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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 100
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping
Paper 98
A Stochastic Thin-Layer Method for an Inhomogeneous Half-space in Antiplane Shear J.H. Lee1, J.K. Kim1 and J.L. Tassoulas2
1Department of Civil and Environmental Engineering, Seoul National University, Korea
Full Bibliographic Reference for this paper
J.H. Lee, J.K. Kim, J.L. Tassoulas, "A Stochastic Thin-Layer Method for an Inhomogeneous Half-space in Antiplane Shear", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2012. doi:10.4203/ccp.100.98
Keywords: stochastic analysis, thin-layer method, inhomogeneous half-space, uncertainty, soil-structure interaction, wave propagation.
Summary
Wave propagation in a layered half-space has many applications in seismology and civil engineering. Exact stiffness matrices and their approximations for a layered half-space were previously presented [1]. The method based on the discrete stiffness matrices is often referred to as a "thin-layer method". A spectral decomposition for solutions to the method was developed [2]. Since the method leads to rigorous and effective numerical models, it has been applied to wave-propagation problems in various layered systems [3]. In the conventional thin-layer method, properties of layered media have been assumed deterministic. However, all natural and man-made systems have intrinsic randomness in material properties. Therefore, a stochastic enhancement of the thin-layer method is highly desirable.
In this paper, a "stochastic thin-layer method" is developed for the analysis of wave propagation in an inhomogeneous half-space in antiplane shear. The shear modulus is assumed uncertain and characterised by a random field with vertically varying statistical properties. Then, it can be expanded using the Hermite polynomial chaos of a zero-mean and unit-variance Gaussian field with a correlation function [4]. Using the Karhunen-Loève expansion, the Gaussian field can be discretized into independent standard normal random variables [5]. The inhomogeneous half-space is represented by thin layers. The layers include not only ordinary layers but also continued-fraction absorbing boundary conditions for the infinite extent of the half-space [6]. Applying the Galerkin method not only in the spatial domain but also in the stochastic domains, a stochastic thin-layer method for an inhomogeneous half-space in antiplane shear is presented. Using the stochastic methods, dynamic responses of an inhomogeneous half-space subjected to a transverse line load on its surface are obtained and verified by comparison with Monte Carlo simulations. The stochastic methods are found to provide accurate probabilistic treatment of half-space dynamics. References
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