A theoretical estimate of the tilt of a surface foundation due to an inclined anchor load applied at the interior of the soil medium

This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.     

Rigid Foundations Resting on an Elastic Layered Soil

A rigid foundation of arbitrary shape resting on a stratified half space (soil), with specific geometrical and elastic properties for its horizontal layers, is examined under the action of a vertical load placed anywhere on the foundation area. On the basis of a purely analytical treatment of the deformability of the soil surface, i.e. without using a finite element discretization of the layered soil mass, a general method is developed in order to determine the contact soil pressures and the resulting settlements through an easily implemented numerical procedure. The possible presence of “inactive” foundation parts not being in contact with the soil surface is taken into account. Parametric studies are performed showing the influence of the variability of the soil layers, as well as of the vertical load location, on the contact pressures developed. In this context, for the cases of a rectangular and a circular foundation the area borders for the location of a vertical load are determined, either for the development of compressive soil pressures all over the footing (core), or for allowing the existence of some inactive part without contact with the soil (zero contact pressure), not exceeding the half of the total foundation surface (limit core).     

Vertical deformation of rigid foundations of arbitrary shape on layered soil media

A numerical procedure is described for the analysis of vertical deformation of smooth, rigid foundations of arbitrary shape on homogeneous and layered soil media. The contact area at the interface of the foundation and soil medium is approximated by square subdivisions. The response of the system is then obtained from the superposition of the influence of the individual subdivisions. The flexibility influence coefficients are based on equivalent smooth, rigid circular areas with the same contact area as the square subdivisions. For foundations on a homogeneous, isotropic elastic half-space, the flexibility coefficients are given analytically by the integrated forms of the Boussinesq's solution. For a layered soil medium, the flexibility coefficients are determined from an axisymmetric finite element analysis which is essentially two dimensional. Thus, there is no necessity for a full three-dimensional finite element analysis. Comparison with solutions obtained using the integral transform technique for smooth, rigid rectangular foundations on a homogeneous, isotropic elastic half-space shows good agreement. Parametric solutions are presented for the response of rectangular foundations on some ‘typical’ soil profiles. The use of a simplified method to estimate the settlement of rectangular foundations on a layered soil medium by superposing solutions for homogeneous, elastic strata is discussed.     

The eccentric loading of a rigid circular foundation embedded in an isotropic elastic medium

This paper examines the problem of the eccentric loading of a rigid circular disc-shaped foundation embedded in bonded contact with an istropic elastic medium of infinite extent. The solution of this problem is achieved by using a Hankel integral transform technique which reduces the problem to two sets of dual integral equations. These systems of dual integral equations represent the equations which govern the axisymmetric and asymmetric states of deformation induced by the loaded foundation. Explicit results are derived both for the displacement and rotation of the circular foundation and for the contact stress at the interface.     

THE SETTLEMENT OF A RIGID CIRCULAR FOUNDATION RESTING ON A HALF-SPACE EXHIBITING A NEAR SURFACE ELASTIC NON-HOMOGENEITY

The present paper examines the elastostatic problem pertaining to the axisymmetric loading of a rigid circular foundation resting on the surface of a non-homogeneous elastic half-space. The non-homogeneity corresponds to a depth variation in the linear elastic shear modulus according to the exponential form G(z)=G₁+G₂e^-ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The mixed boundary value problem associated with the indentation of the half-space by the rigid circular foundation is reduced to a Fredholm integral equation which is solved via a numerical technique. The numerical results presented in the paper illustrate the influence of the near-surface elastic non-homogeneity on the settlement of the foundation.     

油罐基础不均匀沉降主要影响因素的敏感性分析

在上部均布荷载作用下柔性基础基底压力是均匀分布的,基底以下土体在同一深度附加应力呈现中间大、周围小的分布规律,导致基础沉降中间大、周围小。刚性基础的沉降是均匀的,必然导致基底压力的分布为周围大、中间小。软基上的油罐筏板基础是具有一定刚度的基础,但并非刚性基础,因而基底压力分布应该介于柔性基础和刚性基础之间,沉降为中间大、周围小的不均匀分布。基于ABAQUS有限元分析,结合工程实际情况,采用UH模型作为土体本构模型进行了模拟分析,对筏板厚度、地基刚度等影响基础不均匀沉降的主要因素进行敏感性分析,探求变刚度地基在油罐基础不均匀沉降中的影响规律。     

多向荷载作用下层状地基刚性桩筏基础分析

提出一种多向荷载作用下层状地基中刚性桩筏基础的计算方法。基于剪切位移法,采用传递矩阵形式分析了竖向荷载下桩顶面-桩顶面相互作用;引入修正桩侧地基模量,采用有限差分法分析了水平荷载下桩顶面-桩顶面相互作用;基于层状弹性半空间理论,分析了多向荷载下桩顶面-土表面、土表面-桩顶面、土表面-土表面的相互作用关系。建立了桩土体系柔度矩阵,得到了多向荷载下层状地基中刚性桩筏基础的受力和变形的关系以及桩的内力和变形沿桩身分布规律。通过与有限元对比,验证了该方法的合理性和修正地基模量的优越性,并对多向荷载作用下的桩筏基础进行了计算分析,计算结果表明,水平力将会引起桩筏基础的倾斜。     

Analytical solutions for Euler–Bernoulli beam on visco‐elastic foundation subjected to moving load

Analytical solutions for the steady‐state response of an infinite beam resting on a visco‐elastic foundation and subjected to a concentrated load moving with a constant velocity are developed in this paper. The beam responses investigated are deflection, bending moment, shear force and contact pressure. The mechanical resistance of the foundation is modeled using two parameters k_s and t_s — k_s accounts for soil resistance due to compressive strains in the soil and t_s accounts for the resistance due to shear strains. Since this model represents the ground behavior more accurately than the Winkler spring model, the developed solutions produce beam responses that are closer to reality than those obtained using the existing solutions for Winkler model. The dynamic beam responses depend on the damping present in the system and on the velocity of the moving load. Based on the study, dynamic amplification curves are developed for beam deflection. Such amplification curves for deflection, bending moment, shear force and contact pressure can be developed for any beam‐foundation system and can be used in design. Copyright © 2012 John Wiley & Sons, Ltd.     

The behaviour of an elastic non-homogeneous half-space. Part II–circular and strip footings

Solutions developed in the first part of this paper (i.e. describing the response of a non-homogeneous half-space subjected to surface point and line loads) are used in this part to obtain solutions for a variety of surface loadings. Consideration is given to a distributed load acting over a circular area or strip and a rigid disk or strip subjected to applied normal load and moment. It is established that the profiles of surface settlement due to uniformly distributed loads acting over a strip or circular area are strongly dependent on the degree of non-homogeneity. This dependency is reduced when the footing is rigid. When α = 1 the moduli variation is identical to the Gibson soil and the equivalence with the Winkler soil model is established.     

带帽刚性桩复合地基荷载传递机理研究

为了研究带帽刚性桩复合地基荷载传递机理,基于弹性理论和合理假定,采用荷载传递函数法,建立了带帽刚性桩复合地基中桩体沉降及其轴向应力、桩帽下土体竖向位移及其竖向应力、桩帽间土体竖向位移及其竖向应力、桩身侧摩阻力、桩帽边缘土体之间的侧摩阻力与荷载水平、深度之间的控制微分方程。采用微分方程的近似解法,推导出相应地解析表达式。利用桩体荷载沉降关系作为已知条件进行求解,计算结果能够反映带帽刚性桩复合地基荷载传递的一般力学性状规律。     

刚-柔性桩复合地基中刚性桩和自由状态下刚性桩性能比较

刚-柔性桩复合地基中刚性桩的荷载传递规律及变形性状明显不同于自由状态下的单桩,由于复合地基中刚性桩、柔性桩、土的互相作用,桩的工作性状要复杂得多。为了比较两者的承载变形特性,在温州地区进行同根桩在不同状态下静荷载对比试验,在静荷载试验过程中同步检测桩身应力情况,结合测试数据对桩沉降特性、荷载传递机理、压缩量特性进行了分析,分析结果对工程设计施工有一定的借鉴价值。     

含圆柱形弹性夹杂地基沉降量的解析解

研究各向同性地基中含一个圆柱形弹性夹杂的地基沉陷问题。考虑全场的应力、变形特征,运用复变函数的罗朗级数展开技术,构造合适的应力函数,结合夹杂的边界条件和无穷远的性态,获得了全场复势的解析表达。数值结果显示：由于两相材料剪切模量之比的不同,在某个范围内沉陷量大于基底中点沉陷;在这个范围之外,则小于基底中点沉陷。当夹杂埋深为夹杂半径的5倍以上时,就可以运用所得结果,而不致引起太大误差;含圆形隧洞和刚性夹杂的问题可作为特殊情况得到。     

The behaviour of an impermeable flexible raft on a deep layer of consolidating soil

Analytic solutions to the problem of the time-settlement behaviour of raft foundations have been limited in the past to flexible or rigid loadings, and have treated the foundation as being completely permeable. In this paper, solutions are presented for smooth circular rafts of any flexibility causing consolidation of a deep homogeneous clay layer, where the raft may be considered permeable or impermeable. Results for the time-dependent behaviour of contact stresses, pore pressures, raft displacements and moment in the raft are presented.     

Time‐dependent behaviour of a rigid foundation on a transversely isotropic soil layer

An analytical solution is presented in this paper to study the time‐dependent settlement behaviour of a rigid foundation resting on a transversely isotropic saturated soil layer. The governing equations for a transversely isotropic saturated soil, within Biot's poroelasticity framework, are solved by means of Laplace and Hankel transforms. The problem is subsequently formulated in the Laplace transform domain in terms of a set of dual integral equations that are further reduced to a Fredholm integral equation of the second kind and solved numerically. The developed analytical solution is validated via comparison with the existing analytical solution for an isotropic saturated soil case, and adopted as a benchmark to examine the sensitivities of the mesh refinement and the locations of truncation boundaries in the finite element simulations using ABAQUS. Particular attention is paid to the influences of the degree of soil anisotropy, boundary drainage condition, and the soil layer thickness on the consolidation settlement and contact stress of the rigid foundation. Copyright © 2009 John Wiley & Sons, Ltd.     

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。     

刚性桩复合地基沉降计算的简化方法

既简便又具有较好精度的刚性桩复合地基沉降计算方法仍是工程实践中迫切需要而又有待于解决的问题,文中提出了一个解决的简化方法。在刚性桩复合地基中,由于桩间土荷载水平不高,将桩间土荷载-沉降曲线近似为线性。当桩的荷载水平不高时,对桩的沉降可按线性考虑,线性关系可按线弹性方程计算得到。若桩可能进入非线性甚至塑性,则假设桩的荷载-沉降曲线满足双曲线规律,可较好地考虑桩的非线性沉降过程。通过计算单桩承载力特征值下的沉降,然后通过双曲线方程特点得到桩的非线性沉降方程。对于有单桩静载试验的情况,提出直接利用单桩试验曲线建立单桩的双曲线方程。最后依据共同作用时桩和桩间土的变形协调条件和静力平衡方程,即可计算其实际基础下复合地基的沉降,从而得到一个刚性桩复合地基沉降计算的简化方法。工程实例表明,简化是方法既简便又具有较好的精度,可为工程实践提供一个有效实用的计算方法。     

传递矩阵法分析中心集中荷载下圆形刚性板

采用传递矩阵法分析横观各向同性地基上的刚性圆板，分析竖向的弹性模量Ev、水平向的弹性模量Eh、竖直面上的剪切模量Gv以及Eh和Ev的比值n、Gv和Ev的比值m、水平向应力引起的正交水平向应变的泊松比Uh、竖直向应力引起的水平向应变的泊松比Uvh对沉降和基底反力影响；同时采用成层地基进行分析，将其计算结果与常规方法中采用对弹性模量和泊松在计算深度内按深度加权平均的计算结果进行比较。     

深置矩形基础与地基共同作用解析分析

基于集中力作用下的Mindlin解位移公式,推导得到均布荷载作用下的地基柔度系数,对地基上的四周自由板与地基共同作用进行简化计算,得出了考虑埋深时地基基础共同作用的解析公式。在基础板为刚性和弹性、荷载为集中荷载及均布荷载的情况下,对考虑埋深时的Mindlin解与不考虑埋深时的Boussinesq解的计算结果进行比较,表明,埋深比对于基础沉降、地基反力的分布、基础板的弯矩等都有一定的影响。给出了考虑埋深时的沉降修正系数公式,以供工程应用参考。     

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。