墙下条形基础与层状横观各向同性地基共同作用

运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶（Fourier）变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比（Jacobi）正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。     

弹性矩形板下横观各向同性多层地基分析

利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型     

双参数地基上弹性板的动力分析

采用双参数地基模型和基于Mindlin板理论的8节点等参单元,根据Hamilton变分原理,推导了弹性地基上弹性板动力分析的有限元公式,将地基效应和板面质量分布归并到板的刚度矩阵和质量矩阵中,采用边界元法考虑板域外地基变形的影响。分析了四边自由矩形板的自由振动和强迫振动,计算的自由振动固有频率与实测结果相近,发生共振时板的强迫振动动力响应达到峰值,在给定的阻尼比条件下,无阻尼的稳态响应与有阻尼的稳态响应趋于相同,阻尼能够显著降低板的共振响应。     

弹性地基板的分析简化模型

将弹性半空间地基受任意竖向荷载作用下的静力位移积分变换解与弹性半空间地基上四边自由矩形板受任意竖向荷载作用的弯曲解析解相结合,建立了求解板下地基位移的方法。对一些算例进行大量数值计算分析,得出弹性半空间地基上四边自由矩形板板下地基水平位移和竖向位移的分布规律;并基于该位移分布规律,提出地基位移沿深度按一定的函数关系变化的假设,考虑板下地基水平位移,利用板地基系统的总势能最小原理,通过复杂的变分运算,得出弹性地基板的简化模型。在不考虑板下地基水平位移时,该模型退化成双参数地基模型,并给出了求解其上四边自由矩形板的近似边界条件。     

盾构衬砌管片接头力学分析及双直线刚度模型研究

盾构管片接头弯曲刚度K? 是盾构衬砌结构计算中的一个重要参数。根据管片接头构造特征,在传力衬垫和弹性密封橡胶试验资料的基础上,对管片接头进行受力分析,得到管片接头弯曲刚度与接头内力的非线性关系。为了应用方便,建立了实用的管片接头弯曲刚度的双直线模型。该接头刚度模型为梁-弹簧模型法和修正惯用法中的关键参数确定提供了基础,管片的内力计算也更加合理。     

流变性软土地基模型的时效性分析与刚度计算

建立了线性粘弹性半空间地基模型,并给出了地基柔度矩阵和刚度矩阵的计算公式。文中以上海香港广场北块地库深基坑工程为例,对基坑围护结构的变形和内力,将原设计的理论计算值、实测值与本文采用时效性地坛模型的理论计算值进行了对比分析。结果表明,时效性地基模型的理论计算值与实测值较吻合,反映出该地基模型在流变性软土地落中对基坑围护结构的变形和受力分析具有较好的适用性。     

层状横观各向同性地基平面应变问题的扩展精细积分解

利用扩展精细积分法求解横观各向同性地基的平面应变问题。扩展精细积分法具有高精度和较高计算效率的特点,是求解微分方程的有效方法,相比于解析法可以节省大量理论推导工作量。从直角坐标下弹性力学控制方程出发,推导出Fourier变换域内地基的常微分矩阵方程;之后对地基微层元进行消元合并,进一步得到荷载作用在地基内部时层状地基的扩展精细积解。与已有文献的对比验证了方法的精确性,并分析了横观各向同性参数、层状性质和荷载作用点对计算结果的影响。结果表明：土体竖向位移随着横观各向同性参数n的增大而减小,而随着横观各向同性参数m的增大而增大;荷载作用点 的变化只对作用点以上的土体有影响,而上层土体的模量对竖向位移计算结果的影响更为显著,土体成层性对沉降的影响要比对竖向应力的影响更为显著。     

层状地基中地铁施工垂直穿越既有管道变形分析:耦合方法与两阶段方法对比

地铁施工引起的临近既有管道变形是城市轨道交通建设中较为关心的施工问题。目前,针对该领域的研究一般假定地基土体均质,而没有考虑地基的自然成层性,此外大多没有考虑既有管道变形与土体自由位移场相互作用的耦合效应。为此,基于弹性层状半空间地基模型,针对隧道开挖边界引入非均匀收敛变形径向土体位移移动模式,提出了层状地基中地铁施工垂直穿越既有管道变形的耦合分析方法和两阶段分析方法,并进行了算例对比和参数分析。结果表明:耦合方法在分析非均质层状地基时具有较好的计算精度,其精度要高于基于Loganathan和Poulos公式的两阶段方法;同时,地基土体的成层性对既有地下构筑物的变形性能具有较大影响。研究成果可为合理制定城市地铁施工对周围环境影响的保护措施提供一定的理论依据。     

隧道开挖条件下地埋管线的非线性响应分析

隧道开挖引起的地层不均匀沉降造成附近的地埋管线产生额外的变形,甚至破坏。被动管线与土体的相互作用的研究表明,不考虑土体的刚度衰减,较大的土体弹性模量使得管线的最大弯矩计算结果过大,偏于保守,造成不必要的浪费。在被动管线Winkler地基模型分析基础上,引入土体刚度衰减模型考虑土体非线性特性,提出了隧道开挖作用下管线响应的等效线性分析方法。基于自由土体位移场计算管周土体由于隧道开挖引起的附加应变,基于水平受荷桩的环状弹性介质模型考虑由于管土相互作用引起的管周土体应变,从而对被动Winkler地基模型的土体弹性参数进行修正,计算得到管线的最大弯矩。通过与现有的弹性理论方法、离心模型试验结果的对比,验证了针对隧道开挖引起的被动管土相互作用问题,该方法考虑土体非线性特性的合理性。     

基础板厚度对减小不均匀沉降的算例分析

对弹性地基上不同刚度的基础板,利用弹性地基上梁的计算方法进行了不同集中荷载工况下的变形计算。根据计算结果,分析了基础刚度对于弹性地基上基础的最大沉降的影响以及刚度对于基础整体变形的影响。     

Analytical layer element solutions for deformations of transversely isotropic multilayered elastic media under nonaxisymmetric loading

This paper presents the analytical layer element solutions for deformations of transversely isotropic elastic media subjected to nonaxisymmetric loading at an arbitrary depth. The state vectors for the nonaxisymmetric problem are deduced through the substitution of the Hu Hai‐chang solutions into the basic equations for the transversely isotropic elastic media. From the state vectors, the analytical layer element of a single layer is obtained in the Hankel transformed domain. The analytical layer element is an exact and symmetric stiffness matrix whose elements are without positive exponential functions, which can not only simplify the calculation but also improve the stability of computation. On the basis of the continuity conditions between adjacent layers, the global stiffness matrix is obtained by assembling the interrelated layer elements. The solutions for the multilayered elastic media in the transformed domain are obtained by solving the algebraic equation of the global stiffness matrix, which satisfies the boundary conditions. The actual solutions in the physical domain are further obtained by inverting the Hankel transform. Finally, some cases are analyzed to verify the solutions and evaluate the influences of the transversely isotropic character and stratified character of the media on the load–displacement responses. The numerical results show that the variations of the elastic properties between layers have a great effect on the displacements of the multilayered media. Copyright © 2014 John Wiley & Sons, Ltd.     

基于传递-反射矩阵法的层状公路结构动力响应研究

利用传递-反射矩阵方法和叠加原理推导了双轮胎振动荷载作用下弹性层状公路结构的动力响应解,并利用Hankel数值逆变换技术进行了数值求解。弹性层状结构的传递-反射矩阵同时具有单个矩阵尺寸小、矩阵元素只含有负指数项2个优点,计算结果不受土层单元厚度与荷载频率大小的影响,可以大幅提高计算效率和精度。通过将数值计算与室内模型试验结果进行比较,验证了方法的正确性。在此基础上,分析了面层厚度及模量对层状公路结构动应力、动位移的影响程度和规律,得出了一些有意义的结论。研究结果可为公路路面、路基结构设计提供参考。     

An intergranular strain concept for material models formulated as rate equations

The intergranular strain concept was originally developed to capture the small-strain behaviour of the soil with hypoplastic models. A change of the deformation direction leads to an increase of the material stiffness. To obtain elastic behaviour for smallstrains, only the elastic part of the material stiffness matrix is used. Two different approaches for an application of this concept to nonhypoplastic models are presented in this article. These approaches differ in the determination of the elastic stress response, which is used for reversible deformations. The first approach determines an elastic response from the original material model, and the second one uses an additional elastic model. Both approaches are applied on barodesy. The simulations are compared with experimental results and with simulations using hypoplastic models with the original intergranular strain concept.     

Analytical solution of the harmonic waves diffraction by a cylindrical lined cavity in poroelastic saturated medium

This paper presents a model for the analysis of plane waves diffraction at a cavity in an infinite homogeneous poroelastic saturated medium, lined by a lining composed of four equal segments. An elastic boundary layer is placed between the cavity lining and the infinite porous medium. The boundary layer is simulated by ‘elastic boundary conditions’ in which the bulk matrix stress is proportional to the relative displacement between the lining and the surrounding medium matrix boundary. In addition, fluid impermeability through the intermediate layer is assumed. For the frequencies, that differ from the pseudoresonanse frequencies, the problem was reduced to the problem of an ideal elastic medium. A closed‐form analytical solution of the problem was obtained using Fourier–Bessel series, the convergence of which was proven. It was shown that the number of series terms required to obtain a desired level of accuracy can be determined in advance. The influence of the medium porosity on the medium dynamic stress concentration was studied. Copyright © 2006 John Wiley & Sons, Ltd.     

A continuum model of layered rock masses with non-associative joint plasticity

Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd.     

六面体有限覆盖的三维数值流形方法的非线性分析

对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变 模型和 模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。     

Development of the distinct lattice spring model for large deformation analyses

This study develops the distinct lattice spring model (DLSM) for geometrically nonlinear large deformation problems. The formulation of a spring bond deformation under a large deformation is derived under the Lagrange framework using polar decomposition. The results reveal that the DLSM's stiffness matrix under small deformations is the tangent stiffness matrix of the DLSM under large deformations. The formulation of the spring bond internal force under a given configuration is also presented and can be used to calculate the unbalanced force. Using these formulations, three nonlinear solving methods (the Euler method, modified Euler method, and Newton method) are developed for the DLSM with which to tackle large deformation problems. To investigate the performance of the developed model, three numerical examples involving large deformations are presented, the results of which are also in good agreement with the analytical and finite element method solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

传递矩阵法求解弹性半空间单一覆盖层轴对称动力问题的误差分析

为解决弹性半空间单一覆盖层轴对称动力问题中传递矩阵病态的问题,提出了误差分析方法。分3种情况讨论了采用传递矩阵法计算弹性半空间单一覆盖层轴对称动力问题中被积函数处理方法,进而对逆Hankel变换和逆Laplace变换的处理方法进行了简要说明,据此提出了减小误差的方法。通过退化模型对所提出的方法进行了验证,结果表明该方法可有效减小误差,为利用传递矩阵法求解层状半空间动力问题中传递矩阵病态的问题提供了思路。     

列车荷载下上覆弹性层横观各向同性饱和地基的动力响应

基于Biot多孔弹性介质的波动理论,构造了轨道、道碴、枕木及弹性层的横观各向同性饱和地基在列车荷载下的动力计算模型。利用Fourier变换,得到了列车荷载作用下横观各向同性软土地基上弹性层动力响应的解析结果。利用离散Fourier逆变换得到数值计算结果,分析了荷载速度、地基的各向异性参数、弹性层刚度系数及厚度对位移和孔压响应的影响。分析结果表明：弹性层对控制地基振动作用显著,地表振动幅值随荷载速度的增加而增大,软土的横向弹性模量对地表振动及土中孔压有较大影响。