A new solution to estimate the time delay on the topographic site using time domain 3D boundary element method

This study focuses on investigating spatial variation of ground motion that has great influence on the dynamic behavior of the large structures located on the surface topography. One of the most effective parameters on the spatial variation of ground motion is the difference between the arrival time of seismic waves in different points located on the abutments. In this research, a three-dimensional model of the Pacoima Dam site is prepared. The time domain 3 D boundary element method is used to apply non-uniform excitation at the dam supports. This model is subjected to vertically propagating incident SH and P waves. The time delay can be characterized by calculating the value of the time delay for which the cross-correlation between two records is maximized. Finally, to obtain the time delay in a topographic site, a function considering effective parameters such as the height from the canyon base, wave velocity and predominant frequency, is presented. Furthermore, a code was developed for generating the spatially variation of seismic ground motions. The results show that the proposed functions have an acceptable accuracy in estimating the time delay to generate non-uniform ground motion.     

圆弧形凹陷在SH波入射下瞬态反应的解析解

针对现有地震波散射问题的解析解均在频域内给出,其适用的频带较窄,不能获取到可靠的瞬态反应解析解的问题,本文利用宽频带频域解析解进一步获取了不同空间点地震反应的宽频带频响函数,并基于傅里叶变换得出SH波入射下圆弧形凹陷地形瞬态动力响应的解析解.以上述为基础,研究了输入脉冲与实际地震动时凹陷的瞬态反应的基本特征,并重点分析...     

Analysis of the role of diffraction in topographic site effects using boundary element techniques

The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.     

基于改进能力谱方法的位移反应估计

本文阐述了Pushover分析中改进能力谱方法的概念和实施步骤；对不同场地条件下四个中、低层框架结构采用改进能力谱方法估计的目标位移和非线性时程反应分析结果进行了比较，分析，并提供了不同场地条件下两种方法的相对误差，为该方法的实际应用提供了一些参考依据。     

Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods

Using reciprocal theorems for dynamic and static boundary value problems, boundary integral equations are presented for wave propagation in elastic, isotropic media and compressible, inviscid fluids in the time domain as well as in the frequency domain. For the analysis of fluid–soil and fluid–structure systems, suitable coupling conditions are prescribed along the interfaces. The numerical treatment of the boundary integral equations consists of a point collocation and of a discretization of the boundary, in which constant and linear approximation functions are assumed. Step-by-step integration is applied to the time-dependent equations, where again the states are taken to be linear and constant over each time interval. These boundary element procedures are used to analyse the response of dams due to horizontal and vertical ground motions considering dam–water interaction and absorption of hydrodynamic pressure waves at the reservoir bottom or at the far end into the soil medium. Both the frequency response and the impulse generated transient response are investigated.     

基于小波函数的地震动反应谱与峰值位移拟合方法

采用数值方法合成地震动时,除对反应谱拟合外,对峰值位移的拟合和天然地震动非平稳特性的模拟也具有重要的意义和工程应用前景.本文基于小波函数的拟合方法,提出了一种能够同时合成目标反应谱和峰值位移的地震动加速度时程.数值算例表明:该方法具有较快的收敛速度,可用较少的迭代运算实现对目标反应谱和目标峰值位移的较高精度拟合;相较于...     

The reference spectral noise ratio method to evaluate the seismic response of a site

The seismic response of several sites in the Durban area of South Africa has been investigated using a refined version of the spectral ratio (H/V) generated by cultural seismic noise. Two samples of noise separated by an interval of several minutes for the vertical and the two orthogonal horizontal components were taken at each site. Though the two samples differed noticeably in the time as well as in the frequency domain, when the components are considered separately, the ratios of the horizontal to the vertical spectra were very similar for most of the pairs. This similitude was obvious not only in the frequencies of the peaks, but also in the range of amplifications involved. These observations have been used to introduce a refinement to the Nakamura Method. This refinement consists in using as a reference the H/V spectral ratio of a well-known, hard rock site. All the other soft sites of interest are then compared with this standard reference site. This comparison provides valuable information on the frequencies and amplification factors introduced by the critical soft sediments. This refined method will be referred here as the ‘Reference spectral noise ratio’.This method, is compared to a similar one devised to investigate the response of horizontal layers to longitudinal seismic waves, using the ratio of the spectra generated by long- period waves.     

一种基于多项式外推的局部透射边界位移解(外行波为非平面波情形)

一般情况下,通过人工边界向外透射的波动常为非平面波。对于近场非平面波在人工边界上的透射问题,不能采用简单的平面波透射方法。本文针对近场非平面波在人工边界上的透射特点,分析了非平面波沿人工边界法向视波速的变化规律及其近场失稳机制,推导了适合近场非平面波的、人工边界点位移解的不等步距线性外推公式。     

一种基于多项式外推的局部透射边界位移解(外行波为平面波情形)

基于外行波局部法向透射概念，从多项式外推的角度，结合一维和广义二维几何解释，推导建立了外行波为平面波时，人工边界节点位移解的计算公式。对该位移解的精度进行了时域分析，论证了该位移解收敛于数值精确解的必要条件和线性外推位移解的精度与数值精确解匹配的充要条件。在此基础上提出了一次“精确”透射的概念和相应的数学方法，实现了该位移解逼近于数值精确解的优化计算。     

结构动力反应分析的三阶显式方法

本通过对传统动力反应分析方法的总结，阐明了建立隐式和显式方法的一般思路及数学本质，提出了使用系统位移反向向量三阶导数的隐工和实用显式积分方法－3阶显式方法，分析了该显式方法的精度和稳定性，并对建立更高阶隐式和显式方法以及方法的精度和稳定性作了初步讨论。最后，通过算例对本方法、献[1]方法和经典的常平均加速度法（隐式方法、视为精确解）的精度和稳定性进行了比较分析。结果表明，本方法具有明显的优点。     

砂土液化对设计反应谱和场地分类的影响

本文采用有效应力原理分析了液化土层对设计反应谱的影响，分析中考虑了砂层的厚度、埋深和输入地震动等因素。选择Ⅱ类场地，将其标准反应谱合成的三条地震加速度时程在考虑土层非液化下反演到基岩，再正演计算存在液化层时的地面运动时程和反应谱。分析结果表明，从特征周期的变化来看，液化土层使Ⅱ类场地易变为Ⅳ类场地，对地震影响系数的作用则不是很大，但频谱上0．8s是一个分界线，液化土层对分界线以下的高频分量有一定减震效果，对分界线以上的低频分量有显著的放大效应。     

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography.The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.     

Numerical analysis of permafrost effects on the seismic site response

Some of the damage to the infrastructure observed in past earthquakes occurred in Alaska could be related to the existence of permafrost. However, only limited research has been carried out so far to investigate the effects of permafrost on the seismic site response. Permafrost with relatively high shear wave velocity (1000–1500 m/s) extensively exists in the interior of Alaska and causes anomaly in the shear wave velocity profile that may alter the site response. In current design practices, permafrost has been treated as bedrock and its potential effects on site response are ignored. A systematic investigation was conducted to understand the effects of permafrost on the ground motion characteristics using one-dimensional equivalent linear analysis for the MCE, AASHTO and IBC Design Earthquake level hazards. The average surface displacement, velocity and acceleration response spectra for a typical permafrost site were obtained and the worst case scenario was identified. The results show that the presence of permafrost can significantly alter the ground motion characteristics and it may not be conservative to ignore the effects of permafrost in the seismic design of civil structures.     

A new finite element technique for the solution of two-phase flow through porous media

A new upstream weighting finite element technique is developed for improved solution of the two-phase immiscible flow equations. Unlike the upstream weighting technique used by previous investigators, the new technique does not employ finite difference concepts to achieve the required upstream weighting of relative permeabilities or mobilities. Instead, upstream weighting is achieved by (1) representing the relative permeabilities or mobilities as continuous functions expressed in terms of the shape functions and nodal values (2) using asymmetric weighting functions to weight the spatial terms in the flow equations. These weighting functions are constructed such that they are dependent on the flow direction along each side of an element.In conjunction with the proposed technique, two solution schemes for treating the resulting set of non-linear algebraic equations are presented. These are the fully-implicit chord slope incremental solution scheme and the Newton-Raphson solution scheme. Both schemes allow the use of large time steps without being unstable.The proposed numerical technique is applied to two problems (1) the one-dimensional Buckley-Leverett problem (2) the two-dimensional five-spot well flow problem. Results indicate that this technique is superior to not only earlier finite element schemes but also five-point upstream finite difference formulae.     

Introducing an effective coherence function to generate non-uniform ground motion on topographic site using time-domain boundary element method

In this study,a comprehensive parametric analysis was performed on non-uniform excitation of V-shaped topography using the boundary element method in time domain.For this purpose,wave scattering analysis was carried out on a topography subjected to the SV-wave for different predominant frequencies and shape ratios.Based on the numerical results,new coherence and time delay functions are proposed to generate non-uniform ground motion for topographic irregularities.The efficiency and accuracy of the proposed functions for real engineering problems are indicated by comparison with observations reported in previous literature.     

多年冻土场地路基地震动位移性状研究

直接针对目前多年冻土场地道路工程抗震问题研究尚很薄弱这一事实，以在建的青藏铁路工程的抗震设计与地震加固为应用背景，基于若干种较为典型的多年冻土场地路基工况，开展多年冻土场地路基地震动位移性状的研究工作。研究表明，与不同的场地地形条件相比，场地冻土层厚度对路基地震位移响应的影响更加突出，尤其是含冻土融层路基的地震动位移值较不含冻土融层路基的地震动位移值大，因而冻土融层的存在无疑加剧了多年冻土场地路基的震害响应。     

Sensitivity analysis of site effects on response spectra of pipelines

In this paper, a numerical sensitivity analysis of the site effect on dynamic response of pipelines embedded in some idealised soil deposits resting on a halfspace covering a wide range of soil profiles encountered in practice and subjected to vertically propagating shear waves, is presented. The power spectrum of the lateral differential displacement between two distant points due to the site effect is formulated analytically by using an analytical amplification function of a viscoelastic inhomogenous soil profile overlying either a compliant halfspace or a bedrock, represented by a more realistic continuous model. Also, Kanai-Tajimi spectrum parameters are estimated and expressed analytically from the soil profile model. Finally, results in the form of stochastic response spectrum of pipelines, for different key soil and pipeline parameters, are given and discussed.     

Scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space, modeled using the indirect boundary element method

The scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space is modeled using the indirect boundary element method in the frequency domain. The free-field responses are calculated to determine the displacements and stresses at the surface of the canyon, and fictitious distributed loads are then applied at the surface of the canyon in the free field to calculate the Green's functions for displacements and stresses. The amplitudes of the fictitious distributed loads are determined from the boundary conditions, and the displacements arising from the waves in the free field and from the fictitious distributed loads are summed to obtain the solution. The effects of fluid saturation, boundary conditions, porosity, and soil layers on the surface displacement amplitudes and phase shifts are discussed, and some useful conclusions are obtained. It is shown that the surface displacement amplitudes due to saturation and boundary conditions, different porosities, or the presence of a soil layer can be very dissimilar, and large phase shifts can be observed. The resulting wavelengths for an undrained saturated poroelastic medium are slightly longer than those for a drained saturated poroelastic medium; and are longer for a drained saturated poroelastic medium than those for a dry poroelastic medium. As porosity increases, the wavelengths become longer; and a layered half-space produces longer wavelengths than a homogeneous half-space.     

地震动瞬时能量谱与结构位移响应关系研究

本文通过HHT变换得到瞬时能量谱,并以HHT对地震动作用下的结构位移响应进行分析,发现长周期结构动力响应的显著特点:最大结构位移响应总是滞后于地震动激励的最大能量谱值时间.滞后的时间主要取决于结构的动力特性参数(特别是自振周期),也与地震动的类型有关.仿真计算的结果表明:长周期结构的破环与倒塌并不发生在地震动强度最大的时刻,而多数是在地震动末期,甚至在地震动完全消失之后.有益的结论为结构控制设计与安全提供科学依据.     

A new methodology to determine elastic displacement spectra in the near-fault region

The evaluation of the displacement demand especially at small distances from the causative fault, in the so-called near-source region, is a subject of particular interest for earthquake engineering design, in the light of the growing application of the displacement-based design philosophy. This study presents a new methodology to determine the elastic displacement spectra using a sample of near-fault records from small-to-moderate magnitude earthquakes, typical of the seismic activity in Europe. The displacement spectrum is developed using near-fault attenuation relationships available in literature for peak ground velocity that is less sensitive in the procedures applied to correct the accelerograms. Also, the distance from the causative fault and the type of directivity are taken into consideration. The prevailing period corresponds to the maxima of the displacement spectra for zero damping and is used to normalize the spectra, leading to significant decrease of the statistical dispersion. The average bi-normalized spectrum, in terms of the peak ground displacement d_g,max and the dominant period T_d-p, appears to be slightly affected by the soil category and earthquake magnitude. A correlation between the damping correction factor η and the normalized period T/T_d-p is detected and the applicability of several provisions of the current version of Eurocode 8 is examined, including characteristic periods and spectral amplitudes.