SV Waves Research Articles

Exact seismic response of smooth rigid retaining walls resting on stiff soil

SummaryThe assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica, which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed.

Horizontal and vertical motion at the surface of swelling poroelastic layer sandwiched between water and elastic solid

The horizontal and vertical motions at the surface of swelling poroelastic layer in coupled system are investigated. Coupled system means water-swelling porous sediment-elastic solid substrate system. The analytical expressions of horizontal and vertical displacements at the surface of swelling porous solid are evaluated for both incidences i.e., P and SV waves. The closed form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. The horizontal and vertical displacement amplitudes are derived analytically in terms of reflection and transmission coefficients. The horizontal and vertical motion of swelling poroelastic layer is examined through analyzing three key factors: amplification coefficients, displacement amplitudes and displacement ratio. The impacts of wave frequency, thickness of swelling poroelastic layer, incident direction and swelling property of the medium are examined on these three key factor numerically. Numerical results indicate that the surface motion strongly depends on wave frequency, thickness of layer, swelling property of the medium and incident direction.

Standardisation of electrocardiographic examination in corn snakes (Pantherophis guttatus).

Corn snakes are a very common pet reptile species, yet there is an absence of evidence-based literature standardising collection of ECG or detailing ECG deflection morphology in the normal animal. The authors describe a well-tolerated, reproducible technique and detail the cardiac cycle in terms of lead 2 equivalent waveforms and intervals. 29 adult corn snakes. This prospective study evaluated, under species-appropriate, standardised conditions, a technique for producing standard six-lead ECG tracings. Lead 2 equivalent cardiac cycles were described in detail and statistically analysed for sex, weight, length, heart rate and mean electrical axis. High-quality tracings demonstrated common ECG characteristics for this species, including no Q, S or SV waves, prolonged PR and RT intervals, rhythmic oscillation of the baseline, short TP segments, and a right displaced mean electrical axis. An influence of sex, weight or length on heart rate and mean electrical axis was not identified. To the authors' knowledge, this is the first study to describe a standardised technique for recording ECG in significant numbers of normal corn snakes. Ranges have been provided that may be of diagnostic value or form the basis for future development of reference intervals for this species.

Пространственное распределение коэффициента анизотропии в верхней мантии Европы

The radial (transversal) anisotropy of the Earth’s upper mantle was found by comparing the velocity sections of transverse waves obtained by inverse of the dispersion curves of Rayleigh and Love waves. Information on variations in anisotropy with depth was obtained from dispersion curves on fairly uniform oceanic paths. In the oceanic mantle the SH wave velocities obtained from the Love wave data are greater than the SV wave velocities determined from Rayleigh waves, so that the anisotropy coefficient is positive and is about 4% under the Moho boundary and decreases to zero at a depth of about 200 km. The information about the anisotropy of the continents is much more scarce and often contradictory due to a strong lateral inhomogeneity of the crust and upper mantle of the continents. In the European region, some authors reveal the zones where VSV>VSH in the upper mantle, whereas some others confirm VSH>VSV to be everywhere. The uncertainty in the observed values of the anisotropy coefficient is explained by the fact that it was always determined from the results of the Rayleigh and Love wave velocity tomography carried out on the basis of different samples of paths. Accordingly, the values of the SH and SV wave velocities turned out to be averaged over different regions, which led to errors in the estimates of the anisotropy coefficient. To reduce these errors, we proposed an alternative method for estimating the spatial distribution of the anisotropy coefficient: to estimate the anisotropy co-efficient in the beginning at each path and then to fulfill the tomographic inversion for this coefficient. Preliminary results on the distribution of the anisotropy coefficient in the upper mantle of Europe were presented according to an earthquake and seismic noise. However, analysis of the anisotropy coefficient values obtained from the earthquake data and seismic noise has shown that those obtained from noise are usually underestimated. Therefore, in the present study, we used only the data obtained from earthquakes. It was shown that the anisotropy coefficient under the continental part of the European region is close to zero but two areas where VSV>VSH are detected – in the central part of EEP and in southern Italy. In both cases, the negative values of the anisotropy coefficient are observed within the interval of ~60–100 km depth.

Ballistic thermal transport in asymmetric Y-branch three terminal junction

The thermal transport properties of Y-branch three terminal junction are studied by using the scattering-matrix method for in-plane waves. The mode conversion has been considered for two transmitted components (P wave and SV wave). The results show that the phonon mode separation behavior exists not only at low incident frequencies but also at high incident frequencies. The non-integer quantization thermal conductance has been found. Furthermore, the transmission coefficients of acoustic phonon in both branches can be modulated by the phonon nanocavity length L. The work suggests that such Y-branch structure can be act as a thermal shunt.

Effects of Oblique Incidence of SV Waves on Nonlinear Seismic Response of a Lined Arched Tunnel

The incident direction of earthquake motion is an important factor affecting the seismic response of underground structures. In this study, a three-dimensional (3D) oblique incidence method of SV waves is proposed and the effects of incident angles of SV waves on the seismic response of a lined arched tunnel are evaluated. Based on wave field decomposition principle and equivalent node force method and together with viscous-spring artificial boundary, the oblique incidence method of SV waves is implemented by transforming seismic wave field into the equivalent nodal forces acting on the artificial boundaries. By deriving the distance of the incident waves and the reflected wave on free surface to artificial boundaries, this method can comprehensively consider the phase difference of the seismic wave propagation and the influence of the damping effect of the rock medium on the seismic wave propagation. The method is programed into a dynamic finite element program and its effectiveness is examined by a numerical example. Consequently, the oblique incidence method is applied to evaluate the seismic behaviors of the tunnel. The numerical results reveal that (1) the oblique incidence of the seismic wave results in a larger seismic response; (2) the response amplitudes of the stress and displacement increase with the increase of incident angles and reaching the maximum in the case of 30° incident angle; (3) the damage extent increases with an increase in the incident angles, and the oblique incidence of the seismic wave is believed to increase the spatial difference of damage distribution.

Seismic response analysis of the reef-seawater system under obliquely incident P and SV waves

Despite the increasing focus on the seismic safety of reef engineering sites, the current studies on this topic are still based on the hypotheses of uniform seismic excitations or the vertical incidence of seismic waves. In this study, a two-dimensional seismic analysis model for the reef-seawater system under obliquely incident P and SV waves is developed, which considers the fluid-soil-interaction and the wave radiation effects of the fluid and the solid domain. The oblique input of the seismic wave into the reef-seawater model is accomplished through the boundary substructure method. A series of parametric studies are conducted, the ground motion fields on the reef sites are discussed, and the effects of several fundamental factors on the seismic response are comprehensively studied. The results show that under most circumstances, the least favorable load case for the reef site seismic response is the vertical incidence of seismic waves. However, for the horizontal ground motion of the reef site under the P wave, the least favorable incident angle is approximately 30°. In addition, the largest horizontal seismic response usually appears near the downstream side of the reef flat, and the peak velocity and acceleration ratios can reach up to 4 in this area.

Dynamic Response of Rock Slopes under Obliquely Incident Seismic Waves

In this study, the seismic input model of slope is proposed to investigate the dynamic response of the rock slope under obliquely incident seismic wave on the basis of the time‐domain wave analysis method. The model includes viscoelastic boundary considering the infinite foundation radiation damping and the seismic obliquely incident method. The semi‐infinite space numerical example is simulated to verify the validity and accuracy of the model. Based on the established model, the effects of the variation of the seismic wave incident angles and slope angles on the dynamic response of a rock slope are analyzed. The results demonstrate that the changes of the incident angle and the slope angle have no discernible effect on the dynamic response of the rock slope when the P wave is obliquely incident. As the SV wave is obliquely incident, the peak ground acceleration amplification coefficient along the slope surface gradually increases with the increase of the incident angle; when the slope angle gradually increases, the peak ground acceleration amplification coefficient along the slope surface will also gradually increase at the upper part of the slope. The research results can provide some basis for the pseudostatic method to determine the seismic action coefficient.

A numerical study on the transverse seismic response of lined circular tunnels under obliquely incident asynchronous P and SV waves

The numerical analysis of the transverse seismic response of tunnels is an important issue in the design and safety evaluation of tunnel structures, where the spatial variation of earthquake ground motion induced by wave passage effect has been recognized as an important influence factor that cannot be ignored. In this paper, a 2-D transient dynamic finite element modelling technique is applied to investigate the seismic response of two soil-structure interaction systems subjected to obliquely incident plane P and SV waves. Based on the theory of wave input, the incident earthquake motion is modeled as equivalent nodal forces applied on the truncated boundary, and the free field ground response is calculated from the 1-D time-domain finite element method by considering the wave passage effect. The numerical scheme is implemented into the commercial software ABAQUS, and its accuracy is verified by comparing with the analytical solutions of soil-structure interaction problems. Firstly, the verified method is applied to study the transverse seismic response of a circular tunnel embedded in a homogenous elastic half-space under obliquely incident P and SV waves, where the influence of the incident wave type, incident angle, burial depth and tunnel diameter is discussed. Secondly, the response of circular tunnels embedded in a multi-layered non-homogenous elastic foundation is studied, where the influence of tunnel position in the foundation, flexibility ratio between soil and tunnel and stiffness difference of adjacent soil layers in the foundation are extensively investigated. Moreover, comparison is drawn between the tunnel responses in the homogenous and non-homogenous foundation systems, and the importance of conducting asynchronous seismic response analysis of circular tunnels is highlighted.

Wave propagation characteristics at the welded interface of double-porosity solid and double-porosity dual-permeability materials

ABSTRACT In the present study, propagation characteristics (reflection/refraction phenomena) at the welded interface of two dissimilar double-porosity media are investigated. Both the double-porosity materials behave dissipative to wave propagation due to the presence of viscosity in pore fluid. All the waves (i.e. incident, reflected and refracted) are considered as inhomogeneous (i.e. different directions of propagation and attenuation). Reflection and refraction coefficients are calculated theoretically in the form of eight inhomogeneous linear equations. Reflected and refracted waves energy shares are represented with two different energy matrix. For the incidence of and SV waves, the partition of incident energy among various reflected and refracted waves is calculated numerically for particular numerical examples. The impacts of various physical properties (like, pore-fluid viscosity, double-porosity structure, wave-induced fluid flow and permeability) of double-porosity dual-permeability materials on the partition of incident energy are depicted graphically at each angle of incidence. Numerically, the conservation of incident energy during the reflection/refraction process is obtained at each angle of incidence.

A Numerical Study on the Seismic Site Response of Rocky Valleys with Irregular Topographic Conditions

This paper investigates topographic effects of rocky valleys with irregular topographic conditions subjected to vertically propagating SV waves of Ricker type using a boundary element code. Valleys with two intersecting slopes, [Formula: see text] and [Formula: see text], are modelled in order to study their combined effects on ground motion. Presented in the form of pseudo-acceleration response spectra, results of this work can be extended to similar topographies. The main findings are: (i) [Formula: see text] (the first slope angle) and [Formula: see text] (L is the half width of the valley and [Formula: see text] is its corresponding height) have amplifying effects, and [Formula: see text] (the second slope angle) has de-amplifying effects on the site response. (ii) [Formula: see text] has a straight effect on intensifying the effects of both [Formula: see text] and [Formula: see text]. (iii) The combined effects of slope angles have been found to be important in modifying the response so more than a single slope should be considered for seismic analysis. (iv) Engineers should use the maximum amplification of 2.4 in case of valleys with the first and second slope angles below [Formula: see text].

Stress intensity factors of a Griffith crack in a porous medium subjected to a time-harmonic stress wave

In many practices, cracks are filled with fluid and their background materials can be modelled within the framework of poroelasticity. Understanding the crack-tip mechanical behaviors of such a cracked medium subjected to dynamic loads is of importance for prediction of fracture failure. In this paper, based on Biot’s theory of poroelastodynamics, solutions of mode-I and mode-II dynamic stress intensity factors (SIFs) of a Griffith crack are derived for the scattering problem of oblique incidence of in-plane time-harmonic P-SV waves. The crack surfaces are assumed to be permeable, and the crack is saturated by fluid. With the aid of Fourier integral transforms, the problem is reduced to a system of coupled Fredholm integral equations with special emphasis placed on finding the near-field solution. Impacts of incident wave type, material permeability and incident angle on the frequency-dependent behaviors of the SIFs have been shown graphically. It is found that the induced fluid pressure inside the crack can significantly change the effective normal stress so that the magnitude of mode-I SIF is much lower than that of a dry impermeable crack. Furthermore, the diffusion-type fluid flow (scattered slow P wave) can greatly lower the magnitude of mode-I SIF at low frequencies (much smaller than the resonance frequency). The characteristic frequency at which the curves of SIFs decline strongest occurs when the characteristic diffusion length is of the same order of the crack size. The fluid flow can also lower mode-II SIF at low frequencies and the effects are strong in the low permeability case. Specifically, in the case of scattering of SV waves, it is shown that the maximum drop of mode-II SIF in peak with respect to that of the corresponding dry crack in an elastic medium is about 10%. The obtained results reveal significant influences of the presence of pore fluid upon the SIFs, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads.

Layer-effect on variable seismic ground motions of SV-wave scattered by a double-stratified circular-arc crossing by layer-interface

This study is to theoretically investigate and quantify the variability of the seismic surface motions of a double-stratified half space with a circular-arc canyon by the SV wave incidence. Compared with the SH-wave induced scattering by the canyon with the single-layer (ideally homogeneous) medium, the challenge is to simultaneously satisfy the boundary conditions at the ground surface and layer-interface and deal with the relatively complex wave transmission on layer-interface. Theoretical solution for the SV-wave induced scattering by a double-stratified half space with circular-arc canyon is derived explicitly. The present method is validated by reducing the proposed solution with that in the homogenous medium. Then, an example is considered to further verify the derived results by simultaneously satisfying the continuity and zero-stress boundary conditions. The effects of the layer medium, the incident frequencies and incident angles on the ground motion of the double-stratified medium are investigated parametrically and compared with that of the homogeneous case. Results show that the derived solution is theoretically reliable and the layer-effect on the variability of the canyon ground motions is obvious.

Responses of dipole-source reflected shear waves in acoustically slow formations

Abstract In the process of dipole-source acoustic far-detection logging, the azimuth of the fracture outside the borehole can be determined with the assumption that the SH–SH wave is stronger than the SV–SV wave. However, in slow formations, the considerable borehole modulation highly complicates the dipole-source radiation of SH and SV waves. A 3D finite-difference time-domain method is used to investigate the responses of the dipole-source reflected shear wave (S–S) in slow formations and explain the relationships between the azimuth characteristics of the S–S wave and the source–receiver offset and the dip angle of the fracture outside the borehole. Results indicate that the SH–SH and SV–SV waves cannot be effectively distinguished by amplitude at some offset ranges under low- and high-fracture dip angle conditions, and the offset ranges are related to formation properties and fracture dip angle. In these cases, the fracture azimuth determined by the amplitude of the S–S wave not only has a $180^\circ $ uncertainty but may also have a $90^\circ $ difference from the actual value. Under these situations, the P–P, S–P and S–S waves can be combined to solve the problem of the $90^\circ $ difference in the azimuth determination of fractures outside the borehole, especially for a low-dip-angle fracture.

Reflection and Transmission of Plane Elastic Waves at an Interface Between Two Double-Porosity Media: Effect of Local Fluid Flow

We obtain the reflection and transmission coefficients for inhomogeneous plane waves incident on a flat interface separating two double-porosity media described by the Biot–Rayleigh model, which takes into account the effect of local fluid flow (LFF). Three longitudinal and one transverse waves are reflected and transmitted, represented by potential functions specified by the propagation and attenuation directions. The continuity of the energy at the interface for sealed and open-boundary conditions yields a system of equations for the coefficients, and the expressions of the energy ratios for the reflected and refracted waves are derived in closed form. Numerical examples showing the magnitude, phase and energy ratio as a function of frequency and incidence angle are carried out to investigate the influence of the inhomogeneity angle, boundary condition, type of incidence wave and LFF effect. The results confirm that the LFF affects the reflection and transmission behaviors for the incident P1 and SV waves, irrespective of whether the interface is open or sealed. The effect causes interference fluxes between different waves, a consequence of energy conservation at the interface. We also perform full-waveform simulations to validate the results.

Scattering of elastic waves by a 3-D inclusion in a poroelastic half space

Using the indirect boundary element method (IBEM) and Biot's theory, surface displacement associated with the field scattered by a 3-D inclusion in a two-phase poroelastic half space under plane SV waves has been studied. According to single-layered potential theory, scattering waves are constructed by the introduction of uniform loads and fluid sources distributed over the surface of the half space and on the interface between the inclusion and the half space. The magnitudes of these loads and sources are obtained by establishing a boundary integral equation based on continuity boundary conditions. The accuracy of this method is verified by comparing the results of degradation with existing results of cavities in elastic media. The scattering of plane waves due to a 3-D inclusion is investigated from several aspects. Numerical results show that the dynamic coupling effect between the solid frame and pore water and the permeability condition of the poroelastic soil boundary result in a generally larger surface displacement amplitude for dry soil than poroelastic soil when the porosity is n = 0.3. By contrast, the surface displacement amplitude of poroelastic soil is larger than that of dry soil when the porosity is n = 0.36. As the depth of burial decreases and as the inclusion becomes wider and thicker, the scattering effect increases. The peak value of the displacement spectrum curve usually appears near the incident frequency η = 1.

Seismic Response Analysis of Oblique Incident Angle of SV Wave on Immersed Tunnel

On the basis of viscous-elastic artificial boundary, the ground motion input is transformed into the equivalent node load to achieve the oblique incidence of seismic waves. The two-dimensional finite element model of Nanchang Honggu immersed tunnel section is established by using finite element software. The influence of different incident angles on the dynamic response of the immersed tunnel is analyzed under the oblique incident of the SV wave. The results show that the seismic response law of the immersed tunnel is significantly different from that of the vertical incident when the SV wave is obliquely incident. The structural stress of the immersed tunnel is larger at the corner of the immersed tunnel and the junction of the intermediate partition with the floor and the roof. As the incident angle increases, the vertical response of the immersed tunnel structure increases significantly. Therefore, when seismic design analysis of the immersed tunnel is carried out, the influence of the oblique incidence of the ground motion on the dynamic response of the immersed tunnel should be considered.

Lithospheric SH Wave Velocity Structure Beneath the Northeastern Tibetan Plateau From Love Wave Tomography

AbstractThe northeastern (NE) Tibetan plateau has been a prime site to understand the dynamic processes responsible for the rise and lateral growth of the Tibetan plateau. Here we construct a high‐resolution lithospheric scale isotropic SH wave velocity model (down to the depth of 130 km) for the NE Tibetan plateau and its adjacent regions based on the measurements of fundamental‐mode Love wave dispersions (20–100 s) with seismic data recorded by ChinArray II and China Digital Seismic Array using two‐plane wave method. Prominent slow SH wave velocity (VSH) is observed in the midlower crust of the NE Tibetan plateau, specifically in the Qilian Orogenic Belt and the Songpan‐Ganzi Terrane regions, coincident with previously indicated significantly slow SV wave velocity (VSV), probably implying the existence of partial melts in the midlower crust. This low SH wave velocity anomaly could be traced down to the uppermost mantle, indicating a weak and warm lithosphere, which we interpret as a consequence of asthenosphere upwelling after lithospheric mantle removal in the NE Tibetan plateau. The asthenosphere upwelling and associated deep‐seated thermal buoyancy could explain the occurrence of partial melting in the mid‐lower crust and account for parts of high elevations in the NE Tibetan plateau. The western Qinling orogenic belt is characterized with a high velocity anomaly in most of lithosphere, which is inconsistent with the existence of channel flow within the lithosphere along the Qinling orogenic belt from the Tibetan plateau.

1D finite element artificial boundary method for transient response of ocean site under obliquely incident earthquake waves

Ocean site consisting of seawater-seabed-bedrock system is modeled as horizontally layered fluid-poroelastic-solid media. Earthquake wave is assumed as a plane P or SV wave of oblique incidence from the solid bedrock into the site. A time-domain numerical method called one-dimensional finite element artificial boundary (1D-FE-AB) method is proposed to effectively and accurately calculate the transient response of the ocean site under the obliquely incident earthquake waves. In this method, a horizontally line-shaped AB is firstly introduced in the solid bedrock to divide the whole site into the fluid-poroelastic-solid layer and the remaining homogenous solid half space. The former is semi-discretized by FE method along depth, and the latter with the incident earthquake wave is simulated by an exact AB condition. The resulting semi-discrete system with AB is then transformed into a spatially 1D dynamic equation along depth by using the Snell's law of plane body wave propagation in multilayer media. The 1D equation can be solved by the time integration algorithm such as Newmark method. Numerical examples are finally given to demonstrate the effectiveness of the proposed 1D-FE-AB method.

Full Waveform Modelling for Subsurface Characterization with Converted-Wave Seismic Reflection: Residual PP Removal on PS Component Using F-K Filter

The application of converted-wave seismic method in hydrocarbon exploration has increased significantly. Since the conventional seismic ceases to provide an adequate image in complex geology area and it often provides an ambiguous bright spot response. The main principle is that an incident P-wave produces reflected and converted P and SV wave on an interface. Converted-wave seismic uses the multicomponent receiver that records both of vertical component and horizontal component. The vertical component is assumed to correspond to the compressional PP wave and the horizontal correspond to the PS converted-wave. In this and previous research (Viony and Triyoso, 2018), a synthetic seismic data with the shallow gas and the salt dome model are constructed by the full-waveform modelling. The purpose of this study is to improve the imaging quality on the PS section and the PS AVO curve due to the existence of the residual PP events on the horizontal data in the previous study (Viony and Triyoso, 2018). The PS gather has been NMO corrected by the PP velocity. Therefore, the residual PP reflections are well-corrected and the PS reflections are under-corrected. To obtain the more reliable PS data, the residual PP reflections have been removed by rejecting the well-corrected data in f-k filtering process. The results of this study present that the imaging quality and the AVO of the filtered PS is better and more reliable than the un-filtered PS in the previous study (Viony and Triyoso, 2018).