Stiffness matrices for layered soils
01 Dec 1981-Bulletin of the Seismological Society of America (Bulletin of the Seismological Society of America)-Vol. 71, Iss: 6, pp 1743-1761
TL;DR: In this article, the Haskell-Thompson transfer matrix method is used to derive layer stiffness matrices which may be interpreted and applied in the same way as stiffness matrix in conventional structural analysis, and the exact expressions are given for the matrices, as well as approximations for thin layers.
Abstract: The Haskell-Thompson transfer matrix method is used to derive layer stiffness matrices which may be interpreted and applied in the same way as stiffness matrices in conventional structural analysis These layer stiffness matrices have several advantages over the more usual transfer matrices: (1) they are symmetric; (2) fewer operations are required for analysis; (3) there is an easier treatment of multiple loadings; (4) substructuring techniques are readily applicable; and (5) asymptotic expressions follow naturally from the expressions (very thick layers; high frequencies, etc) While the technique presented is not more powerful than the original Haskell-Thompson scheme, it is nevertheless an elegant complement to it The exact expressions are given for the matrices, as well as approximations for thin layers Also, simple examples of application are presented to illustrate the use of the method
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TL;DR: In this paper, exact solutions for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings are derived.
Abstract: Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.
584 citations
TL;DR: A comprehensive review of the literature in the main scientific journals provides historical perspective, methodological issues, applications, and most promising recent approaches as discussed by the authors, and a best-practices guideline is also outlined.
Abstract: Today, surface-wave analysis is widely adopted for building near-surface S-wave velocity models. The surface-wave method is under continuous and rapid evolution, also thanks to the lively scientific debate among different disciplines, and interest in the technique has increased significantly during the last decade. A comprehensive review of the literature in the main scientific journals provides historical perspective, methodological issues, applications, and most-promising recent approaches. Higher modes in the inversion and retrieval of lateral variations are dealt with in great detail, and the current scientific debate on these topics is reported. A best-practices guideline is also outlined.
407 citations
Cites methods from "Stiffness matrices for layered soil..."
...The tiffness-matrix method proposed by Kausel and Roesset 1981 is ssentially a reformulation of the transfer-matrix method, but it ofers the advantage of a simplified procedure for assembling the gloal matrix, according to the classical scheme of structural analysis. he third possibility involves…...
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TL;DR: In this paper, it is shown that large dynamic amplifications appear in the dynamic response of the rail/embankment/ground system as the train speed approaches an apparently critical value.
377 citations
TL;DR: In this paper, the analysis of the dispersion characteristics of surface wave data is presented, with particular attention to reliability and resolution, and different approaches that are used to estimate and interpret dispersion properties are considered.
Abstract: Surface-wave methods (SWMs) are very powerful tools for the near-surface characterization of sites. They can be used to determine the shear-wave velocity and the damping ratio overcoming, in some cases, the limitations of other shallow seismic techniques. The different steps of SWM have to be optimized, taking into consideration the conditions imposed by the small scale of engineering problems. This only allows the acquisition of apparent dispersion characteristics: i.e. the high frequencies and short distances involved make robust modelling algorithms necessary in order to take modal superposition into account. The acquisition has to be properly planned to obtain quality data over an adequate frequency range. Processing and inversion should enable the interpretation of the apparent dispersion characteristics, i.e. evaluating the local quality of the data, filtering coherent noise due to other seismic events and determining energy distribution, higher modes and attenuation. The different approaches that are used to estimate and interpret the dispersion characteristics are considered. Their potential and limits with regard to sensitivity to noise, reliability and capability of extracting significant information present in surface waves are discussed. The theory and modelling algorithms, and the acquisition, processing and inversion procedures suitable for providing stiffness and damping ratio profiles are illustrated, with particular attention to reliability and resolution.
322 citations
TL;DR: In this article, the effects of multiple modes on Rayleigh wave dispersion are discussed to reduce the ambiguity of uniqueness of shear wave velocity (Vs) profiles estimated by the surface wave method.
Abstract: The effects of multiple modes on Rayleigh wave dispersion are discussed to reduce the ambiguity of uniqueness of shear wave velocity (Vs) profiles estimated by the surface wave method. Based on a review of previous studies, dispersion curves of multiple‐mode Rayleigh waves induced by harmonic vertical point loading are derived for both vertical and horizontal particle motions. Also presented is the variation with frequency of the amplitude ratio between horizontal and vertical particle motions. Numerical studies indicate that a stiff soil layer overlying a softer soil layer induces a higher mode or multiple modes, leading to an inversely dispersive characteristic. Consideration of the effects of higher modes is strongly recommended in the inverse process when the observed data show an inversely dispersive trend. The ambiguity of uniqueness of the inverted soil profiles may be reduced by using either the dispersion data of horizontal motion or the amplitude ratio of particle motions in addition to the disp...
304 citations
References
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TL;DR: In this paper, a matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media.
Abstract: A matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media. The method is used to compute phase and group velocities of Rayleigh waves for two assumed three-layer models and one two-layer model of the earth9s crust in the continents. The computed group velocity curves are compared with published values of the group velocities at various frequencies of Rayleigh waves over continental paths. The scatter of the observed values is larger than the difference between the three computed curves. It is believed that not all of this scatter is due to observational errors, but probably represents a real horizontal heterogeneity of the continental crusts.
2,310 citations
TL;DR: In this article, the transmission of a plane elastic wave at oblique incidence through a stratified solid medium consisting of any number of parallel plates of different material and thickness is studied theoretically.
Abstract: The transmission of a plane elastic wave at oblique incidence through a stratified solid medium consisting of any number of parallel plates of different material and thickness is studied theoretically The matrix method is used to systematize the analysis and to present the equations in a form suitable for computation
1,827 citations
TL;DR: In this paper, a numerical procedure is developed for the dynamic analysis of plane, linearly elastic systems consisting of an irregular zone joined to semi-infinite layered zones, where all exciting forces are assumed to be harmonic and perpendicular to the plane of the structure.
Abstract: A numerical procedure is developed for the dynamic analysis of plane, linearly elastic systems consisting of an irregular zone joined to semi-infinite layered zones. All exciting forces are assumed to be harmonic and perpendicular to the plane of the structure. This implies that only shear waves (SH-waves) are generated and that no displacements occur in the plane of the structure. The method employs a finite element analysis of the irregular zone of the structure. The effect of the semi-infinite layered zones is accounted for by boundary conditions developed from a new discrete theory for standing and propagating Love waves in layered systems. The method is used to evaluate the screening effect of a trench and the accuracy of a currently used method to predict the motion of a foundation subject to ground induced vibrations.
283 citations
Dissertation•
01 Jan 1974
195 citations
TL;DR: In this paper, a simple numerical method is developed for the analysis of generalized Rayleigh waves in multilayered elastic media, which completely avoids the use of displacement potentials and leads to a simple eigenvalue problem which may be solved by generally available effective computer codes.
Abstract: A simple numerical method is developed for the analysis of generalized Rayleigh waves in multilayered elastic media. The method which completely avoids the use of displacement potentials leads to a simple eigenvalue problem which may be solved by generally available effective computer codes. Numerical results obtained by the method show excellent agreement with previously published solutions obtained by other theories.
159 citations