移动荷载作用下非均匀地基的动力响应分析

基于线弹性动力学理论,结合坐标变换,建立了移动荷载作用下非均匀弹性半平面地基的动力控制方程,利用半解析法研究了移动荷载作用下二维非均匀地基的动力响应问题。采用傅里叶（Fourier）级数展开,假设了响应函数的级数形式,通过理论推导获得了剪切模量随深度任意变化的非均匀地基在移动荷载作用下各物理量的解析表达式。考虑土体的剪切模量沿厚度方向按幂函数梯度变化,通过数值算例分析并讨论了地基非均匀参数、荷载移动速度以及地基表面的剪切模量等对地基力学响应的影响规律,并与均质地基的计算结果进行了比较。数值结果表明：地基中各点的竖向位移随着土体表面剪切模量和表征土体非均匀性的梯度因子的增大而减小,随着荷载移动速度的增大而增大。在移动荷载作用下,非均匀地基与均匀地基的动力响应有着显著的区别。     

层状半空间中洞室对入射平面SV波的散射

利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面SV波的散射问题。通过自由场反应分析,求得假想洞室边界上各点位移和各单元应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面SV波的放大作用。结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。     

竖向圆形荷载作用下弹性地基半空间问题的解析解

竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。     

关于弹性力学半无限问题的注记

根据两个合理的判断依据,对弹性力学中的楔形体、半平面体、圆锥体和半空间体等经典解答进行了比较分析,发现了半无限平面应变问题和半空间体问题解答之间的关系;通过对解答之间的关系进行研究分析指出,弹性力学中的半无限平面体的符拉芒解答和半空间体的布希涅斯克解答存在局限性。对半无限地基、底部完全位移约束的有限深地基和底部光滑刚性支承的有限深地基在水平表面作用无限均布压力时的应力和位移分量进行了比较分析,认为底部完全位移约束的有限深地基模型较其他两种地基模型更合理些。     

浅层顶管施工引起的土体移动

顶管施工引起包括地面沉降和土的轴向移动在内的土的运动。 土的这些运动可能导致邻近构筑物和管线的损坏。 理论分析和现场实测都显示, 在类似于上海等地的软土地层中顶管施工, 顶管周围土的运动问题是三维的。 基于半解析数值方法的基本原理, 将轴向离散而在径向和环向选取位移函数, 构造了解析解函数。 给出了包括位移函数、刚度矩阵和荷载矩阵在内的理论分析过程, 从而建立了半解析单元法。 利用半解析单元法将顶管施工中三维土运动问题转化成一维数值计算 。 利用所建立的半解析单元法, 就软土地层中顶管工程实例计算了施工所引起的土体位移。 结果表明, 半解析元法用于计算顶管施工中顶管周围土的移动, 可以得到较为满意的结果。 由于计算所需要的单元数减少, 处理该问题所需要的时间也明显减少。 根据分析与计算结果还得到了一些有价值的结论。     

基于边界配点法浅埋隧道开挖引起 周围土体变形的分析

对于浅埋隧道施工引起土层位移的解析解,其边界条件的数学处理上比较困难,因此实际工程的应用中受到限制。为解决这一缺陷,基于弹性力学的Airy应力函数,将半无限平面内土体的应力及位移分布转化为解析函数。然后,采用边界配点的方法,控制地表处的应力边界条件( = 0, = 0)及隧道周边土体的位移边界条件( , )。最后,采用最小二乘法,确定土体应力及位移函数的各项系数,求得浅埋隧道在周边土体产生径向位移的作用下,地表及深层土体位移的半数值半解析解。算例分析表明,该方法可以考虑任意荷载及位移作用的边界条件,能够充分发挥解析法和数值法两者的优点,且计算结果与实测结果较吻合,在预测地表及深层土层位移中具有一定的实用价值,可为进一步采取工程措施控制地层变形提供理论依据。     

非稳态热传导时层状路面体系的温度响应

利用解析层元法推导温度荷载作用下非稳态热传导时层状路面体系的温度响应解答。从热弹性理论平面应变问题的控制方程出发,借助于Laplace-Fourier积分变换,推导出单层介质及下卧半平面的精确刚度矩阵即解析层元,结合有限层法原理及边界条件,组装并求解总刚度矩阵,得到其在变换域内的解答,最后通过相应的积分逆变换得到物理域内的真实解。由于该法刚度矩阵元素中不含正指数项,计算时不会出现溢出或病态矩阵的现象。编译了相应的计算程序,所得结果与有限元模拟结果吻合较好。在此基础上,对有限深度和半平面两种假定条件下的解答进行对比分析,并分析层状路面体系中位移和温度随时间的变化趋势及沿深度的分布规律。分析表明：温度场具有一定的影响深度,超过此深度,有限深度与半平面理论解答基本一致;温度荷载的影响深度与其强度有关,强度越大,其影响深度越深。     

浅层顶管施工引起的土体移动

顶管施工引起包括地面沉降和土地向在内的土地的运动，土的这些运动呆能导致近构筑物和管线的损害。理论分析和现场实测都显示，在类似于上海等地的软土地层中顶管施工，顶管周围土的运动问题是三维的。基于半解析数值方法的基本原理，将轴向离散而在径向和环向选取位移函数，构造了解析解函数。给出了包括位移函数，刚度矩阵和荷载矩阵在内的理论分析过程，从而建立了半解析单元法。利用半解析单元法将顶管施工中三维土运动问题转化成一维数值计算。利用所建立的半解析单元法，就软土地层中顶管工程实例计算了施工所引起的土体位移。结果表明，半解析元法用于计算顶管施工中顶管周围土的移动，可以得到较为满意的结果。由于计算所需要的单元减少，处理该问题所需要的时间也明显减少。根据分析与计算结果还得到了一些有价值的结论。     

饱和半空间瞬态加载衬砌隧道的动力响应研究

工程中,地下衬砌隧道会遇到水压破裂压力、爆炸及突然开挖等瞬态荷载作用,将这些荷载理想化为作用在衬砌内边界上的均布瞬态荷载,研究圆柱形衬砌隧道在突加荷载、阶跃荷载和三角形脉冲荷载作用下的动力响应规律。根据Biot波动理论推导出半空间饱和介质的控制方程;视衬砌结构为弹性材料导出衬砌结构的控制方程。用极大半径凸圆弧近似半空间直边界,采用Graff加法公式进行坐标变换,将直角坐标表示的通解转化为极坐标表示的通解。根据边界条件导出衬砌和土体的位移、应力和孔隙压力的Laplace变换域的解答。利用反Laplace变换数值计算方法,将解答转换为时域解,得出3种瞬态荷载作用下衬砌隧道地面位移峰值、衬砌应力和孔隙压力的分布规律。     

岩土工程半解析半数值方法若干进展

总结了笔者等近年来有关岩土工程半数值半解析方法方面的研究进展,重点介绍了有限层方法、析解法、等积变换法、广义剪切位移法、广义荷载传递函数法等5个方面,充分显示了半数值半解析方法良好的应用前景。     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

Elastic analysis of ground movements around a tunnel considering a buoyant lining moving upwards

A complex variable solution is derived for the ground movements around a tunnel considering the lining at different positions in the drilled hole in a linear elastic half-plane. The soil displacements for three different convergence patterns are presented and compared. It is shown that the surface settlement trough will become flatter and wider when the lining moves upwards; the horizontal displacements are more concentrated in the region below the lining; and the region influenced by displacements is wider. Most calculated settlement troughs can be well represented by Gaussian curves with simple parameters, but the obtained width parameters are larger than the traditional empirical values. The rigorous solution can be used as a simple tool to understand the fundamental mechanism of the lining buoyancy problem and as a benchmark for numerical procedures based on more sophisticated models. The importance of buoyancy effect on the displacement field should be taken into account.     

地震荷载作用下顺层岩体边坡变形特征分析

应用二维离散元程序UDEC计算了地震荷载作用下边坡的位移,并将计算结果与Newmark法计算结果及震后现场实测值进行了对比。结果表明,Newmark法计算得到的位移值较实测值偏小,离散元计算得到的位移结果较Newmark法更接近于实测值。在此基础上,初步分析了地震荷载作用下坡高、坡角、岩层倾角等因素对顺层岩体边坡位移的影响规律。由分析结果可知,地震荷载下顺层岩体边坡的位移并不随坡高增加而单调增大,在坡高约100 m时位移达到最大值,坡高超高100 m位移反而有所降低;当坡高超高200 m后,位移随坡高的变化幅度不大,顺层岩体边坡的位移随坡角增加而单调增大。随岩层倾角增加边坡位移明显增大;当岩层倾角大于层面内摩擦角时,随着岩层倾角的增大,边坡变形增长幅度明显增大。     

简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析

研究了全空间饱和土体中圆形衬砌隧道在径向简谐点荷载作用下的三维动力响应,将衬砌用无限长圆柱壳来模拟,土体用Biot饱和多孔介质模型来模拟,引入两类势函数来表示土骨架的位移和孔隙水压力,并利用修正Bessel方程来求解各势函数,结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答,最后进行Fourier逆变换得到时间-空间域内的响应。通过算例分析了荷载振动频率和土体渗透性对土体和衬砌位移响应及土体孔压的影响。结果表明,饱和土体和弹性土体的位移响应具有明显区别。随着荷载频率的增大,土体和隧道位移幅值减小,土体孔压幅值增大;随着土体渗透性增大,土体位移及孔压幅值减小。     

Semi‐analytical elastostatic analysis of unbounded two‐dimensional domains

Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd.     

A detailed investigation of block dynamic sliding by the discontinuous deformation analysis

An extensive examination of the discontinuous deformation analysis (DDA) in block dynamic sliding modeling is carried out in this paper. Theoretical solutions for a single block sliding on an arbitrarily inclined plane by applying the horizontal/vertical seismic loadings to the sliding block as acceleration time histories or to the base as constraint displacement time histories are derived. As compared with the theoretical solutions, for a single block sliding, the DDA predicts the sliding displacements and block interaction forces accurately under various base incline angles and friction angles under both the harmonic loadings and a real seismic loading. The vertical seismic component may influence the block sliding displacements to different extent, and the DDA can capture these phenomena successfully and give accurate results. For the calculation of the single block relative sliding, both the theoretical and the DDA solutions indicate that applying the seismic accelerations as constraint displacement time histories (derived by integrating the seismic accelerations twice) to the base is equivalent to applying the seismic accelerations as volume forces to the sliding block in the opposite directions. The DDA modeling also demonstrates that this conclusion still stands for the case of multi‐block sliding. Copyright © 2012 John Wiley & Sons, Ltd.     

堆载对既有桥墩桩基础影响距离分析

软土地基对外部环境的变化非常敏感,附近堆载对高速铁路既有桥墩基础可能产生重大影响,必须加以控制。以某高速铁路典型桥墩为例,建立三维有限元模型,分析了实际情况下堆载对桥墩变位的影响,其结果与实测数据吻合良好;然后变化堆载与桥墩之间的距离,详细地分析了不同距离下堆载对桥墩群桩基础的内力和变位的影响。结果表明:堆载与既有桥墩的距离越远,堆载对桥墩桩基础的内力和变位的影响越小。当堆载距离d小于软土层厚度h的4倍时,随d/h的增加,桥墩水平变位下降迅速;当d/h＞4时,随d/h的增加,桥墩水平变位下降缓慢。堆载与桥墩之间的控制距离取决于堆载规模、软土厚度和埋深、桥梁上部结构正常工作条件下所能容许的最大水平变位。     

Seismic Analysis of Shear-Wall Structures with Vertically Installed Dampers

Theapplicationofreinforcedconcrete(RC)shear wallbuildingsisquitecommoninseismicare as.Shearwalls,withlargerigidityandhigh strength,aretheprimarymembersforresistinghori zontalloadsinbuildingstructures.Butunderthe forceofasevereearthquake,shearwallsareprone…     

Computing Displacements in Transversely Isotropic Rocks Using Influence Charts

Summary  This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z=0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.