounded in practice between tow extreme values, its random field is obtained using the Beta distribution. In this study, the Beta field is obtained by a mapping technique on the probability distribution function diagram, and by solving a non-linear equation [2]. However, mean and variance are unchanged through the mapping operation.

In this frame, the seismic response is carried out using Monte Carlo simulations combined with deterministic finite element method (DFEM). This procedure is coded in the computer program for the 3D approximate soil-structure interaction problems FLUSH [3], by enabling it, handling simulation of random soil media, where pre-processing and post-processing aspects are considered. Moreover, it is analysed the level of heterogeneity influence on the acceleration response at ground surface in time and frequency domains. The analysis integrates the influence of, coefficient of variation of the two soil properties and the inter-property correlation coefficient.

Obtained results indicated that as heterogeneity level of the simulated soil increases, as it occurs an important attenuation in the trend of ground surface acceleration in comparison with homogeneous case. The attenuation is significant for small values of mean shear wave velocity corresponding to soft soils condition, and the amplification of the extreme ground surface acceleration is more significant for large values of mean shear wave velocity, corresponding to hard soils condition, interpreted by the resonance phenomena, as soil profile frequency is close to the excitation one. Also, one obtains even with uniform seismic excitation at bedrock, a differential motion at ground surface. This is induced by the spatial variability of soil properties. In frequency domain, it is observed that as the coefficient of variation of shear modulus increases as the fundamental frequency is shifted to left, and the other higher frequencies are significantly damped. This is interpreted by filtering effect of higher frequencies. This result indicates that as heterogeneity of the medium increases as the frequency content is dominated by the lower frequencies and the simulated soil becomes softer. Also, when the inter-property correlation shear modulus fraction of critical damping is growing from negative to positive values, the mean transfer function amplitude is significantly amplified. This result indicates that positive correlation between shear modulus and fraction of critical damping is in favour for seismic waves amplification.

1

G.A. Fenton, "Simulation and Analysis of Random Fields", Ph.D. thesis, Princeton University, 1990.

2

A. Nour, A. Slimani, N. Laouami, "Foundation settlement statistics via finite element analysis", In press, Journal Computers and Geotechnics, 2002. doi:10.1016/S0266-352X(02)00014-9

3

J. Lysmer, T. Udaka, C.F. Tsai, H.B. Seed, "A computer program for approximate 3-D analysis of soil-structure interaction problem - FLUSH-", Earthquake Engineering Research Center. University of California Berkeley, EERC 75-30, 1975.

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