Love Waves in a Viscoelastic Stratum: Explicit Expression for Complex Velocity as a Function of Frequency

ABSTRACT Propagation of Love wave is considered in a two-layered stratum of isotropic viscoelastic solids. The complex dispersion equation for this wave is solved through a complex analysis technique. This gets an analytical expression for complex velocity, as a function of real frequency rather than the complex wavenumber. This complex (phase) velocity is used further to calculate the (complex) group velocity. Numerical example is solved to analyze the dispersion in speed and attenuation of the viscoelastic Love waves.

Forced Vibration of Surface Foundation on Viscoelastic Isotropic Multi-Layered Stratum

A numerical approach is presented for analyzing the forced vibration of a rigid surface foundation. In the analysis, the foundation is discretized into a number of sub square-elements. The dynamic response within each sub-element is described by the Green’s function, which is obtained by the Fourier–Bessel transform and the precise integration method (PIM). Then, a system of linear algebraic equation in terms of the contact forces within each sub-element is derived, which leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for the foundation not only with a simple geometry, such as circular one, but also with irregular shapes. Comparisons between the results obtained by the proposed approach and the thin layered method are made, for which good agreement is achieved. Also, parametric studies are performed on the dynamic response of the foundation, considering the effects of the material damping, stratum depth, Poisson’s ratio and the contact condition of the soil–foundation interface. Several conclusions are drawn concerning the significance of each parameter. Further application of the method can be easily extended to the analysis of a foundation on a viscoelastic anisotropic multi-layered stratum because no further complexity is introduced except the constitutive matrix needs to be modified.

Dynamic Interaction of Two Adjacent Foundations Embedded in a Viscoelastic Soil

This paper studies the dynamic interaction for two adjacent rigid foundations embedded in a viscoelastic soil layer. The vibrations originate from one of the rigid foundations placed in the soil layer, which are subjected to harmonic loads of translation, rocking, and torsion. The dynamic responses of the rigid surface foundations are solved from the wave equations by taking into account their interaction. The solution is formulated using the frequency domain boundary element method (BEM), in conjunction with Kausel–Peek Green’s function for a layered stratum and the thin layer method (TLM) to account for the interaction between the two foundations. This approach allows us to establish a mathematical model for determining the compliance functions of the two adjacent foundations with regard to their spacing, substratum depth, masses, shapes, embedding, load intensity, and frequencies of excitation. The soil heterogeneity was taken into account for the cases of one or two layers of soils over a rigid bedrock and semi-infinite soil. The analysis of the present study indicates that the effect of several parameters on the dynamic interaction response of two adjacent foundations is nonnegligible. In particular, the dominant influence of some parameters, such as the heterogeneity of the soil, shape of the foundations, and the load intensity, compared to the other ones is clearly revealed.

Vibrations Induced by Harmonic Loadings Applied at Circular Plate on Layered Medium

A systematic procedure is developed to calculate ground vibration at any specific location in layered medium due to harmonic loadings applied at a circular plate on the medium. In the procedure, the technique decomposing the interaction tractions between excited plate and layered medium will be employed. The decomposed tractions will automatically match boundary values of general solutions of three dimensional wave equations in cylindrical coordinates. In numerical results, the effect of layered stratum on ground vibration will be investigated and how ground vibration in layered medium decreases with depth will be presented. Also, from the numerical results, one can observe ground vibration may not decay monotonically along distance away from vibration source. The presented scheme is proved to be effective and efficient for accurately predicting near-field ground response to harmonic loadings applied at a rigid circular plate on layered medium. Comments on the presented scheme and numerical results will be given.

Analysis of Axial Load Transfer for Super-Long Single Pile in Layered Ground

Based on the bearing capacity behavior and load transfer mechanism of super-long pile in soft soil, the three-stage hyperbolic softening model is presented as the load transfer function of pile-side soil, and tri-linear model is introduced to simulate the characteristics of sediments in pile end. The differential equations are established by dealing with the states of static equilibrium, with considering the character of layered stratum and pile-soil interaction. The analytical solutions on different states are obtained by power series. Based on transfer matrix method, soil mechanics and elastic theory, a set of analytical equations and calculating method for the axial load-settlement curve of pile top in layered ground are established. Lastly, the calculating parameters are obtained by theoretically approaching to actually measure load-settlement curve in soft soil area. The calculating contrast to adjacent test pile is carried out by the method and the results are satisfactory.