基于平面应变简化假定的桩扭转振动理论精度研究

利用拉普拉斯变换对考虑桩土耦合扭转振动条件下,桩顶受到任意激振扭矩作用的端承桩桩顶频域及时域响应进行解析求解,推导求得了桩顶位移、速度频域响应,桩顶复阻抗的解析表达式和半正弦脉冲激励作用下的桩顶时域响应半解析解;将本文所得理论解与基于平面应变假定的桩基扭转耦合振动的频域解和时域解进行了全面对比研究,具体比较范围涉及土层对桩的局部复阻抗、桩顶复频响应、速度导纳、桩顶复刚度和桩顶时域响应等方面,并得到若干重要结论。研究成果校核了平面应变假定在桩基扭转振动理论研究中的合理运用,为进一步了解桩土耦合振动的内在机理提供理论支持。     

成层粘弹性土中桩土耦合纵向振动时域响应研究

从三维轴对称角度出发,采用粘性阻尼粘弹性连续土介质模型,考虑桩土相互作用效应,对成层土中桩土纵向耦合振动时的桩顶时域响应进行了解析研究。求解时,首先建立定解问题,然后利用拉氏变换先对底部土层进行求解得到其振动位移形式解,然后利用桩土接触界面连续条件来考虑桩土耦合作用,分析底层土中桩段的动力反应,然后利用桩段阻抗函数的传递性,进行逐层递推求解,最终得到桩顶时域和频域响应的半解析解。通过参数影响分析和与工程实测曲线的对比,讨论分析了成层土中桩土耦合振动的响应特性,验证了本文解。基于本文研究可为桩基抗震、防震设计、桩基动力检测提供新的理论支持。     

剪切波速对场地地表地震动参数的影响

本文以江淮地区典型场地资料为原型,将土层剪切波速实测值按照一定比例进行增减,构造多种场地土层地震反应分析模型,选择Taft、E1centro和Kobe三条强震记录作为地震输入,采用一维频域等效线性化波动方法进行了土层地震反应分析.研究结果表明,剪切波速的变异性与场地地表地震动的影响程度与输入基岩地震动的频谱特性、幅值、土层结构等因素有关.地表峰值加速度随着剪切波速的增大而逐渐增大,地表加速度反应谱的特征周期随着剪切波速的增大而逐渐减小.     

A simplified seismic analysis of rigid base liquid storage tanks under vertical exicitation with soil-structure interaction

A study is carried out to evaluate dynamic response of an elastic circular cylindrical tank having a rigid base under a vertical excitation taking into consideration the interaction with the foundation soil. At first, the soil is represented by frequency-independent parameters. Two coupled differential equations, governing the motion of the shell and the base, are solved using a step by step integration technique. The hydrodynamic pressures, acting on the shell and on the base, are derived from a velocity potential function which satisfies the Laplace equation and the appropriate boundary conditions. The response of the simplified model of a tank having a rigid base on a stiff foundation soil is compated to that obtained elsewhere to check the accuracy of the present model. Reasonable agreement is found between the maximum wall displacement and the associated stresses with those found by a more elaborate model. The interaction of the tank and the soil reduces the response than that calculated under the assumption of a rigid foundation soil. A parametric study to examine the effects of the height-to-radius ratio of the tank, and the effects of the shear wave velocity of the soil on the response is conducted. Varieties of foundation models are used to assess the sensitivity of the response to the variation in the soil parameters. Finally, a more representative solution for the problem in the frequency domain is obtained where the soil is appropriately modelled by frequency-dependent parameters. The transfer functions of the response of the tank wall and of the relative base motion are evaluated, and a comparison between the frequency-dependent and the frequency-independent solutions is made.     

STEEP DIP FINITE-DIFFERENCE MIGRATION*

A method is presented to derive approximate versions of the wave equation which allow finite-difference migration for very steep dips (> 50°). It is shown that for conventional finite-difference schemes, in addition to the dip limitation, the maximum acceptable frequency should be specified. A finite-difference migration technique is proposed in the frequency domain. It is derived that finite-difference wave field extrapolation in the frequency domain consists of a space-variant convolution procedure for each frequency component, the space-variance being defined by the lateral variation in the velocity. Finally it is shown that with finite-difference migration, particle velocity data can be easily obtained from pressure data.     

Dynamic response of a tunnel buried in a saturated poroelastic soil layer to a moving point load

The dynamic response of a tunnel buried in a two-dimensional poroelastic soil layer subjected to a moving point load was investigated theoretically. The tunnel was simplified as an infinite long Euler–Bernoulli beam, which was placed parallel to the traction-free ground surface. The saturated layer was governed by Biot’s theory. Combined with the specified boundary conditions along the beam and saturated poroelastic layer, the coupled equations of the system were solved analytically in the frequency–wavenumber domain based on Fourier transform. The time domain responses were obtained by the fast inverse Fourier transform. The critical velocity of the considered structure was determined from the dispersion curves. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium subjected to the underground moving load were investigated. It is concluded that, for coarse materials or fine materials subjected to the high-velocity loading, models ignoring the coupling effects between the pore fluid and the soil skeleton may cause errors. The shear modulus and the permeability coefficients of the saturated soil as well as the load moving velocity had significant influence on the displacement and pore pressure responses.     

Dynamic stiffness and kinematic response of single piles in inhomogeneous soil

The effect of soil inhomogeneity on dynamic stiffness and kinematic response of single flexural elastic piles to vertically-propagating seismic SH waves is explored. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous stratum. A layered soil with piece-wise homogeneous properties is introduced to approximate the continuous inhomogeneity in the realm of a Beam-on-Dynamic-Winkler-Foundation model. The problem is treated numerically by means of a layer transfer-matrix (Haskell–Thompson) formulation, and validated using available theoretical solutions and finite-element analyses. The role of salient model parameters such as pile-head fixity conditions, pile-to-soil stiffness ratio, surface-to-base shear wave velocity ratio and rate of inhomogeneity is elucidated. A new normalization scheme for inertial and kinematic response of such systems is presented based on an average Winkler wavenumber. With reference to long piles in moderately inhomogeneous soils, results indicate that: (a) kinematic pile response is essentially governed by a single dimensionless frequency parameter accounting for pile-to-soil stiffness ratio, pile slenderness and soil inhomogeneity and (b) definition of a characteristic pile wavelength allows an approximate estimation of pile elastodynamic response for preliminary design or analysis. Issues related to domain discretization and Winkler moduli are discussed.     

2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves

The problem of harmonic wave diffraction by tunnels in an infinite poroelastic saturated soil obeying Biot's theory is studied numerically under conditions of plane strain and the effect of poroelasticity on the response is assessed through some parametric studies. The method is based on the theory of Mei and Foda, which considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer at the free boundaries. Both problems are solved numerically by the boundary element method in the frequency domain. Results dealing with the response of a circular tunnel with and without an elastic concrete liner in an infinite poroelastic medium to incident harmonic P and SV plane waves are provided and compared against analytical ones as well as to those corresponding to linear elastic soil behaviour. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

利用数字化速度记录仿真加速度时程与合成场地设计地震波

研究利用测震台网数字化宽频带速度型记录仿真加速度时程,并通过提取其相位信息和拟合场地设计反应谱(目标谱)的方法来获得场地设计地震波的有关技术途径与应用实例,所提供的具体算式采用便于编程和利用快速傅氏变换(FFT)技术进行计算的离散化傅氏正逆变换的复数表达式。有关研究结果可拓宽现有地震观测资料的使用价值,减少地面运动模拟中人造地震波与原始地震记录存在的差异,并可使所合成的设计地震波满足给定的目标谱,且能较好地反映其非平稳性特征,因此在地震工程中具有实际的应用价值。     

Time-domain solution for transient dynamic response of a large-diameter thin-walled pipe pile

The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top.     

土中Love波弥散特性

利用有限单元法及解析法建立和求解了土中Love波特征方程以及位移计算公式．计算结果表明,这一计算方法比纯解析法优越,可以用来分析均质和非均质上中Love波弥散性．本文利用这一方法详细讨论了Love波在上软下硬地基及软夹层地基中的传播特性和弥散特性．上软下硬地基Love波具有弥散性,土层的剪切波及厚度对Love波弥散曲线影响较大,而质量密度的相对变化对Love彼弥散曲线影响较小．软夹层地基中低频时Love波以第一模态波为主,现场所测为第一模态波波速;高频时存在多个高模态波,土中传播的波为这几个高模态波的叠加波,现场所测波速随两传感器的位置不同而有波动．     

含流体孔隙介质中面波的传播特性及应用

基于单相介质中地震波理论的高频面波法已广泛应用于求取浅地表S波的速度.然而水文地质条件表明,普遍的浅地表地球介质富含孔隙.孔隙中充填的流体会显著地影响面波在浅地表的传播,进而造成频散和衰减的变化.本文研究了地震勘探频段内针对含流体孔隙介质边界条件的面波的传播特性.孔隙流体在自由表面存在完全疏通、完全闭合以及部分疏通的情况.孔隙单一流体饱和时,任何流体边界条件下存在R1模式波,与弹性介质中的Rayleigh波类似,相速度稍小于S波并在地震记录中显示强振幅.由于介质的内在衰减,R1在均匀半空间中也存在频散,相速度和衰减在不同流体边界下存在差异.Biot固流耦合系数(孔隙流体黏滞度与骨架渗透率之比)控制频散的特征频率,高耦合系数会在地震勘探频带内明显消除这种差异.介质的迂曲度等其他物性参数对不同流体边界下的R1波的影响也有不同的敏感度.完全闭合和部分疏通流体边界下存在R2模式波,相速度略低于慢P波.在多数条件下,如慢P波在时频响应中难以观察到.但是在耦合系数较低时会显现,一定条件下甚至会以非物理波形式接收R1波的辐射,显示强振幅.浅表风化层低速带存在,震源激发时的运动会显著影响面波的传播.对于接收点径向运动会造成面波的Doppler频移,横向运动会造成面波的时频畸变.孔隙存在多相流体时,中观尺度下不均匀斑块饱和能很好地解释体波在地震频带内的衰减.快P波受到斑块饱和显著影响,R1波与快P波有更明显关联,与完全饱和模型中不同,也更易于等效模型建立.频散特征频率受孔隙空间不同流体成分比例变化的控制,为面波方法探测浅地表流体分布与迁移提供可能性.通常情况孔隙介质频散特征频率较高,标准线性黏弹性固体可以在相对低频的地震勘探频带内等效表征孔隙介质中R1波的传播特征,特别在时域,可在面波成像反演建模中应用.     

浅硬场地剪切波速测试标准差对地震动影响初探

采用Shake 2000程序,以Turkey Flat试验场地为模型,通过输入不同类型下多种强度的地震波,计算研究多工况下剪切波速测试标准差对地表加速度反应谱和峰值加速度的影响。结论为:(1)浅硬场地上剪切波速测试标准差对地震动的影响很大,影响程度与输入地震波的强度和频率以及场地剪切波速计算值有关;(2)如果将反应谱残差大于20%或加速度峰值差别大于20%定义为统计意义上的不可忽略,那么剪切波速测试标准差对计算结果的影响在大多数情况下均不可忽略;(3)当输入波的卓越周期与场地特征周期接近时,浅硬场地上剪切波速测试标准差引起的反应谱变化非常显著;(4)只有当输入波的卓越周期与场地特征周期相差较大且输入波强度偏小时,剪切波速测试标准差引起的反应谱变化才可略去;(5)当浅硬场地上剪切波速实测结果低于统计均值时,地震动计算结果的偏差一般明显大于剪切波速实测结果,高于统计均值时引起的偏差,且地震输入越强表现越明显。     

地下隧道轴向地震动土作用分析

以弹性基岩上覆层状场地中刚性衬砌隧道为模型,采用间接边界元方法求解衬砌隧道所受的沿轴向地震动土作用,通过参数分析揭示轴向动土作用的幅值大小、空间分布等基本规律。研究表明,土-隧道动力相互作用对地震动土作用的空间分布形式影响较小,但对地下隧道所受地震动土作用峰值大小具有显著影响,隧道主要位置点的地震动土作用峰值与隧道相应位置处自由场土层应力相比放大1.7~2.4倍。论文最后提出一个轴向地震动土作用的简化计算方法。     

基于反卷积干涉法的土层地震反应特性研究

美国阿拉斯加安克雷奇德兰尼公园的土层地震反应观测台阵建有6个井下观测点和1个地表观测点, 每个观测点设置一个三分量加速度传感器, 该台阵建成后记录了多次地震事件. 本文通过反卷积地震干涉法对这些地震记录进行土层反应分析, 根据该分析结果提取土层结构的等效剪切波速和阻尼比. 所有层位的地震记录对地表记录的反卷积波形均反映出在土层中传播的上、 下行波, 其上行与下行至每一层的时间差别明显. 根据每一层的到时差, 确定土层中的等效剪切波速和分层等效剪切波速, 该结果与现场土层等效剪切波速测试结果吻合较好; 根据等效剪切波速计算出的土层卓越频率, 其一致性亦较好; 根据上、 下行波的峰值分析确定该场地土层的等效阻尼比, 也与软土的阻尼比经验值相当. 这些参数为后续的土层反应模拟和土结相互作用研究奠定了良好的数据基础. 结果表明, 反卷积干涉法能够用于土层反应分析和土层地震反应特性的提取.      

Signal reconstruction of surface waves on SASW measurement using Gaussian Derivative wavelet transform

Surface wave method consists of measurement and processing of the dispersive Rayleigh waves recorded from two or more vertical transducers. The dispersive phase data are inverted and the shear wave velocity versus depth is obtained. However, in case of residual soil, the reliable phase spectrum curve is difficult to be produced. Noises from nature and other human-made sources disturb the generated surface wave data. In this paper, a continuous wavelet transform based on mother wavelet of Gaussian Derivative was used to analyze seismic waves in different frequency and time. Time-frequency wavelet spectrum was employed to localize the interested seismic response spectrum of generated surface waves. It can also distinguish the fundamental mode of the surface wave from the higher modes of reflected body waves. The results presented in this paper showed that the wavelet analysis is able to determine reliable surface wave spectrum of sandy clayey residual soil.