Jianwen Liang

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

The scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space is investigated by using an indirect boundary element method (IBEM). Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green’s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green’s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

Dynamic Soil-Tunnel Interaction in Layered Half-Space for Incident Plane SH Waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

Scattering and diffraction of plane SH-waves by periodically distributed canyons

A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green’s functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.

The Diffraction of Rayleigh Waves by Twin Circular Cavities in a Poroelastic Half-Space

ABSTRACT The diffraction of Rayleigh waves by twin circular cavities in a poroelastic half-space is investigated using the indirect boundary integral equation method (IBIEM). To satisfy the boundary conditions on the free surface, Green’s functions of compressional and shear wave sources in a poroelastic half-space are derived based on Biot’s theory. It is verified that the IBIEM has great accuracy and numerical stability. Then, the influences of the drainage boundary condition, incident wave frequency, porosity, and cavity spacing on the dynamic responses are investigated by numerical examples. The results show that the amplification effect of the twin cavities is greater in the case of undrained boundary conditions, lower frequencies, and smaller cavity spacings. The porosity of the saturated medium also influences the dynamic responses because the velocity of the Rayleigh wave will change with the porosity of the saturated medium.

IBEM for Impedance Functions of an Embedded Strip Foundation in a Multi-Layered Transversely Isotropic Half-Space

ABSTRACT An indirect boundary element method (IBEM) is developed to study the dynamic impedance functions (stiffness coefficients) of a rigid strip foundation embedded in a multi-layered viscoelastic transversely isotropic (TI) half-space. The proposed IBEM using half-space Green’s functions of distributed loads as fundamental solutions have the merits of fictitious loads being directly applied on the real boundaries without the problem of singularity and of the discretization effort restricted to local boundaries. In addition, the accuracy of the proposed method is not affected by the thickness of the discrete TI layers, as the exact dynamic stiffness matrix is employed. The presented algorithm is verified via comparisons with published results for the isotropic medium. By taking a rigid strip foundation embedded in a homogeneous half-space, a single-layered half-space, and a multi-layered half-space as examples, the effects of material anisotropy, frequency of excitation, and soil layer on the impedance functions are studied in detail. Numerical results show that impedance functions for the TI medium can be significantly different from those of the isotropic case. The variation of TI parameters alters the dynamic characteristics of the TI layered site, which in turn alters the dynamic interaction between the soil and foundation. In addition, the soil sedimentary sequence also has a remarkable influence on the impedance functions.

In-plane dynamic Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic (TI) half-space. The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces, which are then applied to the total system with the opposite sign. By adding solutions restricted in the loaded layer to solutions from the reaction forces, the global solutions in the wavenumber domain are obtained, and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform. The presented formulations can be reduced to the isotropic case developed by Wolf (1985), and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI half-space subjected to horizontally distributed loads which are special cases of the more general problem addressed. The deduced Green’s functions, in conjunction with boundary element methods, will lead to significant advances in the investigation of a variety of wave scattering, wave radiation and soil-structure interaction problems in a layered TI site. Selected numerical results are given to investigate the influence of material anisotropy, frequency of excitation, inclination angle and layered on the responses of displacement and stress, and some conclusions are drawn.

The effect of dynamic characteristics of layered half-space on soil-structure interaction

By a 2-D model of a shear wall on semi-cylindrical rigid foundation in layered half-space for incident SH waves, the effect of dynamic characteristics of the site on the soil-structure interaction is studied by the indirect boundary element method. In order to construct the radiation field, the Greens function of an inclined line in layered half-space is used, avoiding the singularity problem of point source. The parametric studies are performed and it is shown that the dynamic response of the shear wall-foundation system in layered half-space is essentially different from that in homogeneous half-space; impedance ratio of bedrock to soil layer, as well as the thickness of soil layer could all introduce evident influence.