Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space,which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves.The indirect boundary element method is used,combined with the Green's function of distributed loads acting on inclined lines.It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homogeneous half-space,and that the mechanism of soil-tunnel interaction is also different much from that of soil-foundation-superstructure interaction.For oblique incidence,the tunnel response for in-plane incident SV-waves is completely different from that for incident SH-waves,while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.     

分层土-隧道相互作用体系地震响应分析

为研究地震作用下非均质场地各个土层放大效应以及分层土-隧道的地震响应,以大连某实际工程为背景,基于地震作用下隧道结构动力响应的理论,采用收敛约束法,通过ABAQUS构建分层土-隧道三维有限元模型,并结合振动台试验,验证模拟的准确性;将自由场与有隧道场地进行对比,并结合加速度和傅里叶曲线对模拟数据进行分析。结果表明：(1)土体性质和激励大小对地震波的传递有影响,随着场地由浅到深逐渐增加,峰值加速度逐渐放大,不同分层介质的主要频率和频谱形状发生明显变化;(2)隧道会放大远场的加速度响应,略微降低近场的动力响应;(3)软弱夹层的存在对地震动的放大作用也有明显影响,不同分层介质的不同特性导致土层刚度不同,从而影响地震作用下层状土-隧道的动力相互作用。     

Soil pressure and pore pressure for seismic design of tunnels revisited: considering water-saturated,poroelastic half-space

This paper describes a systematic study on the fundamental features of seismic soil pressure on underground tunnels, in terms of its magnitude and distribution, and further identifi es the dominant factors that signifi cantly infl uence the seismic soil pressure. A tunnel embedded in water-saturated poroelastic half-space is considered, with a large variety of model and excitation parameters. The primary features of both the total soil pressure and the pore pressure are investigated. Taking a circular tunnel as an example, the results are presented using a fi nite element-indirect boundary element(FE-IBE) method, which can account for dynamic soil-tunnel interaction and solid frame-pore water coupling. The effects of tunnel stiffness, tunnel buried depth and input motions on the seismic soil pressure and pore pressure are also examined. It is shown that the most crucial factors that dominate the magnitude and distribution of the soil pressure are the tunnel stiffness and dynamic soil-tunnel interaction. Moreover, the solid frame-pore water coupling has a prominent infl uence on the magnitude of the pore pressure. The fi ndings are benefi cial to obtain insight into the seismic soil pressure on underground tunnels, thus facilitating more accurate estimation of the seismic soil pressure.     

Application of a second-order paraxial boundary condition to problems of dynamics of circular foundations on a porous layered half-space

A half-space finite element and a consistent transmitting boundary in a cylindrical coordinate system are developed for analysis of rigid circular (or cylindrical) foundations in a water-saturated porous layered half-space. By means of second-order paraxial approximations of the exact dynamic stiffness for a half-space in plane-strain and antiplane-shear conditions, the corresponding approximation for general three-dimensional wave motion in a Cartesian coordinate system is obtained and transformed in terms of cylindrical coordinates. Using the paraxial approximations, the half-space finite element and consistent transmitting boundary are formulated in a cylindrical coordinate system. The development is verified by comparison of dynamic compliances of rigid circular foundations with available published results. Examination of the advantage of the paraxial condition vis-á-vis the fixed condition shows that the former achieves substantial gain in computational effort. The developed half-space finite element and transmitting boundary can be employed for accurate and effective analysis of foundation dynamics and soil–structure interaction in a porous layered half-space.     

Stochastic dynamic analysis of a layered half-space

A stochastic thin-layer method is developed for the analysis of wave propagation in a layered half-space. A random field of shear moduli in the layered system is considered in terms of multiple correlated random variables. Expanding the random moduli and uncertain responses by means of Hermite polynomial chaos expansions and applying the Galerkin method in the spatial as well as stochastic domains, stochastic versions of thin-layer methods for a layered half-space in plane strain and antiplane shear are obtained. In order to represent the infinite half-space, continued-fraction absorbing boundary conditions are included in the thin-layer models of the half-space. Using these stochastic methods, dynamic responses of a layered half-space subjected to line loads are examined. Means, coefficients of variance, and probability density functions of the half-space responses with a varying correlation coefficient of the shear moduli are computed and verified by comparison with Monte Carlo simulations. It is demonstrated that accurate probabilistic dynamic analysis is possible using the developed stochastic thin-layer methods for a layered half-space.     

层土动力Green函数数值计算中若干问题的探讨

动力Ｇｒｅｅｎ子数数值计算技术是动力边界元法得以实施的关键技术之一。本文 无对两类层状介质动力Ｇｒｅｅｎ函数的频域解进行了比较,在此基础上,文中着重探讨了在土－结构相互作用问题中应用显式动力Ｇｒｅｅｎ函数时的若干数值计算问题,包括土层的子层离散和波数的计算以及半空间的模拟等。     

弹性层状半空间中凸起地形对入射平面SH波的放大作用

对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。     

瑞雷波斜入射下层状半空间中沉积谷地周围的三维散射研究

针对层状半空间中沉积谷地对斜入射瑞雷波的三维散射问题, 采用直接刚度法计算自由场波场, 以层状半空间中移动斜线均布荷载动力格林影响函数求解三维散射波场, 建立了求解该问题的间接边界元方法. 通过与已有结果的比较, 验证了该方法的正确性, 并以均匀半空间以及弹性基岩上单一土层场地中沉积谷地为例进行了计算分析. 研究结果表明: 层状半空间与均匀半空间中沉积谷地对瑞雷波的散射存在显著差别; 层状半空间中瑞雷波的振动模态对沉积附近位移幅值有着重要影响; 土层刚度和厚度等参数也对沉积附近位移幅值大小及空间分布有着显著的影响.      

Study on Electrical Potential by Buried Source Electrode within the Horizontally Layered Half-space Model

The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered half-space model by a point current source within the surface layer or the bottom layer.Finally,the electrical potential by a source electrode in any layer of a layered half-space model is presented.     

Dynamic analysis of a layered half-space subjected to moving line loads

Using a thin-layer method enhanced by continued-fraction absorbing boundary conditions, dynamic responses of a layered half-space subjected to a series of constant and time-harmonic line loads moving at a constant speed are studied. The thin-layer method for moving line loads is formulated for plane-strain as well as antiplane-shear conditions and is verified by comparison of computed responses of a homogeneous half-space subjected to a single constant load on its surface against available analytical solutions. Next, time-harmonic loads on a homogeneous half-space are examined. The study continues with both constant and time-harmonic loads on a layered half-space. Finally, multiple constant and time-harmonic loads are considered. The formulation and results demonstrate the effectiveness and versatility of the method in problems of dynamic response of layered media to moving loads.     

弹性层状半空间中无限长洞室对斜入射 平面SH波的三维散射(Ⅱ) 数值结果与分析

以基岩上单一土层场地为例, 计算分析了在斜入射平面SH波作用下弹性层状半空间中无限长洞室附近的地表位移. 研究表明, 层状半空间中地下洞室对波的散射与均匀半空间情况存在显著差别. 层状场地由于考虑了场地自身的动力特性, 使得洞室附近地表位移幅值的空间变化更为复杂, 基岩与土层刚度比、 土层厚度对散射效应均有着重要影响. 随着基岩与土层刚度比的增大, 地表位移幅值整体上逐渐增大; 随着土层厚度的增大, 土层对地表位移幅值的影响逐渐减小. 在频域解答的基础上, 给出了层状半空间中洞室对斜入射SH波散射的时域解答, 并以Ricker波为例进行了数值计算.      

成层半空间深埋电极产生的电位分布

首先给出了点电流源在均匀半空间中所产生电位的解析表达式;其次研究了源电极位于表层和底层时成层半空间介质中的电位分布;最后研究了源电极位于任一层时成层半空间介质中的电位分布.     

Dynamic stiffness of foundation on layered soil half-space using cone frustums

Approximate dynamic-stiffness coefficients of a disk on the surface of a single layer on a half-space may be calculated using cone models. This concept is generalized to the case of a horizontally stratified site consisting of many layers on a homogeneous half-space. After constructing the so-called ‘backbone cone’ determining the radii of the disks at all interfaces, the dynamic-stiffness matrices of the layers (modelled as cone frustums) and the dynamic-stiffness coefficient of the underlying half-space (modelled as a cone) are assembled to that of the site. The dynamic-stiffness matrix of a layer is a complex-valued function of frequency because radiation of energy in the horizontal direction is considered. In this model of the layered half-space the properties of the cone reproduce themselves (cloning). The advantages of using cone models are also present for the layered half-space; in particular, no transformation to the wave-number domain is performed.     

三维层状黏弹性半空间中球面SH、P和SV波源自由场

采用刚度矩阵方法结合Hankel积分变换,求解了层状黏弹性半空间中球面SH、P和SV波的自由波场.首先,在柱坐标系下建立层状黏弹性半空间的反轴对称(柱面SH波)和轴对称(柱面P-SV波)情况精确动力刚度矩阵.进而由Hankel变换将空间域内的球面波展开为波数域内柱面波的叠加,然后将球面波源所在层的上下端面固定,求得固定层内的动力响应和固定端面反力,将固端反力反向施加到层状黏弹性半空间上,采用直接刚度法求得固端反力的动力响应,叠加固定层内和固端反力动力响应,求得波数域内球面波源动力响应.最后由Hankel积分逆变换求得频率-空间域内球面波源自由场,时域结果由傅里叶逆变换求得.文中验证了方法的正确性,并以均匀半空间和基岩上单一土层中球面SH、P和SV波为例分别在频域和时域内进行了数值计算分析.研究表明基岩上单一土层中球面波自由场与均匀半空间情况有着本质差异;基岩上单一土层中球面波位移频谱峰值频率与场地固有频率相对应,基岩面的存在使得基岩上单一土层地表点的位移时程非常复杂,振动持续时间明显增长;阻尼的增大显著降低了动力响应的峰值,同时也显著减少了波在土层的往复次数.     

DYNAMIC CROSS-INTERACTION BETWEEN FLEXIBLE SURFACE FOOTINGS BY COMBINED BEM AND FEM

A combined boundary and finite element method is developed and applied to study the dynamic behaviour of a system of flexible surface footings of arbitrary shape bearing on an elastic half-space. The proposed method employs the frequency domain Green's function for the surface of the elastic half-space while a layered plate model is used for the flexible footing. Both the footing and the surface of the half-space are discretized by 8-noded quadratical isoparametric elements, and the meshes are identical. Thus, the compatibility of displacements and equilibrium of forces between the footing and the half-space are fully satisfied. This model provides a better approximation of the stress concentration at edges of relatively rigid footings. Numerical examples demonstrating the effects due to the excitation frequency, the relative rigidity and the distance between footings on the interaction between two square footings are presented. The external forces can be either harmonic or transient.     

Seismic response of foundations embedded in a layered half-space

An integral equation technique to determine the response of foundations embedded in a layered viscoelastic half-space when subjected to various types of seismic waves is presented. The technique is validated by comparison with previous results for rigid hemispherical and cylindrical foundations embedded in a uniform half-space. Illustrative results for rigid cylindrical foundations embedded in layered media are also presented.     

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.     

Seismic response of a cylindrical shell embedded in a layered viscoelastic half-space. I: Formulation

A method to obtain the three-dimensional harmonic response of a infinitely long cylindrical shell of circular cross-section embedded in a layered viscoelastic half-space and subjected to harmonic plane waves impinging at an oblique angle with respect to the axis of the shell is presented. The procedure combines an indirect integral representation for the field in the exterior half-space with a model of the pipeline or tunnel based on Donnell shell theory. The integral representation for the soil is based on the use of moving Green's functions for the layered viscoelastic half-space. The accuracy of the formulation is tested by comparison of results obtained by using different discretizations. Extensive comparisons with previous two- and three-dimensional results for the case of a shell embedded in a uniform half-space and some new numerical results for a shell embedded in a multilayered half-space are presented in a companion paper.     

层状半空间中洞室对平面SH波的放大作用

利用间接边界元法,求解了弹性层状半空间中洞室对入射平面SH波的放大作用问题,并以基岩上单一土层中洞室对入射平面SH波的放大作用为例进行了数值计算分析。本文模型的特点之一是考虑了层状场地的动力特性,因而更接近于实际工程;特点之二是计算精度非常高。研究表明,层状半空间中洞室对波的放大作用与均匀半空间中情况有着本质的差别;层状半空间中洞室附近地表动力响应由土层动力特性和洞室对波的散射二者共同决定。土层动力特性不仅影响洞室附近地表位移的幅值,还会影响地表位移的频谱。在土层的前几阶共振频率附近,随着基岩与土层剪切波速比的增大,土层的影响随之增大,而随着土层厚度的增加,土层的影响随之减小,并逐渐趋于均匀半空间情况。     

Dynamic interaction between rigid foundations in a layered half-space

A computationally efficient boundary integral equation technique to calculate the dynamic response of a group of rigid surface foundations bonded to a layered viscoelastic half-space and subjected to external forces and seismic waves is presented. The technique relies on an iterative scheme which minimizes in-core memory requirements and takes advantage of any geometrical symmetry of the foundations. Extensive results for the case of two rigid square foundations placed at different separations and bonded to a viscoelastic half-space are presented. It was found that the choice of discretization of the foundations has a marked effect on the calculated impedance functions for extremely small separations. Illustrative results for a case of several closely-spaced foundations bonded to a layered half-space are also presented.