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。     

Linear and nonlinear vibration of non-uniform beams on two-parameter foundations using p-elements

A hierarchical finite element is presented for the geometrically nonlinear free and forced vibration of a non-uniform Timoshenko beam resting on a two-parameter foundation. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. With the enriching degrees of freedom, the accuracy of the computed results and the computational efficiency are greatly improved. The arc-length iterative method is used to solve the nonlinear eigenvalue equation. The computed results of linear and nonlinear vibration analyses show that the convergence of the proposed element is very fast with respect to the number of Legendre orthogonal polynomials used. Since the elastic foundation and the axial load applied at both ends of the beam affect the ratios of linear frequencies associated with the internal resonance, they influence the nonlinear vibration characteristics of the beam. The axial tensile stress of the beam in nonlinear vibration is investigated in this paper, and attention should be paid to the geometrically nonlinear vibration resulting in considerably large axial tensile stress in the beam.     

土与结构间接触面的非线性弹性-理想塑性模型及其应用

将非线性弹性理论与弹塑性理论相结合,对于土与结构间接触面提出了一种非线性弹性-理想塑性模型,用于模拟土与结构相互作用体系的变形与破坏机理。推导建立了这种接触面单元的应力-应变关系和弹塑性系数矩阵,并且讨论了这种模型在基坑开挖与支护分析应用中所面临的数值计算问题。最后针对某一基坑工程实例,应用这种接触面模型进行了数值计算与分析,结果表明,该模型能够较合理地模拟接触面上的变形机理与受力状态。     

Finite element modelling of thick plates on two‐parameter elastic foundation

This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two‐parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18‐node zero‐thickness isoparametric interface element interacting with a thick Reissner–Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C⁰ continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd.     

隧道开挖引起邻近单桩水平反应分析

隧道开挖会降低邻近桩基承载力,如何更为合理评价桩基水平附加响应是需要解决的问题。基于Pasternak双参数地基模型和三折线弹塑性荷载传递模型,采用两阶段分析法,并考虑侧向土体作用及地基土层的非均质特性,提出了更符合实际的单桩水平反应简化分析方法。通过与Winkler地基梁法及边界元法的对比分析,验证了方法的合理性。结合对单桩水平反应的多种影响因素进行参数分析,通过各因素相应的修正系数来对基准工况中单桩最大水平反应进行修正,得到计算工况中单桩的最大水平位移和最大弯矩。分析结果表明,桩基水平位移计算时可忽略侧向土体作用,而弯矩计算时应予以考虑;桩基计算工况的最大水平位移 最大弯矩 与平均地层损失比 呈现线性关系,而与隧道半径R、隧道轴线深度H、桩距隧道中心线距离x及桩身柔度系数 均呈现非线性关系。     

大规模超长群桩基础工作性能的数值模拟

超长桩基础在土木工程中的应用越来越多,但对其工作性状的研究相对滞后。以某超长群桩基础工程为例,用三维非线性有限元方法分析了超长单桩及群桩的工作性能。计算中桩、土和承台的有限元模型均用8节点六面体等参单元,桩-土界面用有厚度的接触面单元模拟;混凝土的应力-应变关系用线弹性模型,土体用非线性Duncan-Chang弹性模型模拟;承台施工过程用分级加荷的方法模拟,承台混凝土的硬化过程用变化模量的方法模拟。计算结果表明,超长单桩的承载性状属摩擦桩,其桩身失稳的原因是桩侧土体的破坏;在群桩基础中,不同位置基桩的工作性能不完全相同,承台周边桩的工作性能与单桩类似,而与内部桩的差别较大;现行规范中推荐的群桩效应系数和有限元计算结果间存在较大差别,表明现行规范可能不适用于超长群桩基础,对超长群桩基础的工作性能进行深入研究是必要的。     

圆形板基础下地基强度和变形非线性性状研究

采用Drucker弹塑性模型、SAP91非线性有限元程序、Vizi CAD微机有限元前后处理系统计算、分析了轴对称问题，即圆形板情况下，基础板几何尺寸、基础刚度、边界条件、基础埋深对基础沉降量、塑性区开展的影响，结果表明基础沉降随基础几何尺寸增大而增大，随基础刚度、埋深的增大而减小；基础刚度、几何尺寸、埋深的加大都能提高地基承载力。     

Finite element simulations of the behavior of piled‐raft foundations using a multiphase model

Finite element simulations of the behavior of a piled raft foundation have been carried out using a multiphase model conceived as an improved homogenization approach. According to this model, the ground reinforced by a group of piles is treated as a homogeneous continuous medium. In this approach, no specific interface elements are necessary to account for the mechanical interaction between the piles and the ground: this interaction is described by means of two scalar parameters, one stiffness parameter and one which can easily be derived from the maximum ground‐pile friction. The implementation of the model into a finite element code provides an efficient tool for the analysis of the influence of the pile number or length on the settlement and bearing capacity of a square piled raft foundation and of the way the total applied load is shared between the raft and the piles. Results are compared with a standard 3D finite element analysis. The comparison highlights the fact that the proposed approach remains to be improved to account for tip resistance. Copyright © 2012 John Wiley & Sons, Ltd.     

移动荷载作用下Winkler地基板的等参元分析

采用基于Mindlin板理论的8节点等参单元和Newmark逐步积分法,对Winkler地基上的弹性薄板和厚板在移动荷载作用下的动力响应进行了分析,并与已有的薄板有限条法分析结果进行了对比。考察了荷载移动速度、地基基床系数、系统阻尼比对地基板动力响应的影响。分析结果表明,系统存在固有的共振速度,地基基床系数是确定共振速度的最重要因素,薄板与厚板的挠度响应模态有很大差异。结果证明了该方法的有效性和准确性,对实际工程有重要的应用价值。     

砂土地基的黏性特性及其有限元模拟

采用非线性弹塑黏性有限元法模拟了砂土地基变速率加载室内试验,再现了砂土地基荷载-沉降曲线对加载速率突变、砂土蠕变以及应力松弛等加载情况下的响应和瞬时黏性中砂土黏性随加载进行的衰减现象。在有限元分析中,以非线性三要素模型为理论框架构建了可以综合考虑砂土黏性特性的弹塑黏性本构模型,用动态松弛法进行有限元求解,最后通过有限元与室内试验的对比分析研究了砂土地基所具有的黏性特性,同时验证了非线性三要素弹塑黏性模型用于模拟砂土黏性特征的合理性和正确性。     

软黏土强度非均质性对复合加载模式下桶形基础破坏包络面的作用分析

针对非均质软黏土地基上复合加载模式下桶形基础的破坏包络面,运用大型有限元分析软件ABAQUS进行了三维非线性数值分析。通过比较系统的数值计算与分析,考察了软黏土非均质性对复合加载模式下桶形基础破坏包络面形状的作用及影响。结果表明：软黏土地基的不排水抗剪强度对于力矩为0的平面内,其应力归一化的破坏包络面影响不大,而在水平荷载与竖向荷载为0的平面内,其应力归一化的破坏包络面具有一定影响。通过与有关模型试验的对比分析,在一定程度上验证了有限元计算模型与数值分析结果的合理性。     

Modeling of Beams on Reinforced Granular Beds

The paper describes a mechanical model for estimating the flexural response of a strip footing, supporting a column (imposing a concentrated load), resting on a compacted granular bed overlying a reinforcement layer for example, geogrids, geomats etc. below which lies a loose soil deposit. The footing is idealized as a beam and the reinforcing element is assumed to have finite bending stiffness and negligible frictional resistance. The upper and lower soil layers are idealized by a series of linear and discrete springs (Winkler springs) of different stiffness values. To find the response of such a model the governing differential equations have been derived and expressed in a nondimensional form. A closed form analytical solution of the same has been obtained subjected to appropriate boundary conditions. Using the present approach the resulting solution for a degenerated case of a long beam is found to be identical to the same of Hetenyi (1946, Beams on elastic foundations, University of Michigan press, Ann Arbor, MI). Parametric studies reveal that the ratio of flexural rigidity of upper and lower beam and the ratio of stiffness of the upper and lower soil layers affect significantly the response of the foundation.     

圆形浅基础承载力计算新模型及验证

通过假定地基发生整体剪切破坏,给出滑动破坏面,考虑地基土的塑性平衡区随着基础埋置深度的不同而扩展到最大可能的程度,并且计及基础两侧土的抗剪强度对承载力的影响,采用极限平衡法,理论上推导出了圆形浅基础承载力。结合工程实例．并利用有限元程序（ADINA）进行数值模拟,进一步验证了浅基础破坏模式的正确性,以及理论推导的可靠性。     

筏板基础与地基的共同作用计算分析——以北京市中关村航空科技园配套工程为例

在高层建筑地基、基础和上部结构三者相互作用的过程中,地基起主导作用,其次是基础,另外还受到上部结构刚度的约束作用。本文以筏板基础为例,介绍一种有限单元方法,把地基按分层变化的有限压缩层模式,将基础与地基视为两种不同的弹性体,在同时满足静力平衡和变形连续的条件下,引入上部结构在底层柱脚处对基础的约束作用,同时求得地基反力和基础内力,最后以一具体实例来论证之。     

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。     

基于界面元法的向家坝重力坝深层抗滑稳定分析

重力坝的深层抗滑稳定分析多采用刚体极限平衡分析方法和非线性有限元法,但通常的刚体极限平衡法不能反映坝基岩体渐近失稳过程和破坏的力学机制,非线性有限元法则难以解决坝基中软弱结构面位移不连续问题。结合向家坝工程,建立了泄④坝段的计算模型,采用界面元法进行了大坝深层抗滑稳定分析,给出了坝基中破坏区的范围和分布,以及坝基的渐进破坏过程和可能滑体的抗滑稳定安全系数等成果,为坝基处理措施提供了重要的技术参考依据。研究结果表明,所建立的分析方法可以自然描述坝基岩体各种介质的错动、张开和滑移等不连续变形的特征,可用于重力坝坝基的深层抗滑稳定 分析。     

Interference effect of two closely-spaced shallow strip foundations on geogrid-reinforced sand

Summary Geotextiles and geogrids are now being used extensively in many civil engineering construction works. This study presents some laboratory model test results for the ultimate bearing capacity of an isolated, and two closely-spaced, strip foundations resting on unreinforced sand, and sand reinforced with layers of geogrid. Based on the model test results, the variation of the group efficiency with the centre-to-centre spacing of the foundation has been determined.     

Dynamic Response of Machine Foundation on Layered Soil: Cone Model Versus Experiments

This paper presents the experimental validation of analytical solution based on cone model for machine foundation vibration analysis on layered soil. Impedance functions for a rigid massless circular foundation resting on a two layered soil system subjected to vertical harmonic excitation are found using cone model. Linear hysteretic material damping is introduced using correspondence principle. The frequency-amplitude response of a massive foundation is then computed using impedance functions. To verify the solution field experiments are conducted in two different layered soil systems such as gravel layer over in situ soil and gravel layer over concrete slab (rigid base). A total 72 numbers of vertical vibration tests on square model footing were conducted using Lazan type mechanical oscillator, varying the influencing parameters such as depth of top layer, static weight of foundation and dynamic force level. The frequency-amplitude response in general and in particular the resonant frequencies and resonant amplitudes predicted by cone model is compared with the results of experimental investigation, which shows a close agreement. Thus the cone model is reliable in its application to machine foundation vibration on layered soil.     

地震作用下复合地基-筏板-上部结构相互作用体系的动力弹塑性分析

基于复合地基-上部结构相互作用的静力分析已取得一定的研究成果,但其在动力荷载作用下,特别是地震作用下的动力响应却相当匮乏。首先借助有关试验通过ABAQUS和EERA的模拟分析,验证了基于Drucker-Prager屈服准则的弹塑性模型能较好地反映土体非线性动力特性以及采用有限元与无限元耦合的方法对土体无限边界的模拟。在此基础上,针对实际问题建立了刚性桩复合地基-筏板-上部结构体系整体有限元模型,对其进行动力弹塑性时程分析,并讨论了该复合地基与桩基对地震响应的差异。深入研究了不同强度地震作用下,刚性桩复合地基的工作机制,包括桩体、褥垫层、筏板的动力响应以及上部结构的地震反应和抗震性能。结果表明,小震时褥垫层基本没有减震效果,大震时复合地基的抗震性能优于桩基。地震越强烈,减震效果越明显,但作用有限,减震系数一般在0.8以上,可为工程实践提供参考。     

基于Winkler模型的双向增强体复合地基沉降计算

将加筋体和复合地基垫层作为一个整体薄板加以考虑,在考虑薄板非线性变形及加筋体水平抗力作用的基础上,基于虚功理论及Winkler弹性地基模型,建立了双向增强体复合地基加固区沉降计算方法。该方法能综合反映上部荷载、面积置换率、垫层及桩间土刚度、桩土应力比等主要因素的影响。以其为基础,设计完成了2组双向增强体复合地基室内模型试验,得到了其相应的荷载-沉降曲线及桩土应力比数据。模型试验与工程实例计算分析表明,加筋垫层的水平抗力对于降低复合地基沉降量是有利的,其影响不容忽视,同时验证了该方法的合理性和可行性。