Green''''s functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot's equation and the dynamic-stiffness matrices of a poroelastic soil layer and half-space, Green's functions were derived for uniformly distributed loads acting on an inclined line in a poroelastic layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green's functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.     

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green＇s functions

Few studies of wave propagation in layered saturated soils have been reported in the literature. In this paper, a general solution of the equation of wave motion in saturated soils, based on one kind of practical Biot‘s equation,was deduced by introducing wave potentials. Then exact dynamic-stiffness matrices for a poroelastic soil layer and halfspace were derived, which extended Wolf‘s theory for an elastic layered site to the case of poroelasticity, thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site. By using the integral transform method, Green‘s functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given. Finally, the theory was verified by numerical examples and dynamic responses by comparing three different soil sites. This study has the following advantages: all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications. The present theory can degenerate into Wolf‘s theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.     

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 halfspace 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.     

斜入射平面SH波在层状半空间中沉积谷地周围的三维散射

The indirect boundary element method （IBEM） is used to study three-dimensional scattering of obliquely incident plane SH waves by an alluvial valley embedded in a layered half-space. The free-field response of the layered half-space is calculated by the direct stiffness method, and dynamic Green＇s functions of moving distributed loads acting on inclined lines in a layered half-space are calculated to simulate the scattering wave field. The presented method yields very accurate results since the three-dimensional dynamic stiffness matrix is exact and the moving distributed loads can act directly on the valley boundary without singularity. Numerical results and analyses are performed for amplification of obliquely incident plane SH waves around an alluvial valley in a uniform half-space and in single layer over half-space. The results show that the three-dimensional responses are distinctly different from the two-dimensional responses, and the displacement amplitudes around alluvial valleys in a uniform haft-space are obviously different from those in a layered half-space.     

Green’s function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green’s function,an essential representation of water-saturated ground under moving excitation,to simulate ground borne vibration from trains.First,general solutions to the governing equations of poroelastic medium are derived by means of integral transform.Secondly,the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground,which results in the matrix of the Green’s function.Then the Green’s function is combined into a train-track-ground model,and is verified by typical examples and a field test.Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area.The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure.The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil.When the train speed is equal to the velocity of the Rayleigh wave,the Mach cone appears in the simulated wave field.The proposed Green’s function is an appropriate representation for a layered ground with shallow ground water table,and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.     

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated,poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.     

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free ...     

Cone model for two surface foundations on layered soil

In this paper, the cone model is applied to the vibration analysis of two foundations on a layered soil half space. In the analysis, the total stress field in the subsoil is divided into the free-field and the scattering field. Seed＇s simplified method is adopted for the free-field analysis, while the cone model is proposed for analyzing the dynamic scattering stress wave field. The shear stress field and the compressive stress field in the layered stratum with two scattering sources are calculated by shear cone and compressive cone, respectively. Furthermore, the stress fields in the subsoil with two foundations are divided into six zones, and the P wave and S wave are analyzed in each zone. Numerical results are provided to illustrate features of the added stress field for two surface foundations under vertical and horizontal sinusoidal force excitation. The proposed cone model may be useful in handling some of the complex problems associated with multi-scattering sources.     

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fic...     

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation

This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green’s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot’s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of ...     

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary...     

张衡地动仪（1）：诞生的历史

The emergence of Zhang Heng＇s seismoscope has a profound historical background. This paper intends to explore the formation and material basis of Zhang Heng＇s scientific thought. It appears that the simple intention of ＂observing visions and distinguishing good fortune or misfortune＂ was his motivation to develop the seismoscope. Tracing its historical background, the authors proposed in this paper that the development of this seismoscope started around 128 A.D., and based on perceptual knowledge, two ideas about earthquakes came into being, i. e. , earthquake location could be judged according to the instrument shaking direction, and the earthquake and earth split were essentially different. In the instrument manufacture, Zhang Heng advocated a principle of ＂making utensils to imitate cosmos ＂. By this principle, the following three problems were readily solved： the seismoscope imitated the response of the suspension system to earthquakes （ i.e. natural seismoscope） . Technically, the trigger mechanism of the latch was used for reference, and it recorded the physical evidence of earthquake occurrence by an ingenious way of a ball dropping from a dragon＇s mouth. The solution of these three key problems lead to the emergence of the seismoscope in 132 A.D. and the successful detection of an earthquake in 134 A.D. His invention deepened humanity＇s knowledge of natural laws, and promoted the development of science and technology in that time and later.     

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fi ctitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verifi cation of the accuracy is performed by: (1) checking the satisfaction extent of the boundary c...     

Some Analyses on Effects of Site Classification on Ground Motion Characteristics in the Chi-Chi, Taiwan Earthquake

According to the epicenter distance and the site classification, the 404 groups of earthquake recordings of the main shock of the Chi-Chi, Taiwan China earthquake in 1999 are catalogued. Based on these data, we analyze the statistical features of duration, PGA, envelopes and the response spectra ratio of the horizontal and vertical components of the acceleration recordings. The results of these analyses show that the effect of site classification on the acceleration of various components is obvious; furthermore, fault direction also has certain effects on the characteristics of the horizontal components of ground motion. The detailed research results are as follows： （ 1 ） the duration of the horizontal components of acceleration records increases with the softening of the site; （2） the direction of fault slip has some effects on PGA＇s attenuation features; （3） the average envelopes of acceleration records at different distances and site dames are basically single peak functions of time and the envelopes of horizontal and vertical components of ground motion are obviously different; （4） with the same epicenter distance, EW/NS response spectrum ratios tend to approximate 1.0 as the site becomes softer and the period shorter. V/H response spectrum ratios in short periods （〈 0. 1s） increase with the softening of site, however, V/H ratios within the long-period range （ 〉 characteristic period） decrease with the softening of the site, and the decrease of V/EW ratio speeds up relatively.     

Local site effects evaluation by surface wave and H/V survey methods in Senirkent (Isparta) region,southwestern Turkey

This study aimed to investigate the site characterization of the Senirkent Basin(Isparta) by using the microtremor(H/V) and surface wave analysis(ReMi) methods. Senirkent district, which is located on the foothill of the Kap? Mountain, are prone to seismic and landslide hazards. After the last landslip disaster(1995), the city has continued to develop on the alluvial basin. The microtremor data collected at 41 stations were analyzed. The predominant frequency and the amplification of the soil were found to be in the range of 1.8–6.6 Hz and 0.8–6.8, respectively. These are 4.0-6.8 Hz and 1-2.5 around the slope of the Kap? Mountain and 0.8-3.6 Hz and 3.0-6.6 at alluvium deposits of the valley. The ReMi data collected along 41 profiles were analyzed to obtain a V_(s30) map. The soil classifications were done by using V_(s30) values according to NEHRP soil classification criteria. The results showed that the southern area of the study had better soil conditions with V_(s30) between 360-1160 m/s and soil class between C and B. The alluvium deposits on the north are relatively low with V_(s30) in the range of 260-360 m/s and soil class D.     

STUDY ON THE DYNAMIC PROCESS OF RILL EROSION OF LOESS SLOPE SURFACE

1 mTRODUCTIONAs a woridwide concem, excessive water erosion induces land degradation, causes losses of plantnutrients, and Ieads to off site enVironmental problems such as sedimentahon streams and reservoirs. mllerosion, which results from concentraed flow in a lindted and confined space, plays imPortant roles inthe erosion systCm on uPland areas. Data listed in Table l show its contribution and imPoftance to thetOtal slope soil losses. In the last decades, stodies on the physical mecha…     

Stochastic seismic response of multi-layered soil with random layer heights

This paper deals with the effect of layer height randomness on the seismic response of a layered soil. These parameters are assumed to be lognormal random variables. The analysis is carried out via Monte Carlo simulations coupled with the stiffness matrix method. A parametric study is conducted to derive the stochastic behavior of the peak ground acceleration and its response spectrum,the transfer function and the amplification factors. The input soil characteristics correspond to a site in Mexico City and the input seismic accelerations correspond to the Loma Prieta earthquake. It is found that the layer height heterogeneity causes a widening of the frequency content and a slight increase in the fundamental frequency of the soil profile,indicating that the resonance phenomenon is a concern for a large number of structures. Variation of the layer height randomness acts as a variation of the incident angle,i.e.,a decrease of the amplitude and a shift of the resonant frequencies.     

Dynamic responses of a sediment-filled valley with a fluid layer subject to incident waves

The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb’s singular solutions, i.e., the integralsolutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..     

The Green''''s function of the harmonic horizontal force applied at the interior of the saturated half-space soil

IntroductionThe wave propagation problems in saturated soil are very important for the civil engineering, geophysics and seismology. Biot (1956,1962) established the theory of wave propagation in saturated soil firstly, and hereafter many researchers have used Biot theory to study wave propagation problems in saturated soil. By using integral transform and potential function method, Philippacopoulos (1988) studied the Lamb(s problem of a vertical point force applied to the surface of saturate…     

Evaluating some factors that affect feasility of using ground penetrating radar for landmine detection

Ground penetrating radar （GPR） is one of the promising technologies that can be used to detect landmines. Many factors may affect the ability of GPR to detect landmines. Among those factors are： 1） the type of landmine material （metallic or plastic）, 2） conditions of the host soil （soil texture and soil moisture）, and 3） the radar frequency utilized. The impact of these factors on the ability of GPR to detect landmines is investigated by studying their effect on the dielectric permittivity contrast between the landmine and the host soil, as well as on the attenuation of the radar waves. The impact of each factor was theoretically reviewed and modeled using the Matlab and Mathcad software packages. Results of the computer modeling were correlated with GPR data acquired for metallic and plastic landmine types. It was found that the ability of GPR to detect landmines depends to a great extent on the landmine type, water content of the host soil, utilized radar frequency, and soil texture. The landmines are much easier to detect than plastic landmines for any soil conditions and any radar frequency. Increasing the soil＇s moisture content, regardless of soil texture, eases the detection of the plastic landmine and worsens the detection of the metallic mines. Increasing the percentage of clay in the soil causes the same effect as the moisture content. However, higher radar frequency delivers better results for landmine detection as long as the percentage of clay and the moisture content in the soil remains low. The results of this study are expected to help in selecting optimum radar antennae and data acquisition parameters depending on the landmine type and environmental conditions.