Keywords: seismic, shear modulus, soil profile depth, heterogeneity, Monte Carlo simulation, thin layer method.

This paper deals with the seismic behavior of a heterogeneous soil profile, composed by a set of superposed layers extending horizontally to infinity, and having random properties [1,2,3]. Stochastic soil profile seismic analysis is carried out via Monte Carlo simulations combined with Deterministic Thin Layer Method (DTLM) [3]. Soil property of interest is shear modulus, modeled herein as spatially random field, by choosing the lognormal distribution [4,5,6]. The analysis considers also soil profile height as uncertain, which is integrated into global stochastic formulation, for the purpose to investigate repercussions of the uncertainty regarding bedrock depth on the probabilistic seismic response in time and frequency domains. In this study, statistics regarding extreme ground surface acceleration as well as the mean transfer function are calculated by performing a parametric study, which integrates the influence of coefficient of variation of both soil profile height and soil shear modulus.

Obtained results indicate that the variability of both, shear modulus and soil profile height, significantly influence the seismic behavior of soil profile in time and frequency domains.

In time domain, one observes that as the heterogeneity level of the simulated soil increases, as it occurs an important attenuation in the trend of ground surface acceleration in comparison with the homogeneous case for all values of shear wave velocity, and for different levels of heterogeneity. On the other hand, the dispersion of extreme ground surface acceleration is important as the heterogeneity level is increasing. Also, one observes that the variability of the soil profile height influence the extreme ground surface acceleration, even no trend is clear regarding the mean values curves, but it is well indicated that as the variability of the soil profile height increases, as the dispersion becomes important, this is valid for all heterogeneity levels.

In frequency domain, one observes for all heterogeneity levels, as the variability of the soil profile height increases as the mean transfer function amplitude is significantly attenuated (low and high frequency content) without any influence on the frequency content. Also one observes that as the heterogeneity level increases as the fundamental frequency is shifted to left, and the other higher frequencies are significantly attenuated. This is interpreted by filtering effect of higher frequencies.

The analysis carried out in this study makes in evidence the importance of accounting for the uncertainty regarding soil profiles height in any stochastic soil dynamic investigation. Despite the model used is this paper is simple, as 1D problem is adopted, but it provides guidance for sophisticated models to achieve more realistic modeling of soil media.

1

E. Kausel and R. Peek, "Dynamic loads in the interior of a layered stratum: An explicit solution." Bulletin of Seismological Society of America, 72(5), 1459-1481, 1982.

2

E. Kausel,"Thin layer method: Formulation in the time domain." International Journal of Numerical Methods in Engineering, 37, 927-941, 1994. doi:10.1002/nme.1620370604

3

M. Badaoui, A. Nour, A. Slimani and M.K. Berrah, "Consolidation statistics via Monte Carlo combined with Deterministic Thin Layer Method", in Proceedings of the third international conference on Engineering Computational Technology, Topping B.H.V., and Bittnar Z. (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 51 (CD-ROM), 2002. doi:10.4203/ccp.76.51

4

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

5

A. Nour, "Stochastic investigation of heterogeneous media via finite element analysis" (In French), Ph.D. thesis, University of Algiers, USTHB/FGC, March 2004.

6

A. Nour, A. Slimani, N. Laouami and H. Afra, "Finite element model for the probabilistic seismic response of heterogeneous soil profile", Journal of Soil Dynamics and Earthquake Engineering, 23(5), 331-348, 2003. doi:10.1016/S0267-7261(03)00036-8

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