埋置基础扭转振动的实用化计算

根据弹性半空间理论及基础振动试验和数值计算的最新成果,采用方程对等法推演出埋置块体基础扭转振动的实用化计算公式。采用该实用化计算公式和弹性半空间理论分别对复杂形状的埋置块体基础在谐和扰力矩作用下的扭转振动动力响应进行计算,并将计算结果进行了比较,两者结果吻合,振幅误差为9.13%。该实用化计算公式具有概念明确,计算简单的优点,对于任意形状、任意埋置状况的动力设备块体基础都实用,对于结构工程的地震响应计算具有参考意义。     

忽略TTI介质对称轴倾角的可行性

假设横向各向同性(TI)介质的对称轴是垂直的(VTI)或者水平的(HTI)能给实际资料处理带来便利,然而实际TI介质的对称轴往往是倾斜的(TTI),忽略对称轴倾角可能给各向异性参数提取和成像带来偏差,因此需要研究是否能、以及什么条件下能忽略TTI介质对称轴倾角.本文通过理论研究和数值分析研究了与TTI介质弹性性质最接近的VTI介质(OAVTI)的弹性常数和各向异性参数与原TTI介质的弹性常数和各向异性参数之间的联系与差别.结果表明:OAVTI介质各向异性参数与原TTI介质各向异性参数之间的差别可统一表示成F(α₀/β₀,ε,δ,γ)ξ²的形式,其中F(α₀/β₀,ε,δ,γ)是无量纲各向异性参数(ε, δ, γ)的线性函数,ξ是对称轴倾角;ξ的大小对各参数的误差起主导作用,一般不建议忽略20°~25°以上的对称轴倾角;当ξ较小时,即使是对强各向异性的TTI介质作VTI近似,引起的P波各向异性参数误差也很小,因此在纵波资料处理中忽略TTI介质对称轴倾角通常是可行的;即使在小ξ条件下,倾斜对称轴对SV波也有显著影响,因此在转换波资料处理中,不建议忽略TTI介质的对称轴倾角.本文的研究为分析忽略TTI介质对称轴倾角的可行性提供了理论依据和简便的判据.     

横向各向同性地层(VTI)井孔声弹效应对弯曲波的影响

本文发展了建立在地层参考状态为各向同性介质假定下的现行井孔声弹性理论,就井外为横向各向同性面与井轴垂直的、具有9个独立三阶弹性模量的横向各向同性介质(VTI井况),水平面内受双轴应力作用下给出了一个简洁的与井内压力、应力差、应力和以及多极源偏振方位角有关的井孔弯曲波声弹公式,并且导出了平面纵、横波速度的声弹公式.数值考察了弯曲波速度之改变量的灵敏系数随频率的变化、受井外水平双轴应力作用时两种偏振的偶极弯曲波频散曲线以及对应不同方位径向偏振的横波速度.研究结果表明弯曲波声弹公式与5个二阶弹性系数以及7个独立的三阶弹性模量有关;而且由内压引起的井孔弯曲波声弹性公式中的三阶弹性模量仅与6个独立的弹性模量有关.横向各向同性介质井孔弯曲波速度的交叉现象仍是判断地应力存在的标志;一个重要的认识是受双轴应力作用的弯曲波速度变化在低频区主要与c₁₄₄和c₁₅₅两个三阶弹性模量有关,而且此认识与径向偏振的平面横波一致.在缺乏足够实验条件情况下,对VTI情况,以c₁₄₄,c₁₅₅和c₁₂₃三个独立的量进行测量,然后可暂不考虑三阶弹性模量的各向异性,建立简化的应力反演公式.反之,如果已知地层的地应力信息,由简化的声弹公式可以反演三阶弹性模量c₁₄₄,c₁₅₅和c₁₂₃.     

西北太平洋岩石圈有效弹性厚度及其构造意义

本文引入滑动窗口导纳技术(MWAT),计算西北太平洋岩石圈有效弹性厚度(Te).首先,基于SIO V15.1海底地形模型,模拟研究了MWAT法计算Te的精度,表明当Te5km时,误差在±1km以内,当Te≥5km时,相对误差在10%以内.分别采用GEBCO、SIO V15.1和BAT_VGG海底地形模型,构建了西北太平洋Te,通过对获得的洋壳密度参数和实测导纳与模型导纳之差的均方根进行分析,结果表明,BAT_VGG模型更适用于Te计算.西北太平洋Te均值为13.2km,标准差为6.9km,以板块冷却模型为参考,主要分布在150℃~450℃等温线深度范围内.白垩纪和侏罗纪时期岩石圈Te分布在150℃~300℃等温线深度范围内,且未随海山加载时岩石圈年龄增大而增大,说明海山加载时岩石圈年龄不是影响其强度的唯一因素.南太平洋超级海隆活动,以及研究区域广泛存在的断裂带构造,都曾对本区域岩石圈演化产生过重要影响,可能是本地区岩石圈Te较小的构造原因.     

Axisymmetric dynamic response of the multi-layered transversely isotropic medium

By virtue of the precise integration method (PIM) and the technique of mixed variable formulations, solutions for the dynamic response of the multi-layered transversely isotropic medium subjected to the axisymmetric time-harmonic forces are presented. The planes of cross anisotropy are assumed to be parallel to the horizontal surface of the stratified media. Four kinds of vertically acting axisymmetric loads are prescribed either at the external surface or in the interior of the soil system. Thicknesses and number of the medium strata are not limited. Employing the Hankel integral transform in cylindrical coordinate, the axisymmetric governing equations in terms of displacements of the multi-layered media are uncoupled. Applying mixed variable formulations, more concise first-order ordinary differential matrix equations from the uncoupled motion equations can be obtained. Solutions of the ordinary differential matrix equations in the transformed domain are acquired by utilizing the approach of PIM. Since PIM is highly accurate to solve the sets of first-order ordinary differential equations, any desired accuracy of the solutions can be achieved. All calculations are based on the corresponding algebraic operations and computational efforts can be reduced to a great extent. Comparisons with the existing numerical solutions are made to confirm the accuracy of the present solutions proposed by this procedure. Several examples are illustrated to explore the influences of the type and degree of material anisotropy, the frequency of excitation and loading positions on the dynamic response of the stratified medium.     

多波多分量高斯束叠前深度偏移

本文对基于弹性波动理论的多波多分量高斯束偏移进行了完整且详细的分析和公式推导,实现了3D空间多分量(矢量)波场的直接成像.由于当前多数基于弹性波动方程的偏移方法只是假设应力边界条件为自由地表边界条件,这种假设不符合垂直地震剖面(VSP)和海底电缆(OBC)等地震数据.为此本文详细分析了实际应用中常见的三种弹性各向同性介质模型的应力边界条件:自由空间、海底和自由地表模型.在上行传播假设情况下,获得了应力边界条件与位移边界条件的关系式.在此基础上,准确推导了3D多波多分量高斯束波场延拓和偏移成像公式,并在偏移过程中实现了完整的多波型自动分离.由于常规的互相关成像条件不适用于矢量波场成像,本文引用了散度/旋度互相关成像条件.通过约定PS转换波的正向旋转方向解决了3D空间PS成像极性翻转问题.利用2D和3D模型数据偏移成像验证了我们所提出的多波多分量高斯束偏移方法的可行性.     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

劈裂注浆复合土体平面等效弹性模型理论研究

控制隧道开挖引起的土体沉降变形是劈裂注浆的主要目的之一,隧道在劈裂注浆后复合土体的等效弹性参数取值直接关系着隧道在劈裂注浆后沉降变形的预测精度。首先在对已有劈裂扩散模型研究的基础上,按面积等效原则提出了隧道劈裂注浆后复合土体的二维简化等效单元体模型,并基于均质化理论按变形协调原则推导了二维简化单元体模型的等效弹性参数解析解。然后采用有限元方法分别计算并分析了模型在简化前后的等效弹性参数;同时把二维简化等效单元体模型的有限元计算结果和解析计算结果也做了对比分析。最后基于解析结果分析了土体和浆液结石体各自的弹性参数以及浆液注入率对等效弹性参数的影响。结果表明：（1）按面积等效原则对模型进行简化处理的方法是可行的,可以按照简化模型进行弹性阶段的理论分析;（2）解析结果与有限元结果具有良好的一致性,说明了解析结果的合理性;（3）复合土体的等效弹性模量和等效泊松比主要受浆液注入率和浆液固结体本身模量的影响;浆液固结体的泊松比对等效弹性模量的影响几乎可以忽略。     

横观各向同性地基上刚性矩形基础分析

对横观各向同性地基上刚性矩形板进行了求解。首先,利用表面受矩形均布荷载作用下的层状横观各向同性地基的位移解答,获得地基的柔度矩阵;然后,通过刚性矩形基础与层状横观各向同性地基的协调条件,建立刚性矩形基础与横观各向同性地基共同作用的方程,进而求得基础的地基反力。通过编制相应的程序,确定了合理的网格划分值;最后,进行算例分析,分析了地基横观各向同性性质、矩形刚性基础的长宽比以及地基分层性对地基反力的影响。分析表明：以上3种因素对地基反力有重要影响。     

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