层状地基上弹性地基梁的有限元-边界元耦合分析

将地基视为多层各向同性弹性体,对Euler-Bernoulli梁进行有限单元离散分析,对地基-梁接触面采用边界积分法求解,根据地基-梁接触面的竖向位移协调和光滑接触条件,应用有限元与边界元耦合的方法推导出各向同性成层弹性地基上的Euler-Bernoulli梁的半数值半解析解。基于文中理论,编制了相应的程序,通过与现有文献对比,验证了文中理论的正确性,对比分析了分层地基与等效均匀地基两种模型上的弹性地基梁。研究结果表明,分层地基与等效均匀地基两种模型上弹性地基梁性状差异较大,实际弹性地基梁计算中应采用分层地基模型。     

Transverse seismic kinematics of single piles by a modified Vlasov model

Within the framework of soil–pile interaction, a novel displacement scheme for the transverse kinematic response of single piles to vertically propagating S waves is proposed on the basis of the modified Vlasov foundation model. The displacement model contains a displacement function along the pile axis and an attenuation function along the radial direction. The governing equations and boundary conditions of the two undetermined functions are obtained in a coupled form by using Hamilton's principle. An iterative algorithm is adopted to decouple and solve the two unknown functions. In light of the governing equation of the pile kinematics, a mechanical model is proposed to evaluate the present method on a physical basis considering material damping. The coefficient of the equivalent Winkler spring is derived explicitly as function of the displacement decay parameter γ and soil Poisson's ratio. A parametric study is performed to investigate the effects of the soil–pile system properties on the kinematic response of single piles. The results show that the dimensionless pile length controls the transverse kinematics of piles. In terms of the theory of beams on elastic foundation, the classification limits of the dimensionless pile length may be π ∕ 4 and π, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

Response of Euler–Bernoulli beam on spatially random elastic soil

A new method is developed for analysis of flexible foundations (beams) on spatially random elastic soil. The elastic soil underneath the beams is treated as a continuum, characterized by spatially random Young’s modulus and constant Poisson’s ratio. The randomness of the soil Young’s modulus is modeled using a two-dimensional non-Gaussian, homogeneous random field. The beam geometry and Young’s modulus are assumed to be deterministic. The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics. The differential equations are solved using the finite element and finite difference methods to obtain the beam and soil displacements. Four different beam lengths, representing moderately short, moderately long and long beams are analyzed for beam deflection, differential settlement, bending moment and beam shear force. The statistics of the beam responses are investigated using Monte Carlo simulations for different beam-soil modulus ratios and for different variances and scales of fluctuations of the soil Young’s modulus. Suggestions regarding the use of the analysis in design are made. A novelty in the analysis is that the two-dimensional random heterogeneity of soil is taken into account without the use of traditional two-dimensional numerical methods, which makes the new approach computationally efficient.     

线性分布基床系数弹性地基梁有限单元法改进

弹性地基梁法常用于研究土和结构的相互作用,对于均布荷载和边界条件简单的弹地基梁,采用理论解即可方便地进行计算。侧向荷载作用下桩体、嵌入式挡墙一般根据弹性地基梁理论进行分析,并假定基床系数随深度增加。对于基床系数呈线性分布或呈均匀分布但边界条件复杂的弹性地基梁理论求解困难,通常采用有限差分法或有限单元法近似求解。采用有限单元法计算线性分布基床系数弹性地基梁时,若单元划分数量不够,就存在计算精度不足的问题。采用加权余量法推导了更为精确的2节点5次位移函数和相应的单刚矩阵,得出了线性分布荷载作用下挠度的5次多项式近似解,从而实现只需划分很少的单元数,节点位移及单元内位移的分布即可达到较高的计算精度,极大地提高了计算效率,单元内力的分布可直接由位移函数导出,简化了后处理计算程序。     

弹性地基中厚板弯曲问题的无网格LRPIM分析

无网格局部径向点插值方法（LRPIM）的形状函数具有Kronecker delta函数的特性,便于施加位移边界条件,不需要进行特殊地处理。采用局部加权残值法推导了双参数弹性地基中厚板的离散系统方程,利用无网格LRPIM对四边简支和四边固支以及筏式双参数弹性地基中厚板的弯曲问题进行了分析和计算。算例表明,用无网格LRPIM分析弹性地基中厚板问题具有非常灵活和易于实现等优点。     

变基床系数弹性地基梁解法及其应用

从实测的P-S曲线（基地压力与沉降的关系）出发,将P-S曲线拟合成分段线性函数,把分段线性函数的斜率作为基床系数,推导出变基床系数弹性地基梁的基本理论方程式,并将它变换成与常基床系数弹性地基梁相同的方程形式,从而,可以用初参数法解出它的一般解。此方法可以推广到变截面梁和非均质地基的情况。     

非线性弹性地基上矩形薄板的主参数共振

分析非线性弹性地基上受参数激励小挠度矩形薄板的主参数共振问题,由冯卡门方程和伽辽金方法得到系统的非线性振动方程,它是杜分-马休型方程,应用非线性振动的多尺度法得到平均方程。数值计算结果表明：阻尼系数、地基系数、几何参数对主参数共振曲线影响明显。     

桩基承台梁受力分析的幂级数解答

将桩基承台梁视为置于弹性地基上的有限长梁,将竖向桩体及承台梁下桩间土体视为刚度不同的弹簧系列,基于Winkler弹性地基梁理论,推导出考虑桩土共同工作的承台梁竖向位移控制微分方程,并给出其幂级数半解析解,进而导得了在集中荷载、外加弯矩及分布荷载共同作用下桩基承台梁的竖向位移、转角、弯矩及剪力的计算公式。最后通过与链杆法、Newmark法的比较,验证了本文幂级数解答的正确性。在此基础上,探讨分析了基桩差异性、承台梁下土体作用、桩径及荷载形式等因素对桩基承台梁受力变形的影响。研究表明：当考虑上述因素影响时,桩基承台梁的竖向变形、弯矩及桩顶反力均发生不同程度的变化,因此,在实际的设计计算中应予以考虑。     

Analysis of beams on tensionless reinforced granular fill‐soil system

In this paper, a beam subjected to end concentrated loads has been modeled and analyzed to estimate its flexural response. The beam has been assumed to rest on reinforced earth beds with reinforcing elements having some finite bending stiffness. The reinforcing elements have been idealized as beams with smooth surface characteristics. The foundation system has been assumed to react only in compression (tensionless foundation), i.e. the separation between the upper beam and the ground surface has been taken into consideration. Winkler springs of different stiffnesses have been used to idealize the upper dense and lower poor soils. As the analysis considers the separation between the upper beam and the soil, the weight of the upper beam has been taken into account. The governing differential equations have been derived and presented in a non‐dimensional form. These equations have been solved using finite difference method with the help of appropriate boundary and continuity conditions. The response of the foundation system has been compared with the case when the beam is in perfect contact with the ground surface. The parametric study shows that the response of the model is greatly affected by the length ratio of beams, ratio of stiffness of upper and lower soil layers, ratio of flexural rigidity of upper and lower beams and weight of the upper foundation beam. Copyright © 2008 John Wiley & Sons, Ltd.     

加固膨胀土路堑边坡中框架梁的内力计算

锚杆框架梁是一种较好的加固膨胀土路堑边坡方式,但其设计理论依据仍不统一,未形成成熟的规范,多依靠工程经验。Winkler地基梁和半无限弹性体理论被用来计算框架梁的内力,在Winkler假设的前提下,着重分析了现浇梁和预制梁在不同长度条件下的内力分布。结果表明：框架梁的设计完全依据膨胀力是欠合理的,建议采用Winkler地基梁和半无限弹性体理论计算框架梁的内力,并结合工程实例,提出了相关的建议。     

Adaptive analysis of infinite beams dynamics problems using the periodic configuration update method in the time domain

This paper proposes a new approach for the assessment of the dynamic response of continuously supported infinite beams under high‐speed moving loads. A change in the representation of equations of motion in the dynamics of discrete structures is proposed to obtain an improved accuracy of the numerical integration in the time domain. The proposed numerical method called the “periodic configuration update” or “PCU method” is applied to solve the problem of a vertical moving harmonic load on an infinite classical Euler‐Bernoulli beam resting on a continuous viscoelastic foundation. This study shows the superiority of the proposed method in comparison with other methods presented in the literature that suffer from the material time derivative, i.e., convective terms, that arises from the Galilean transformation. To confront this numerical problem, the PCU method retains the principle of the spatial follow of loads while zeroing the relative velocity with the traversed beam via a step‐by‐step adaptive integration of the equation of structural dynamics. The dynamic load is modeled with high theoretical velocities that can reach the critical velocity of the studied beam with different angular frequencies belonging to moderate frequency range. A parametric study is carried out to analyze the influence of key parameters on the convergence. The obtained results show a high efficiency of the PCU method for solving these types of problems relative to the dynamics of high speed trains/tracks.     

Beams on nonlinear winkler foundation with gaps

The analysis of beams on a Winkler foundation is very common in engineering. In many practical problems nonlinear foundation behavior should be considered. In some cases a gap may exist between the beam and the nonlinear foundation. Based on an exact solution for a finite beam on linear elastic foundation, an iterative procedure for a piecewise linear foundation is formulated. The approach is implemented in a continuous beam computer program and demonstrated in numerical examples.     

框架式预应力锚固系统分阶段可靠性分析

将框架梁在张拉阶段或工作阶段时纵梁与横梁的破坏、梁的正截面与斜截面的破坏以及锚杆的破坏等主要失效模式视为串联系统,提出了框架预应力锚索的分阶段系统可靠性计算模型。在张拉阶段,将锚索力按照位移协调和静力平衡的原则分配在纵、横梁上,然后按Winkler弹性地基梁模型分别计算单片梁的内力;在工作阶段,将侧向土压力系数视为随机变量,框架梁视为土压力作用下的简支梁来计算其内力。基于各失效模式功能函数之间的相关系数矩阵,导出了预应力锚索框架的系统可靠性计算方法并编制了计算程序。对某工程实例的计算结果表明,预应力锚索框架的失效概率主要由纵梁在工作阶段和张拉阶段的正截面失效概率及锚杆的失效概率三者共同决定,而假设此3种失效模式相互独立的系统失效概率与考虑失效模式相关性的系统失效概率误差为8.1%。     

Calculation of the Internal Forces and Numerical Simulation of the Anchor Frame Beam Strengthening Expansive Soil Slope

Anchor frame beam is an excellent method for strengthening the expansive soil cut slope. It can effectively prevent cracks and fissures of expansive soil slope from expanding. There are plentiful engineering experiences that are important for the design of anchor frame beam. However its design theory is still not uniform and there is not any code to be followed. The assumption of Winkler foundation beam and semi-infinite elastic theory are used for calculating the internal forces of the frame beams. At the meantime FLAC^3D software is used for simulating anchor frame beam strengthening expansive soil cut slope. Main parameters, such as length, range interval and angle of the anchor, are researched so as to acquire how to influence slope deformation. The internal force distributing of different length beams is analyzed. The results indicate that it is absurd to design frame beams just by expansive force. It is suggested that the internal forces of pre-cast and cast-in-place beams be calculated with Winkler foundation beam and semi-infinite elastic theory. The numerical results show that ratio of slope has an impact on the slope deformation, and that the angle and the range interval of the two neighboring anchors influence the slope deformation. The pertinent proposal for designing frame beam is offered based on an actual project so as to optimize the design.     

基于初参数法的多心圆拱隧道衬砌结构内力与变位求解

基于初参数解析方法的原理,建立了混凝土衬砌弹性地基圆弧曲梁内力和变位求解的初参数矩阵方程。对于多心圆拱隧道衬砌结构,利用曲梁初参数矩阵方程,以及结构的对称性和圆拱弧段交接点处内力平衡和变位协调条件,求解出了矩阵方程中初参数值,可进一步应用初参数矩阵方程求解圆拱弧段各点的内力与变位值。实例计算表明,其解析思想是可行有效的,可为类似衬砌结构设计提供一条可靠的内力分析途径。     

间断伽辽金法(DGM)求解弹性地基梁问题

间断伽辽金法使用节点位移一类未知数作为测试函数,削弱了内部单元边界上的一阶及n阶导数的连续性,大大降低了构造形函数的难度,特别适合控制方程为高阶微分方程问题的求解。基于间断伽辽金法的基本原理,推导了弹性地基梁四阶微分控制方程的积分“弱”形式,编制了计算程序,进行了数值计算和收敛性分析。计算结果表明：用间断伽辽金法求解弹性地基梁问题是十分有效率的。     

瑞利波在非均匀饱和地基中的传播特性

考虑地基横观各向同性和非均匀性,建立孔隙率、密度、剪切模量及渗透系数同时随深度变化的非均匀饱和地基模型,模型中考虑参数间的耦连影响,并引入非均匀因子表征地基的不均匀程度。基于Biot多孔介质理论建立以土骨架位移和孔隙水压力为基本未知量的控制方程,采用微分算子法对控制方程进行解耦求解,推导出非均匀饱和地基中瑞利波的频散方程。将推导结果分别退化到均匀饱和地基和单一弹性地基,验证了结果的正确性。通过数值算例,对非均匀饱和地基中瑞利波的传播速度、衰减系数及位移分布进行分析。结果表明：在低频区,饱和地基的非均匀性对瑞利波传播速度、衰减和位移都有显著影响,质点运动轨迹也由此发生变化;随着频率的升高,这种影响逐渐减小,当频率趋于无穷大时,瑞利波速度收敛于弹性地基中的波速;地基非均匀性增大了瑞利波的传播阻抗性,瑞利波位移加速衰减,传播深度小于均匀饱和地基。随着非均匀性增大,质点竖向位移的衰减快于水平位移,这种差异造成质点椭圆运动轨迹的扁率减小。此外,地基中非均匀土层厚度越小,则地基非均匀程度越高,对瑞利波的传播影响越大。     

某电厂工程场址地质灾害防治工程研究

建设工程场址紧邻某露天矿北采坑,最近距离不足10 m,且在场址地基中连续分布厚1.5～3.0m软弱夹层,该软弱夹层南倾并出露于露天采坑边坡,与采坑边坡构成顺向坡.因该场址所处周边环境的特殊性以及特定的地层结构,使得本工程可能遭受场地整体滑移、边坡滑动等地质灾害威胁,且危害后果严重.对场址地基整体稳定性验算与采坑边坡稳定性的计算表明：场址地基整体稳定性可满足规范要求,而采坑高边坡则处于不稳定状态,必须进行工程加固.综合考虑本场区地层结构、周边环境与危害后果等,提出了削坡减载十预应力格构锚固主体加固方案,同时辅以截排水与工程监测措施.依据锚固段岩土体力学特性,确定了各锚杆锚固力,采用Winkler弹性地基梁和连续梁模型计算了格构梁的内力.对削坡、锚固后边坡的稳定性验算表明：其安全稳定性可满足规范要求.     

基坑悬臂支护桩双参数弹性地基杆系有限元法

对地基抗力双参数法在基坑悬臂支护桩位移和内力计算方面进行了探讨,即采用地基土抗力系数随深度按双参数非线性变化的假设,以弹性地基杆系单元模拟,支护桩则按弹性梁单元模拟。对某基坑悬臂支护桩进行数值模拟反分析表明,通过试算调整可获得适合于实际设计计算的地基抗力双参数,该法应用到福州市某基坑悬臂桩的实际分析和设计中获得了较为满意的结果,可供悬臂支护桩设计计算时参考。