Dynamic response analysis of submerged soil by thin layer element method

A thin layer element method is formulated to compute the dynamic response of submerged soil. The formulation is based on Biot's equation describing the dynamic behavior of fluid-saturated elasto-porous medium. The dynamic response of submerged soil is computed for various cases by using the developed formulation. The effects of submerged conditions are examined for submerged soil deposits with a water level at and above the ground surface. It is found that both submerged conditions and water body above the ground surface can considerably affect the dynamic response of soil deposits.     

含孔隙介质的分层半空间表面瑞利波的衰减特性

以分层半空间内部含有一层孔隙介质为物理模型进行数值计算,研究半空间表面瑞利波的传播和衰减特性.为更加接近实际,结合瑞利波的激发特性,确定了瑞利波的主衰减曲线,并主要以此进行规律分析.针对速度递增和含低速层这两种典型的地质模型,讨论了瑞利波的传播衰减在不同地质模型下的特性,并分析了各自的规律.结果表明,在这两种模型下瑞利波的主衰减曲线都受孔隙介质所处空间位置影响产生比较明显的变化,但衰减系数极大值对应的波长与模型的表层厚度存在较明显的线性对应关系,利用这一关系,可以在实际勘探中快速得到表层介质厚度.另外,通过对比分析还可以看到,瑞利波主衰减曲线随孔隙介质的孔隙度和渗透率的变化都强于主频散曲线的变化,表明衰减曲线对孔隙度和渗透率的变化更加敏感,理论上更加适合进行介质参数反演工作.综合对比结果,我们认为瑞利波主衰减曲线中包含了更丰富的介质参数信息,如果能够有效利用,将可以提高瑞利波勘探的准确性和应用范围.     

A plane strain soil-structure interaction model

A plane strain model for dynamic soil-structure interaction problems under harmonic state is presented. The boundary element method is used to study the response of a homogeneous isotropic linear elastic soil. The far field displacement at the free surface is approximated by an outgoing Rayleigh wave. The finite element method is used to describe the response of the building, of the foundation and possibly of a finite part of the inhomogeneous non-linear soil. Two coupling procedures are described. The model is applied to a problem previously studied in the antiplane case. Incident P, SV and Rayleigh waves are considered. The results show an amplification and an attenuation of the structure motion with frequency when incident Rayleigh waves and P, SV body waves are respectively considered.     

完全匹配层吸收边界在孔隙介质弹性波模拟中的应用

模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射. 本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹配层的构建及其有限差分算法实现. 首先,本文通过均匀孔隙模型的数值解与解析解的对比,验证所提出的数值方法的正确性;然后,本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能,将完全匹配层与廖氏和阻尼吸收边界进行了对比,研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力. 数值结果表明,在孔隙介质中,完全匹配层作为吸收边界能十分有效地吸收衰减外行波,无论对体波还是面波,是一种高效边界吸收算法.     

Transient mechanical wave propagation in semi-infinite porous media using a finite element approach

In this study, we propose a numerical investigation in the time domain of the mechanical wave propagation of an impulsional load on semi-infinite soil. The ground is modelled as a porous saturated viscoelastic medium involving complete Biot theory. All the couplings and a hysteretic Rayleigh damping are taken into consideration. An accurate and efficient finite element method using a matrix-free technique and an expert multigrid system are applied. Our results present the displacements of the fluid and solid particles over the surface and in depth. The arrival times of body and surface waves are studied. Particularly, the compressional wave of the second kind is highlighted. The influence of the different couplings and more specifically, the influence of the permeability on the response of the soil are analyzed.     

Dispersion function of Rayleigh waves in porous layered half-space system

Rayleigh wave exploration is based on an elastic layered half-space model. If practical formations contain porous layers, these layers need to be simplified as an elastic medium. We studied the effects of this simplification on the results of Rayleigh wave exploration. Using a half-space model with coexisting porous and elastic layers, we derived the dispersion functions of Rayleigh waves in a porous layered half-space system with porous layers at different depths, and the problem of transferring variables to matrices of different orders is solved. To solve the significant digit overflow in the multiplication of transfer matrices, we propose a simple, effective method. Results suggest that dispersion curves differ in a lowfrequency region when a porous layer is at the surface; otherwise, the difference is small.     

Three-dimensional dynamic soil–structure interaction analysis in the time domain

A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd     

黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演

瑞利波具有能量大、信噪比高等特点,可以用来反演介质内部的力学信息,近年来在浅层地球物理勘探、深层地震学研究以及超声波无损检测等多个领域都有较广泛的应用。目前大多数瑞利波的应用中都假设介质是弹性的,然而实际中岩石、土壤和金属等介质都在一定程度上体现出了黏弹性。当介质的黏弹性较强时仍然采用弹性假设研究其中瑞利波的反演将增大误差,因此有必要考虑黏弹性介质中的瑞利波反演,但是目前这方面的研究仍不够深入。本文研究黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演问题,给出其在半空间中联合反演的方法,并对该方法的误差进行分析。     

A comparative analysis of seismic response of shallow buried underground structure under incident P,SV and Rayleigh waves

In this study, A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P, SV and Rayleigh waves are established, based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input. After verifying the calculation accuracy, a comparative study on seismic response of a shallow-buried, double-deck, double-span subway station structure under incident P, SV and Rayleigh waves is conducted. The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves. The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves. At the bottom of the side wall, the top and bottom of the center pillar of the underground structure, the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close, and are significantly larger than the calculation result under the incidence of P wave. At the center of the side wall and the top floor of the structure, the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave. In addition, the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions, and the magnification effect in the vertical direction is more significant. Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves, sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.     

饱水介质波动分析的谐波输入初始间断的处理方法

本文以饱水两相介质的土力学模型为研究对象,在假定两相介质为弹性介质条件下,采用了显式有限元法和透射边界进行了饱和弹性半空间动力响应问题的研究。为避免谐波输入初始间断的影响,文中提出了一个处理函数,并以弹性半空间为算例,对饱水介质和单相介质分别进行了在底边界P波垂直入射时的动力响应分析,验证了该处理函数的有效性和实用性。     

小应变硬化模型(HSS)在Rayleigh波作用下场地响应分析中的应用

为研究冲击荷载或地震作用下产生的,以Rayleigh波为主的面波对浅层地表土体动力响应特征以及数值模拟中土层阻尼的设置方法,以厦门地区浅层的素填土及粉质黏土为研究对象,采用有限元动力分析,土体本构采用小应变硬化模型(HSS),利用模型本身的滞回环特性,输入变化的小应变参数,考察HSS模型的小应变参数对场地动力响应的影响,并与土体采用摩尔-库伦模型结合Rayleigh阻尼("MC+Rayleigh阻尼")的计算结果进行对比。研究表明:当采用带有滞回环的HSS模型时,波速随初始剪切模量Gref0的增大而增大,但振幅减小,残余变形量也有所减小;小应变参数γ0.7对波的影响较小;HSS模型能够给出残余变形量,而"MC+Rayleigh阻尼"由于本构模型为理想弹塑性模型,在卸载重加载条件下表现为纯弹性行为,无法反映出卸载重加载过程中塑性应变的积累及其累积阻尼效应;但HSS模型还不能够全面反映循环加载作用下塑性体积应变的累积,因此在考虑滞回阻尼的基础上,仍然建议借助Rayleigh阻尼来更加全面地模拟土体的实际阻尼特性。     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

Axisymmetric soil–structure interaction by global–local finite elements

A version of the global–local finite element method is presented for studying dynamic steady-state soil–structure interaction wherein the soil medium extends to infinity. Herein, only axisymmetric behaviour is considered. In this approach, conventional finite elements are used to model the structure and some portion of the surrounding soil medium considered to be homogeneous and isotropic. A complete set of outgoing waves in the form of spherical harmonics for the entire space is used to represent the behaviour in the half-space beyond the finite element mesh and these are termed the global functions. Full traction and displacement continuity is enforced at the finite element mesh interface with the outer region. On the free surface of the half-space in the outer field, traction-free surface conditions are enforced by demanding that a sequence of integrals of the weighted-average tractions must vanish. Numerical examples are presented for the response of different shaped foundations, resting on the free surface or at various submerged levels, due to a normal seismic plane compressional wave. Plots of differential scattering cross-sections show the angular distribution of the energy (its directional nature) of the scattered field.     

Analysis of Rayleigh waves in saturated porous elastic media by finite element method

A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.     

Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field where deformations are relatively small, a linear elastic constitutive behaviour is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model based on a subdomain formulation. First, the case of vibratory pile driving is considered, where the contributions of different types of waves are investigated for several penetration depths. In the near field, the soil response is dominated by a vertically polarized shear wave, whereas in the far field, body waves are importantly attenuated and Rayleigh waves dominate the ground vibration. Second, the case of impact pile driving is considered. A linear wave equation model is used to estimate the impact force during the driving process. Apart from the response of a homogeneous halfspace, it is also investigated how the soil stratification influences the ground vibration for the case of a soft layer on a stiffer halfspace. When the penetration depth is smaller than the layer thickness, the layered medium has no significant influence on ground vibrations. However, when the penetration depth is larger than the layer thickness, the influence of the layered medium becomes more significant. The computed ground vibrations are finally compared with field measurements reported in the literature.     

Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid

Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO₂ mixture.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

Forward modeling of Rayleigh surface waves for analytical characterization of dominant dispersion trends

Forward modeling is of critical importance for inversion analysis of surface wave methods to obtain shear-wave velocity (V_S) profiles of soil sites. The dynamic stiffness matrix (DSM) method can provide forward modeling of Rayleigh surface waves to simulate complex wave propagation in layered soil sites. However, contamination from body waves and interference of multiple Rayleigh wave modes can reduce the accuracy of theoretical dispersion curves, especially at irregular soil sites with embedded low-velocity or high-velocity layers. An analytical method is developed herein to combine the techniques of the multichannel analysis of surface waves method with the DSM method to improve the accuracy of the theoretical dispersion analysis for soil sites. The proposed method implements multichannel analysis of the analytical displacement responses to capture dominant dispersion trends. Comparison of the results obtained with the new method against those from the transfer matrix method and the literature indicates that the new method can (1) effectively minimize the effects of contamination caused by body waves and interference from several Rayleigh wave modes, and (2) generate accurate dominant dispersion trends for soil sites with various stiffness profiles, especially for the high-frequency dispersion characteristics of the profiles with embedded low-velocity layers.     

Plane-layered models for the analysis of wave propagation in reservoir environments1

The long-wavelength propagation and attenuation characteristics of three geological structures that frequently occur in reservoir environments are investigated using a theoretical model that consists of a stack of fine and viscoelastic plane layers, with the layers being either solid or fluid. Backus theory properly describes fine layering and a set of fluid-filled microfractures, under the assumption that interfaces between different materials are bonded. The effects of saturation on wave attenuation are modelled by the relative values of the bulk and shear quality factors. The anisotropic quality factor in a fine-layered system shows a variety of behaviours depending on the saturation and velocities of the single constituents. The wave is less attenuated along the layering direction when the quality factors are proportional to velocity, and vice versa when inversely proportional to velocity. Fractured rocks have very anisotropic wavefronts and quality factors, in particular for the shear modes which are strongly dependent on the characteristics of the fluid filling the microfractures. When the size of the boundary layer is much smaller than the thickness of the fluid layer, the stack of solid-fluid layers becomes a layered porous media of the Biot type. This behaviour is caused by the slip-wall condition at the interface between the solid and the fluid. As in Biot theory, there are two compressional waves, but here the medium is anisotropic and the slow wave does not propagate perpendicular to the layers. Moreover, this wave shows pronounced cusps along the layering direction, like shear waves in a very anisotropic single-phase medium.