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It is well known that local soil conditions play a key role in the amplification of earthquake waves. In particular, a liquefiable shallow soil layer may produce a significant influence on ground motion during strong earthquakes. In this paper, the response of a liquefiable site during the 1995 Kobe earthquake is studied using vertical array records, with particular attention on the effects of nonlinear soil behaviour and liquefaction on the ground motion. Variations of the characteristics of the recorded ground motions are analysed using the spectral ratio technique, and the nonlinearity occurring in the shallow liquefied layer during earthquake is identified. A fully coupled, inelastic finite element analysis of the response of the array site is performed. The calculated stress–strain histories of soils and excess pore water pressures at different depths are presented, and their relations to the characteristics of the ground motions are addressed.

Long period microtremors with periods ranging from 0.5 to 10 seconds were measured in the Anchorage metropolitan area. Two horizontal components of motion were recorded at 81 sites uniformly distributed throughout the basin with spatial resolution of about 2 km. Recording at each site was done for 300 seconds with a sampling rate of 20 Hz. Repeated measurements were performed at a bedrock reference site simultaneously with the measurements in the field. The measurements were completed in six days. In addition, multiple recordings were obtained concurrently at the reference bedrock site and a sediment site. Based on these measurements the Fourier spectra were calculated for each of the site. Ground motion amplification is determined in terms of spectral ratio of horizontal spectral amplitudes at a sediment site and the reference bedrock site. Mean spectral ratio contours were evaluated for different period bands. The results show that for period band 3 to 5 seconds the spectral ratio contours agree well with the ground failure susceptiblity map of Anchorage.

Large modifications of seismic waves are produced by variations of material properties near the Earth's surface and by both surface and buried topography. These modifications, usually referred to as "site response", in general lead to larger motions on soil sites than on rock-like sites. Because the soil amplifications can be as large as a factor of ten, they are important in engineering applications that require the quantitative specification of ground motions. This has been recognised for years by both seismologists and engineers, and it is hard to open an earthquake journal these days without finding an article on site response. What is often missing in these studies, however, are discussions of the uncertainty of the predicted response. A number of purely observational studies demonstrate that ground motions have large site-to-site variability for a single earthquake and large earthquake-location-dependent variability for a single site. This variability makes site-specific, earthquake-specific predictions of site response quite uncertain, even if detailed geotechnical and geological information is available near the site. Predictions of site response for average classes of sites exposed to the motions from many earthquakes can be made with much greater certainty if sufficient empirical observations are available.

An analytical solution for diffraction of both plane and cylindrical SH waves induced by a horseshoe shaped cavity with an inverted arch is presented in this paper. The geometry of the cavity is assumed to be composed of two circular arcs. By introducing an auxiliary boundary, the whole physical region is divided into two computational regions. The scattered wavefield in the open region and the standing wavefield in the enclosed region are presented by means of the wave function expansion method. Both of the wavefields are given in terms of the wave function series with unknown coefficients. By applying the Graf’s addition formula, two systems of equations for seeking the unknowns are derived by taking advantage of the boundary conditions based on the region-matching strategy. The problem of wave scattering is finally solved after seeking the solutions of the two systems of equations through standard matrix techniques. Then the effects of the excitation frequency, the cavity embedment depth and cavity geometry are discussed. The differences in terms of ground motions under different excitations and the influence of source location under cylindrical waves are also examined.

To elucidate the ground motion amplification due to soil and topographic effects, an analytical formulation based on wavefunction expansion is derived for the scattering of plane SH waves by a semi-cylindrical valley partially filled with a crescent-shaped soil layer. The site responses consisting of both soil and topographic effects from the partially filled alluvial valley and the pure topographic contribution from the homogeneous valley of the same geometry are calculated and compared. It is found that the soil amplification effects are usually larger than the topographic amplification effects within the alluvial valley, while the topographic effects dominate the amplification pattern of ground motions outside the alluvial valley. Generally, the maximum soil amplification generally far outweighs the maximum topographic amplification. The material parameters and filling degree of the soil layer are found to affect the magnitude and the pattern of ground motion amplitude on the valley surface depending on the irregular topography, the frequency content and obliquity of the wave incidence.

A stochastic function model of seismic ground motions is presented in this paper. It is derived from the consideration of physical mechanisms of seismic ground motions. The model includes the randomness inherent in the seismic source, propagation path and local site. For logical selection of the seismic acceleration records, a cluster analysis method is employed. Statistical distributions of the random parameters associated with the proposed model are identified using the selected data. Superposition method of narrow-band wave groups is then adopted to simulate non-stationary seismic ground motions. In order to verify the feasibility of the proposed model, comparative studies of time histories and response spectra of the simulated seismic accelerations against those of the recorded seismic accelerations are carried out. Their probability density functions, moreover, are readily investigated by virtue of the probability density evolution method.

In this paper, a series of 1-g shaking table model tests were carried out to investigate the seismic behavior of a relatively stiff rectangular tunnel structure installed in soft clay bed, accounting for different ground motions with varying peak accelerations. Using a validated numerical analysis procedure, a suite of three-dimensional (3D) finite element (FE) analyses was performed to systematically study the factors of tunnel burial depth, seismic intensity, flexural rigidity of the middle column and tunnel wall thickness on the seismic response of rectangular tunnel structures installed in clayey ground. It was found that, with the increasing burial depth, the seismic response of rectangular tunnel structure became more intense due to the increased inertial force arising from the overlying clay; in terms of improving the seismic performance of tunnel structure, increasing tunnel wall thickness seemed more effective than increasing flexural rigidity of the middle column. Furthermore, it was found that the existing simplified approaches generally tended to overestimate the earthquake-induced racking distortions of rectangular tunnels installed in clayey ground. A new semi-empirical relationship was derived for better correlating the racking ratio with flexibility ratio for rectangular tunnels embedded in soft clays, which could provide a useful reference for the seismic design and risk assessment of similar clay-tunnel systems.

In this paper, empirical mode decomposition technique is used to analyze the spatial slip distribution of five past earthquakes. It is shown that the finite fault slip models exhibit five empirical modes of oscillation. The last intrinsic mode is positive and characterizes the non-stationary mean of the slip distribution. This helps in splitting the spatial variability of slip into trend and the remaining modes sum as the fluctuation in the data. The fluctuation component indicates that it can be modeled as an anisotropic random field. Important parameters of this random field have been estimated. The effect of these modes on ground motion is presented by simulating both acceleration and displacement time histories.

Pounding of adjacent buildings or parts of buildings due to earthquake shaking is often implicated as a significant source of damage. The majority of theoretical studies of pounding have focused on determination of the minimum separation required to prevent pounding. While this is useful for design of new structures, a great many existing structures are not sufficiently separated to preclude pounding. For these existing structures it is clearly useful to have a measure of the expected level of damage that may occur in future earthquakes. This paper attempts to assess the effects of pounding from measured earthquake records. The concept of Maximum Impact Velocity Spectrum (MIV) is introduced. The MIV records the envelope of the maximum impact velocity obtained during the earthquake for all separation distances as a function of the structure's natural period. Several measured earthquake records are considered and some surprising results are obtained.