Search

Abstract The subject of in-plane soil-structure interaction of a shear wall on a rigid circular foundation embedded in a linear elastic half-space under an incident plane P wave is revisited. It is known that satisfying the zero stress condition on the ground surface has been the major obstacle when developing an analytic solution of this model. Early solution procedures approximated the ground surface by the surface of a large cylinder. In this paper, two sets of closed-form solutions are derived based on the new approaches: one approach neglects the boundary conditions on the ground surface, while the other includes all boundary conditions by means of the weighted residue method. The objective of this work is to study the relative importance of these boundary conditions and evaluate the results generated from these two solution procedures. Foundation and building responses, as well as surface displacement and stress are compared for the two solutions and to previously published approximate solutions. Highlights • Dynamic soil-structure interaction in homogeneous half-space. • Shear beam building on semi-cylindrical foundation. • In-plane excitation by plane P waves. • Significance of surface boundary conditions on amplitudes of scattered waves. [ABSTRACT FROM AUTHOR]

In-plane soil-structure-interaction of a shear wall on a rigid circular foundation embedded in a linear elastic half-space, excited by an incident plane SV wave, is solved by relaxing the zero-stress boundary conditions on the ground surface. An approximate solution of this model was previously presented for the cylindrical approximation of the ground surface. This paper formally neglects such boundary conditions, and as a result, the complexity of the formulation is significantly reduced. Solutions for foundation and building motions in frequency space are compared to the previous results and it is shown that the present approximate solution provides excellent and almost identical results. The objective of this paper is to provide further insight on the role and the effects of surface boundary conditions for this type of problem. [ABSTRACT FROM AUTHOR]

This paper presents an analytic solution of a three-dimensional Soil-Structural Interaction (3D SSI) model in which the building and foundation are idealized as cylindrical thin-rod and rigid hemisphere. The ground is a stress-free elastic, isotropic, homogenous half-space, and excitation is vertically incident plane P-wave. Analytic three-dimensional (3D) solutions are presented which satisfy the stress-free boundary conditions at the half-space surface. Foundation motions, relative responses of building and surface displacement of soil around building are analyzed and discussed. A comparison with related two-dimensional (2D) SSI close-form solution is also described. [ABSTRACT FROM AUTHOR]

The analytical solution of a two-dimensional moon-shaped alluvial valley embedded in an elastic half-space is analyzed for incident plane SH waves, using the wave function expansion and the Discrete Cosine Transform (DCT). A series of solutions with different depth-to-radius ratios have been computed, analyzed, and discussed. It is shown that amplification of incident motions along the thinning valley segment can be significant. The phenomena of combined action of the waves resulting from (a) turning (reversing the direction of propagation), (b) focusing, and (c) diffraction from the half space into the valley have been examined with an emphasis on the significance for surface-motion amplification and the power to damage man-made structures. [ABSTRACT FROM AUTHOR]

An indirect boundary element method (IBEM) is developed to study the scattering and diffraction of plane qP- and qSV-waves by a canyon in a multi-layered transversely isotropic (TI) half-space. First, the exact dynamic stiffness matrix for in-plane motion is constructed to determine the free fields of the multi-layered TI half-space for incident plane qP- and qSV-waves. Dynamic Green's functions for uniformly distributed loads acting on an inclined line are then derived and the scattered fields are expressed as the summation of dynamic responses of a set of fictitious distributed loads applied on the canyon surface. Finally, the boundary condition is introduced to determine the densities of the distributed loads and the total dynamic responses are recovered by adding the free fields to the scattered fields. The proposed IBEM has the merits of distributed loads being directly applied on the real boundary of the irregularity without the problem of singularity, and the discretization effort being restricted to the surface of the canyon. Comparisons with existing numerical solutions for the isotropic (special) case are conducted to confirm the validity of the proposed formulations. And parametric studies are performed in both the frequency and time domains to investigate the influence of material anisotropy, frequency of excitation, incident angle and layering on the surface motions. Numerical results show that the surface motions for the TI medium can be significantly different from those of the isotropic case and that the responses are highly dependent on the TI parameters, especially for the layered TI half-space. [ABSTRACT FROM AUTHOR]

The model studied in this paper presents an extension of previous work for a shear wall on a semi-circular rigid foundation in an isotropic homogeneous and elastic half-space. The objective is to develop a soil-structure interaction model that can later be applied to the case of a flexible foundation. As shown in the Introduction below, Luco considered the case of a rigid foundation subjected to vertical incident plane SH waves, and Trifunac extended the solution for the same rigid foundation subjected to SH waves but for arbitrary angles of the incidence. In this paper, a new approach and model are presented for the same semi-circular rigid foundation with a tapered-shape (instead of rectangular) superstructure. The analytical expression for the deformation of the semi-circular rigid foundation below this tapered shear wall with soil-structure interaction in an isotropic homogeneous and elastic half-space is thus derived. Results are then compared with those of Trifunac discussed in the section below. This problem formulation can and will later be extended in the case of a flexible foundation that is semi-circular or arbitrarily shaped. [ABSTRACT FROM AUTHOR]

Abstract: A well-defined boundary-valued problem of wave scattering and diffraction in elastic half-space should have closed-form analytic solutions. This two-dimensional (2-D) scattering around a semi-circular canyon in elastic half-space subjected to seismic plane and cylindrical waves has long been a challenging boundary-value problem. In all cases, the diffracted waves will consist of both longitudinal (P-) and shear (S-) rotational waves. Together at the half-space surface, these in-plane longitudinal P- and shear SV-waves are not orthogonal over the infinite half-space flat-plane boundary. Thus, to simultaneously satisfy both the zero normal and shear stresses at the flat-plane boundary, some approximation of the geometry and/or wave functions often has to be made, or in some cases, relaxed (disregarded). This paper re-examines this two-dimensional (2-D) boundary-value problem from an applied mathematics points of view and redefines the proper form of the orthogonal cylindrical-wave functions for both the longitudinal P- and shear SV-waves so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite-canyon surface are then comparatively less complicated to solve. This is now a closed-form analytic solution of the 2-D boundary-valued problem satisfying the half-space zero-stress boundary conditions exactly. [Copyright &y& Elsevier]

Abstract: The three-dimensional scattering by a hemi-spherical canyon in an elastic half-space subjected to seismic plane and spherical waves has long been a challenging boundary-value problem. It has been studied by earthquake engineers and strong-motion seismologists to understand the amplification effects caused by surface topography. The scattered and diffracted waves will, in all cases, consist of both longitudinal (P-) and shear (S-) shear waves. Together, at the half-space surface, these waves are not orthogonal over the infinite plane boundary of the half-space. Thus, to simultaneously satisfy both zero normal and shear stresses on the plane boundary numerical approximation of the geometry and/or wave functions were required, or in some cases, relaxed (disregarded). This paper re-examines this boundary-value problem from the applied mathematics point of view, and aims to redefine the proper form of the orthogonal spherical-wave functions for both the longitudinal and shear waves, so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite canyon surface will be easy to satisfy. [Copyright &y& Elsevier]

Abstract: The paper presents an exact, analytical solution to the boundary-valued problem of the two-dimensional scattering of anti-plane (SH) waves by a shallow, semi-elliptical hill on an elastic half-space, based on the method of wave-function expansion in elliptical coordinate and elliptical cosine half-range expansion. It is expressed in terms of an infinite system of simultaneous linear equations that is later truncated for numerical computation. Some numerical results when semi-elliptical tends to semi-circular are compared with the existing results presented by Lee et al. (2006) [12]. Complicated effects on ground motion due to the existence of an elliptical hill at various aspect ratios and angles of wave incidence are illustrated. [Copyright &y& Elsevier]

Abstract: The ground motion and wave propagation resulting from the scattering of anti-plane (SH) waves by a deep semi-elliptical hill on an elastic half-space are investigated. The solution is the closed-form one based on the method of wave-function expansion, and the expansion of elliptical sine and cosine over the half-range [−π/2, π/2]. The analysis shows that the interference of ground motion depends on several factors such as frequency of the incident waves, incident angle, and the aspect ratio of elliptical hills. Similar to part I: Shallow Hill, numerical results when semi-elliptical tends to semi-circular are compared with the work done by Lee et al. [17]. [Copyright &y& Elsevier]

Abstract: This paper presents a closed-form wave function analytic solution of two-dimensional scattering and diffraction of anti-plane SH-waves by a two-dimensional foundationless structure that corresponds to a shear wall on an elastic half-space. A wave-function expansion method is used to solve this model by first prescribing a set of wave functions with undetermined coefficients and then assembling them together based on the stress and displacement boundary conditions on the surface between the structure and half space. This results in a set of infinite equations to be solved by truncating to a finite set. The amplitudes and residuals of the displacement and stress distributions around the structure and nearby ground surface will be discussed carefully. While the solution is analytical, the computation of the numerical results involves the evaluation of complicated integrals. This analytic solution will be helpful to the understanding of propagation of seismic or other stress waves within the superstructure(s) undergoing earthquakes or other blast loads. [ABSTRACT FROM AUTHOR]

Abstract: The average velocity of shear waves in the top 30m of soil, ν L , has become the parameter used by many engineering design codes and most recently by published empirical-scaling equations to estimate the amplitudes of strong ground motion. Yet there are few studies to determine whether this is a meaningful parameter to use—and whether estimates that do use it are reliable. In 1995, the authors studied this problem and concluded that ν L should not be used. We reported then that an older site characterization in terms of the soil site parameter proposed by Seed et al. , s L , worked better because it included a measure of the thickness of the soil layers to considerably greater depths. Our report, however, made no difference; numerous papers continued to be published based only on scaling in terms of ν L , and worse, they also ignored the geological site conditions. The purpose of this paper is to emphasize that the average shear-wave velocity in the top 30m of soil should not be the only site parameter used to scale strong-motion amplitudes. While the search continues for the more meaningful site parameters to use in empirical scaling of strong earthquake ground motion, it is better to use s L to describe the amplification of seismic waves by soil deposits near the surface. [ABSTRACT FROM AUTHOR]

Abstract: The zero-stress boundary conditions at the surface of the half-space in the presence of surface and sub-surface cavities for in-plane, incident cylindrical P- and SV-waves have always posed challenging problems. The outgoing cylindrical P- and SV-waves can be represented by Hankel functions of radial distance coupled with the sine and cosine functions of angle. Together, at the half-space surface the P- and SV-wave functions are not orthogonal over the semi-infinite radial distance from 0 to infinity. Thus, to simultaneously satisfy the zero in-plane, normal, and shear stresses, an approximation of the geometry is often made. This paper presents an analytical formulation of the boundary-valued problem, where the Hankel wave functions are expressed in integral form, changing the representation from cylindrical to rectangular coordinates, so that the zero-stress boundary conditions at the half-space surface can be applied in a more straightforward way. It is sometimes desirable to use alternate, simpler, or approximate solutions to the boundary-valued problems, without going to great lengths to have all of the boundary conditions satisfied. The free-stress boundary conditions at the half-space surface to be solved here are among the most complicated boundary conditions to be satisfied in the present class of problems. It is thus of interest to illustrate what the solution would be like if the half-space boundary conditions are not imposed—in other words, if they are “relaxed.” A section of this paper is devoted to this approach, and the results of the solutions with the half-spaced, stress-free boundary conditions “imposed” and “relaxed” are presented and compared. The method introduced here may also be applied to more complicated wave-propagation problems, like the diffraction problems involving surface and sub-surface inhomogeneities in a poroelastic half-space medium. [Copyright &y& Elsevier]

Abstract: This paper discusses surface displacements, surface strain, rocking, and energy partitioning during reflection-of-plane waves in a fluid-saturated poroelastic half-space. The medium is modeled by Biot''s theory, and is assumed to be saturated with inviscid fluid. A linear porosity-modulus relation based on experimental data on sandstones is used to determine the material parameters for Biot''s model. Numerical results in terms of angle of incident waves and Poisson''s ratio are illustrated for various porosities and degrees of solid frame stiffness. The results show that the amount of solid frame stiffness controls the response of a fluid-saturated porous system. A poroelastic medium with essentially dry-frame stiffness behaves like an elastic medium, and the influence of pore fluid increases as dry-frame stiffness is reduced. The effects of a second P-wave become noticeable in poroelastic media with low dry-frame stiffness. [Copyright &y& Elsevier]

Although most analytical research on soil-structure interaction (SSI) has assumed a rigid building foundation, numerical and experimental studies have shown that the dynamic response of a structure supported on flexible foundation will differ significantly from the same response on a rigid foundation. The analytical solutions have provided physical insights into the nature of the SSI problems and offered benchmarks to verify the approximate and numerical methods, among others. To this end, in this paper, we present an analytical solution of a tapered shear beam on an elastic semi-circular foundation excited by incident plane SH waves. • Two-dimensional Soil-structure interaction with flexible foundation. • Compared to rigid foundation elastic foundation scatters less of incident wave energy back into half space. • Elastic foundation allows more of the incident wave energy to enter the structure. • Response spectrum method cannot be used for incident waves shorter than twice the foundation width. [ABSTRACT FROM AUTHOR]

The vibrations of a ground-track system subjected to moving train loads are investigated by using a semi-analytical method combining with the substructure technique. In the coupled system, the ground is modeled as a multi-layered transversely isotropic (TI) half-space, and the track is modeled as a three-layered beam structure, which consists of the rails, sleepers and ballast. The two substructures are coupled by the compatibility condition of vertical displacement at the ballast centerline. The displacement and stress responses of the layered TI ground due to the reaction of the track are then obtained by employing the stiffness method. And solutions in the physical domain are recovered by Fourier synthesis of the frequency-wavenumber domain responses. The proposed semi-analytical model has the merits of all parameters having explicit physical meaning, which is very convenient for engineering application, and of the accuracy being not affected by the layers' thickness because of the exact dynamic stiffness matrix. The derived formulations are verified by comparison with the existing solutions for the isotropic medium that is a special case of the more general problem addressed. Numerical calculations are first performed for the case of a single wheel axle load moving at subsonic, transonic and supersonic speeds, and then for the case of the X-2000 high speed train of the Swedish National Railway travelling at a speed of 200 km/h. Numeric results show that the vibrations of the ground-track system can be very different when soil anisotropy is considered. And the variation of the TI parameters alters the resonance frequencies of the ground, which in turn alters the interaction between the track and ground. • A semi-analytical method is proposed to study vibrations of a Transversely Isotropic (TI) ground-track system. • The method gives accurate results and is very convenient for engineering application. • The method can serve as benchmark for the much more complex numerical methods. • Soil anisotropy should be considered to assess the train-induced vibrations accurately. [ABSTRACT FROM AUTHOR]

Few studies have investigated the wave propagation of spherical sources in a layered half-space. In this paper, based on Biot's theory of poroelastic media, the exact anti-axisymmetric (cylindrical SH-waves) and axisymmetric (cylindrical P1-P2-SV waves) stiffness matrices for a layered poroelastic half-space are derived. Then the dynamic responses due to buried spherical SH-, P1-, P2- and SV-waves in a layered poroelastic half-space are studied by using the direct stiffness method combined with the Hankel transform. The present solutions are in good agreements with those in a uniform pure elastic half-space as well as a uniform poroelastic half-space. These solutions have the advantages that all of the parameters in the solutions have explicit physical meanings and the thickness of discrete layers does not affect the precision of calculation; thus, the presented formulations are very convenient for engineering applications. Numerical calculations are performed in both the frequency and time domains by taking buried spherical SH-, P1- and SV- waves in a uniform poroelastic half-space and in a single poroelastic layer over a poroelastic half-space as examples. The numerical results show that wave propagation of spherical sources in a layered half-space can be significantly different from that in a uniform half-space; the dynamic responses are highly dependent on the saturated parameters, vibration frequency and the surface drained condition; the presence of the underlying half-space makes the time histories of the dynamic responses in a single layered half-space much more complicated with much longer duration. [ABSTRACT FROM AUTHOR]

Considering the fluid-soil coupling of saturated soil and seawater-saturated soil-structure dynamic interaction, the Hankel function integral transformation method is employed herein to obtain an analytical solution to the scattering and diffraction problem posed by the plane SV-waves in an undersea lined tunnel. This study is based on the porous medium wave function theory of saturated soil proposed by Biot and the ideal fluid medium wave theory. The impact of factors, such as the incident angle, frequency, water depth, buried depth of tunnel, porosity, and Poisson's ratio of the saturated soil, on the horizontal and vertical displacement at the seawater–saturated soil interface, and on the pore water pressure and total circumferential stress at the saturated soil–tunnel interface, are computed and analyzed. • Analytical solution to scattering of plane SV waves by a circular lined tunnel in an undersea saturated half-space is obtained. • The Hankel function integral transformation method is employed herein. • The effects of water depth, saturated soil parameters and wave characters on the seismic responses of the tunnel and undersea layer are analyzed. [ABSTRACT FROM AUTHOR]

Abstract: Linear and especially non-linear analyses of spatially extended structures, such as pipelines and bridges, often requires specification of time histories of ground motion at an array of closely spaced points. As the number of dense accelerograph arrays worldwide is small, and the number of earthquake observations is limited, synthetic motions with desired characteristics become necessary. This paper presents a method for synthesizing such motions, which is an extension of the SYNACC method, developed first in the early 1970s for synthetic accelerations, velocities and displacements at a point, and later extended to synthetic near surface strains, rotations and curvatures of ground motion at a point. It consists of unfolding in time a site specific Fourier amplitude spectrum of ground acceleration, obtained by an empirical scaling model, by representing the ground motion as a superposition of traveling wavelets of Love and Rayleigh waves and body waves, which propagate with phase and group velocities consistent with the dispersion characteristic of the site geology, approximated by parallel layers. Uniform hazard Fourier spectra or any specified target Fourier spectrum can also be used. Derivations of the point strains, rotations and curvatures are also presented. The method is illustrated for scenario M6.5 and M7.5 earthquakes and three dispersion models. [Copyright &y& Elsevier]

Abstract: The scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space is modeled using the indirect boundary element method in the frequency domain. The free-field responses are calculated to determine the displacements and stresses at the surface of the canyon, and fictitious distributed loads are then applied at the surface of the canyon in the free field to calculate the Green''s functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions, and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of fluid saturation, boundary conditions, porosity, and soil layers on the surface displacement amplitudes and phase shifts are discussed, and some useful conclusions are obtained. It is shown that the surface displacement amplitudes due to saturation and boundary conditions, different porosities, or the presence of a soil layer can be very dissimilar, and large phase shifts can be observed. The resulting wavelengths for an undrained saturated poroelastic medium are slightly longer than those for a drained saturated poroelastic medium; and are longer for a drained saturated poroelastic medium than those for a dry poroelastic medium. As porosity increases, the wavelengths become longer; and a layered half-space produces longer wavelengths than a homogeneous half-space. [Copyright &y& Elsevier]

Abstract: An analytical solution for the scattering and diffraction of incident plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space is derived by the wave function expansion method. The solution is utilized to analyze the dependence of the computed surface motions on the incident frequencies, incident angles, porosity, boundary drainage and Poisson''s ratio. It is shown that, depending on the incident angles, the surface displacement amplitudes around a canyon in a dry poroelastic half-space and saturated poroelastic half-space can be very different. The surface displacement amplitudes of an undrained saturated poroelastic half-space are close to those of a drained saturated poroelastic half-space. For low porosity, the surface displacement amplitudes of a saturated poroelastic half-space are almost identical to those of a dry poroelastic half-space, and drainage condition has little influence on the surface displacement amplitudes. But for high porosity, the effect of drainage condition becomes significant, and for the same porosity, the displacement amplitudes of an undrained saturated half-space will be larger than those of a drained saturated half-space. Poisson''s ratio is also an important factor affecting the surface displacement amplitudes around the canyon, both in drained and undrained conditions, but leads to larger effects for an undrained saturated half-space than for a drained saturated half-space. Large pore pressures are found around the canyon and their amplitudes depend on the incident angles and frequencies. Below the surface, the amplitudes of pore pressures are less than they are at the surface, especially for high frequencies. [Copyright &y& Elsevier]

This paper extends the two and a half-dimensional (2.5D) indirect boundary element method (IBEM) from the isotropic medium to the transversely isotropic (TI) saturated case, to study the three-dimensional (3D) scattering behavior of a two-dimensional (2D) geometric canyon cut in a multi-layered TI half-space. This method, conquering the drawbacks of both 2D and 3D simulations, can realistically assess the ground motion with less computation effort. The 3D exact stiffness matrix (Ba and Liang 2017) is adopted to solve the free-fields, through which the system with a great number of layers can be conveniently handled and the precision is not affected by layer's thickness. And the Green's functions for moving distributed loads in a multi-layered TI saturated half-space are derived in detail within the framework of Biot's theory (1962a, b), which is subsequently utilized to construct the scattered fields. The accuracy is illustrated by comparison with a verification example (Liang and Liu 2009) for a 2D isotropic case. The effects of some key parameters (anisotropy degree, incident angle, drainage condition, permeability and layering) on dynamic response are investigated through numerical implementations in frequency domain. The results show that material anisotropy has a noticeable influence on the displacement and pore pressure, and the influence becomes prominent for high incident frequency. The displacement amplitude is rather sensitive to permeability, whereas its distribution is hardly affected by permeability. Furthermore, the existence of layer complicates the scattering mechanics of layered system, heavily relating to material anisotropy. • The 2.5D IBEM is proposed to study 3D scattering of a 2D canyon in a TI saturated half-space. • The moving Green's functions of layered TI saturated half-space are semi-analytically derived. • The method can realistically assess the ground motion with less computation effort. • Material anisotropy has a noticeable influence on displacement and pore pressure responses. [ABSTRACT FROM AUTHOR]

Many natural soils and rocks are not only saturated but are also anisotropic. Due to the fundamental importance of having an understanding of the free-field response of an anisotropic half-space subjected to incident seismic waves, the surface displacements, surface strain, rocking, and pore pressure due to reflection of plane waves in a transversely isotropic (TI) saturated half-space are discussed. The governing equations in u- w formulation are first derived and the plane harmonic wave solution of these equations is then proposed. The free-field response is finally determined by specifying the stress free and surface drainage conditions at the boundary. The half-space surface can be either completely permeable or impermeable, and the excitation includes incident plane qP1- and qSV-waves. The proposed formulations are verified by comparing our results with those for the isotropic half-space. A parametric study is performed to illustrate the influences of the material anisotropy, surface drainage condition and permeability on the surface motions. Numerical results show that the surface motions of the TI half-space are significantly different from those of the isotropic case. The surface motions of the TI half-space are much more dependent on the TI parameters when the incident waves are qSV-waves than when they are qP1-waves because the dynamic responses change sharply as the incident angles approach the critical angles. In contrast with the isotropic case, with an identical angle of 45°, the total reflection angle of the TI half-space varies with the TI parameters. In general, the surface motions of the permeable surface are smaller than those of the impermeable surface, particularly in response to incident qSV-waves. • Free field response of a TI saturated half-space for incident plane waves is presented. • The solution is of great importance in solving wave scattering and SSI problems. • The free field response of qSV-waves is more dependent on the TI parameters. • Material anisotropy should be considered to provide more accurate free field results. [ABSTRACT FROM AUTHOR]

It has been well established that source-path-site effects have had an essential impact on the seismic analysis of major infrastructure over the past few decades, where the accurate and efficient modeling of seismic wave propagation can become a critical issue. In this study, a two-step approach combining the frequency-wavenumber (FK) technique with the spectral element (SE) method is developed based on the concept of domain reduction to simulate three-dimensional (3D) ground motion due to point dislocation sources. In the first step, the seismic responses for the dislocations in a layered half-space crustal model are solved exactly using the FK method and converted into effective input seismic loads around the region of interest. In the second step, the local wavefields of a 3D complex site are finely simulated using the SEM, while absorbing conditions are imposed at five boundaries of the SE model to achieve absorption of the outward scattered energy. The semi-analytical FK method is well-matched to the propagation frequencies because it allows the broadband synthesis associated with engineered systems to be addressed without additional calculations. When the FK is combined with the SEM, it is feasible to efficiently simulate earthquake ground motions covering a broad range of frequencies in the region of interest. Comparisons with the results of existing studies and the traditional SEM show that our approach is accurate and robust for arbitrary geometries and point sources. To further illustrate the efficiency and general applicability of the proposed method, three examples are presented. The results demonstrate that the two-step approach can consider the effects of the seismic source, propagation path, and local site geological conditions on the earthquake ground motions and serve as an effective forward modeling tool for reducing the computational cost. • The FK and SEM are hybridized to simulate seismic response of a 3D complex layered site. • The presented methodology is programmed and well verified by comparison with existing solutions. • The effects of the source-, propagation-, and site conditions on ground motions are studied. • The proposed two-step approach reduces computational cost in source-path-site modeling. [ABSTRACT FROM AUTHOR]

In this paper, the method of combining indirect boundary element method (IBEM) with the region-matching technique is used to solve the seismic responses of a three-dimensional (3D) hill in a layered half-space subjected to spherical P, SV, and SH waves. The direct stiffness method and Hankel transform method are used to solve the free field of spherical wave source field, and the scattering field is constructed by Green's function in half-space. The correctness and accuracy of this method are verified by comparing with the results of several literatures. This method can be used to deal with arbitrary-shaped hill topography, and has the advantages of wide applicability, high accuracy and fast convergence. Taking Gaussian hill topography as an example, the scattering phenomenon of hill under the incidence of spherical P, SV and SH waves is studied, and the influences of hill topography, source location and frequency on site seismic responses are explored. The results show that: Existence of the hill topography has evident focusing effect, which significantly enlarges the seismic response on the hill surface, and the hill has evident isolation effect in the process of energy propagation; With higher frequency of the incident wave, the fluctuation amplitude of displacement on the hill surface increases; The fluctuation amplitude of horizontal displacement on the hill surface is SV wave > SH wave > P wave, and the vertical displacement is P wave > SV wave. • The scattering of spherical P, SV, and SH waves by 3D hill in a layered half-space is studied. • Combining the direct stiffness method and Hankel transform method, the free field of spherical wave source are derived. • Assuming that the incident wave is spherical wave, the near-source topographic effect caused by hills is revealed. • The method can deal with 3D arbitrary-shaped hill topography, and has the merits of high accuracy and easy convergence. [ABSTRACT FROM AUTHOR]

An indirect boundary element method (IBEM) is proposed to solve the scattering of qP-, qSV- and SH-waves by a three-dimensional (3D) arbitrary-shaped alluvial valley embedded in a layered transversely isotropic (TI) half-space. First, the 3D dynamic Green's functions for the uniformly distributed loads acting on an interior inclined plane in a multi-layered TI half-space are derived by means of exact stiffness matrix method combined with the Fourier transform. Next, the deduced 3D Green's functions are used as fundamental solutions to formulate a special IBEM, and the IBEM is further used to investigate the surface motion of a 3D surface irregularities in a multi-layered TI half-space subjected to incident body waves. Compared to the traditional BEM adopting Green's functions for the concentrated loads as the kernel, the new method has the merits of higher precision and none of the problem of singularity. By comparing our results with the published ones, accuracy of the presented 3D Green's functions as well as IBEM solution are verified. To further demonstrate the general applicability and effectiveness of the present method, taking a semi-ellipsoidal alluvial valley in a single TI layered half-space as an example, numerical calculations are performed in both the frequency and time domain. Results in frequency domain show that material anisotropy has an important influence on the surface motion of semi-ellipsoidal alluvial valley. In general, the displacement amplitudes decrease as the degree of anisotropy increases. Displacement amplification spectra are significantly different among the various materials, which strongly depend on the incident angles and the observation points. Results in time domain show that with the increase of the degree of anisotropy, the peak ground acceleration (PGA) of each point inside the valley gradually decreases. Compared with the case of isotropic, the difference of PGA can reach 53.8%. • Scattering of a 3D arbitrary-shaped alluvial valley in a layered TI half-space is studied by using an IBEM. • Dynamic Green's functions for uniformly distributed loads acting on an inclined plane are derived. • The method has the merits of high precision and none of the problem of singularity. • The ground motion considering anisotropy is assessed both in the frequency and time domains. [ABSTRACT FROM AUTHOR]

Free-field response of a layered medium is of fundamental important for studying wave propagation and SSI problems, however, few researches have been conducted on this subject. In this paper, a transfer matrix method is presented to solve the free-field motion of a multi-layered transversely isotropic (TI) poroelastic half-plane subjected to incident plane qP1-, qP2- and qSV-waves. First, the displacement and stress expressions are obtained by solving the governing differential equations for a TI poroelastic medium. Then, the transfer matrices are derived by the continuity of tractions and displacements at layer interfaces, a transfer matrix solution for free-field response of the multi-layered TI poroelastic half-plane under obliquely incident seismic waves is presented. The free surface of the stratified system can be considered either completely drained or undrained. The accuracy of theoretical formulations is verified through comparison with existing layered TI as well as homogeneous saturated medium models. Numerical examples of varying key parameters are given out to evaluate the ground seismic responses. Results show that both anisotropy and porous property of medium have very important effect on the resonance frequency and peak amplitude. Meanwhile, due to the filtering and amplification mechanism of soil layer to ground motion, thicker layers have a more obvious amplification effect on low-frequency components and a certain "isolation" effect on high-frequency components. • Transfer matrix method for free-field response of a multi-layered TI poroelastic half-plane is proposed. • Free surface is considered either completely drained or undrained condition. • The method is validated by existing layered TI and homogeneous saturated medium models. • Displacement responses of layered system for different parameters are given. [ABSTRACT FROM AUTHOR]