地铁列车振动作用下近距离平行隧道的弹塑性动力响应

利用有限元数值方法,对地铁列车振动荷载作用下近距离平行隧道结构的二维弹塑性动力响应进行模拟,分析了单列列车荷载以及双列列车荷载作用下土体-隧道结构体系的加速度和内力响应时程曲线。研究表明,列车动力荷载作用下的内力值要比无列车荷载作用下的内力值有较大程度的增加;在单列列车荷载作用下,另一相邻平行隧道的加速度响应、弯矩、轴力峰值要比列车运行所在隧道相应点处的响应值要小;在双列列车荷载作用下隧道结构体系动力响应值要比单列列车荷载作用下的动力响应值有显著增加。     

TECHNICAL NOTE. Model study of H-piles subjected to combined loading

A series of model tests on H-piles subject to lateral and vertical loading have been performed so that the experimental data could be used to calibrate a finite element programme. Experiments on model H-piles in dry silca sand were performed to determine the influence of lateral displacements on the vertical load-carrying capacity of the piles. The results from the nonlinear finite element computer program were compared to the experimental results and were found to be conservative. The experimental results showed greater pile capacities and lower bending moments than were predicted by the finite element program.     

Numerical studies of anchored sheet pile wall behavior constructed in cut and fill conditions

The construction of sheet pile walls may involve either excavation of soils in front or backfilling of soils behind the wall. These construction procedures generate different loading conditions in the soil and therefore different wall behavior should also be expected. The conventional methods, which are based on limit equilibrium approach, commonly used in the design of anchored sheet pile walls do not consider the method of construction. However, continuum mechanics numerical methods, such as finite element method, make it possible to incorporate the construction method during the analyses and design of sheet pile walls. The effect of wall construction type for varying soil conditions and wall heights were investigated using finite element modeling and analysis. The influence of construction method on soil behavior, wall deformations, wall bending moments, and anchor forces were investigated. The study results indicate that walls constructed by backfill method yield significantly higher bending moments and wall deformations. This paper presents the results of the numerical parametric study performed and comparative analyses of the anchored sheet pile walls constructed by different construction methods.     

基于有限元的弯矩计算中若干问题探讨

在岩土工程的数值计算中,除了将岩土材料本身划分为实体单元外,设置在岩土体中,与岩土材料相互作用的其他材料也常常划分为实体单元,比如桩基、堤坝防渗墙和面板等。由于对桩基、防渗墙等往往需要利用内力和弯矩进行设计,这就提出了如何利用有限元得到的应力和位移信息计算结构弯矩的问题。通过对一悬臂梁的计算分析就这一问题进行探讨,发现用应力计算弯矩为提高精度需要划分较多单元。用位移计算可以减少单元划分的工作量,但计算易出现振荡,结果不可靠。同时,对剪切闭锁现象等进行了探讨。     

Analytical and 3D numerical modelling of full-height bridge abutments constructed on pile foundations through soft soils

The scope of this paper is the analysis of full-height bridge abutments on pile foundations, installed through soft soils, with a commercially available finite element software and soil model. Well-documented centrifuge test data were used as reference. Excess pore pressures developed in the clay layer, vertical and horizontal movements of the soft clay, pile displacements and bending moments, and abutment wall bending moments were chosen for comparison, since they are the most critical parameters for observation and design. Additionally, the validity of an analytical method (SIMPLE), which was proposed to analyse the piled abutments subjected to nearby surcharge loading, is discussed. This soil-structure interaction problem has been investigated over the last three decades, using either field or centrifuge tests, accompanied by FE analyses. Special modelling techniques and advanced soil models were used in these numerical studies to establish the most representative field behaviour. However, since the codes or techniques used in these advanced FE analyses are neither very practical nor easily accessible, it is difficult to employ them consistently in design. Thus, the results of this study are intended to provide some guidelines for designers, and to bring insight about the interacting mechanisms into the design process.     

Prediction of elastic settlement of rectangular raft foundation — a coupled FE–BE approach

A numerical method of analysis is proposed for computation of the elastic settlement of raft foundations using a FEM–BEM coupling technique. The structural model adopted for the raft is based on an isoparametric plate bending finite element and the raft–soil interface is idealized by boundary elements. Mindlin's half-space solution is used as a fundamental solution to find the soil flexibility matrix and consequently the soil stiffness matrix. Transformation of boundary element matrices are carried out to make it compatible for coupling with plate stiffness matrix obtained from the finite element method. This method is very efficient and attractive in the sense that it can be used for rafts of any geometry in terms of thickness as well as shape and loading. Depth of embedment of the raft can also be considered in the analysis. Copyright © 1999 John Wiley & Sons, Ltd.     

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。     

General Analytical Solution for Laterally-Loaded Pile-Based Miche Model

Piles subjected to lateral loading can create problems in soil-structure interaction. Several differing methods of analysis have been proposed to solve the problem of laterally loaded piles, resulting in the determination of pile bending and the bending moment as a function of depth below soil surface. These piles are widely used to support laterally loaded piles, such as bridge pillars, offshore platforms, communication towers and others. This study presents an analytical solution to Miche’s problem as a continuous function of depth: deflection and moment, as well as a dimensional plots to be used in projects involving piles subjected to laterally loading only including data concerning laterally loading test and pile geometry. A new formula is presented to calculate the pile head displacement as well as an equation to determine maximum moment for a generalized Miche model and further analysis. In addition, this paper proposes an equation for the determination of constant horizontal subgrade reaction \((n_{h})\) based on the CPT in-situ test and the geometric characteristics of the pile. Calibration of the analytical model showed good fit and conservative results regarding inclinometer data from an bored pile and good agreement with the literature results.

     

斜坡桩水平循环特性模型试验及有限杆单元解

为了揭示斜坡效应和循环弱化效应共同影响下的斜坡桩水平循环特性,进行了不同循环次数、荷载幅值及坡度下的单向水平循环加载试验,并将水平静载试验作为对照,揭示了桩顶位移、桩身弯矩及地基反力等变化规律。综合考虑二阶效应及桩-土相互作用的影响,对单元刚度矩阵进行了改进,提出了有限杆单元解。将理论预测曲线等与实测曲线及幂级数法计算结果进行了对比,验证了有限杆单元解的合理性。结果表明：桩身弯矩及位移均随循环次数非线性增加,最大弯矩位置逐渐从无量纲深度z_α=1.25下移到z_α=1.75;桩顶无量纲位移y0,α与循环次数n之间的关系符合幂函数y0,α=An0.11;当荷载幅值由20 N增加到40 N时,最大无量纲弯矩由0.010增加到0.029,位置均保持在z_α=1.7附近;当坡度由30°增加到60°时,最大无量纲弯矩由0.011(z_α=1)增加到0.025(z_α=2.5)。     

Deformation analysis of reinforced soil retaining walls—simplistic versus sophisticated finite element analyses

Over the last two decades, different kinds of modular block have been increasingly used in the geogrid-reinforced soil retaining walls. The simulation of such wall behavior, which involves interactions between different structural components and backfill soils, requires a rigorous numerical procedure. Finite element is usually a preferred method, but this procedure, especially the soil constitutive models, is of different degrees of sophistication. It is always an issue of how simple or sophisticated should an analysis be conducted in replicating the actual behavior. In this article, a full-scale test wall was used to validate simplistic and sophisticated finite element analyses. Different types of finite element and material models were used in the two kinds of analysis to differentiate the level of simplicity or sophistication. The results obtained from stress-deformation analyses are presented and compared. It is shown that for wall construction that involves static loading conditions, simplistic nonlinear elastic and sophisticated elastoplastic analyses produced close and acceptable results.     

Numerical study of group effects for pile groups in sands

The OpenSees finite element framework was used to simulate the response of 3×3 and 4×3 pile groups founded in loose and medium dense sands. Several numerical static pushover tests were conducted to investigate the interaction effects for pile groups. The results were then compared with those from centrifuge study. It is shown that our simulations can predict the behaviour of pile groups with good accuracy. Special attention was given to the three dimensional distribution of bending moment. It was found that bending moment develops in the plane perpendicular to the loading direction. In addition, bending moment data from simulations was used to derive p–y curves for individual piles, which were used to illustrate different behaviour of individual piles in the same group. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical prediction of tunnel performance during centrifuge dynamic tests

In this paper, a comparison between numerical analyses and centrifuge test results relative to the seismic performance of a circular tunnel is provided. The considered experimental data refer to two centrifuge tests performed at Cambridge University, aimed at investigating the transverse dynamic behaviour of a relatively shallow tunnel located in a sand deposit. For the same geometry, different soil relative densities characterise the two tests. The four seismic actions considered, of the pseudo-harmonic type, are characterised by increasing intensity. The 2D numerical analyses were performed adopting an advanced soil constitutive model implemented in a commercial finite element code. The comparison between numerical simulations and measurements is presented in terms of acceleration histories and Fourier spectra as well as of profiles of maximum acceleration along free-field and near-tunnel verticals. In addition, loading histories of normal stress and bending moments acting in the tunnel lining were considered. In general, very good agreement was found with reference to the ground response analyses, while a less satisfactory comparison between observed and predicted results was obtained for the transient and permanent loadings acting in the lining, as discussed in the final part of the paper.     

侧装式弯曲元高压冻融试验装置研制与初步应用北大核心CSCD

研究深土冻融过程的声波响应特性,对于声波技术应用于深厚表土层人工冻结工程有重要意义。深土原位冻融始终处于高地应力环境下,但目前声波测试装置尚不具备高压冻融条件下的测试功能。为此本文结合弯曲元测试技术,研制了侧装式弯曲元高压冻融试验装置,以了解高应力条件下深土冻融过程的剪切波速。该试验装置主要由试样承压舱、加载系统、控温系统、数据采集系统和弯曲元测试系统构成。系统核心单元——试样承压舱采用双层筒结构,内筒为聚四氟乙烯筒,外筒为钢筒,弯曲元探头设置于内层筒侧壁。通过数值计算确定内筒壁厚8mm,外筒壁厚15mm,该结构可满足高应力下承压舱的抗变形、隔热和隔振要求。利用弯曲元测试系统研究了声波走时确定方法,以及激励波形和频率等测试参数。根据测试结果,本试验条件下声波走时采用初达波法确定,激励波形采用方波,高密度冻土和未冻土的激励频率分别选择4kHz和5kHz。最后,利用该装置测试了有载条件下深部黏土不同负温下的剪切波速,初步验证了装置的适用性。     

桩基础荷载对邻近已有隧道影响的有限元分析

目前,城市密集的高层建筑桩基础对临近隧道的影响问题越来越突出,为了更好地理解桩群荷载对已建成隧道的影响,主要进行了两方面的研究：（1）利用平面应变有限元方法分析了桩列荷载作用对邻近已有隧道的变形及受力影响,并研究了桩群参数变化（包括桩间距以及桩基础与隧道结构净距）对现存隧道的影响;（2）分析计算了上海太平洋2期广场工程对邻近地铁1号线隧道的影响。分析结果表明：隧道单侧存在桩列荷载作用时,隧道变形以沉降为主,水平位移较小,同时隧道结构向桩基础方向产生一定扭曲,这对于运营地铁是十分不利的;桩基础荷载造成隧道所受弯矩分布向桩基础方向偏转;随着桩间距、桩与隧道净距的增加,隧道拱顶下沉量以及弯矩变化最大值相应减小,沿隧道方向桩间距变化影响大于垂直隧道方向桩间距变化影响。     

Mode I crack propagation in concrete under fatigue: microscopic observations and modelling

In this study, three‐point bending tests were carried out on notched beams to investigate mode I crack propagation in plain concrete under fatigue. The first part of the study focused on microscopic observations of the crack growth features. Microscopic observations were made using the replica method associated with scanning electron microscopy (SEM). Observations of fatigue crack growth both on the surface and inside the specimens are presented as a comparison between the observed crack lengths and those estimated by the compliance calibration method. In the second part, a finite element model of mode I crack propagation under fatigue is presented. According to the cohesive crack concept, a cohesive force distribution on the crack at various loading stages is assumed, according to both the stress‐crack opening relation worked out by Hordijk (1991; Thesis, Technische Universiteit) and a new proposed relation with hysteresis loop. Finite element computation is used to evaluate the crack extension in the bending beams. Numerical predictions are discussed in comparison with experimental results. Copyright © 2002 John Wiley & Sons, Ltd.     

刚性桩加固软土路基失稳破坏数值模拟

为控制路堤的整体稳定性,刚性桩现已常用于软土路基的加固。本文引入了桩体的断开机制,采用有限元软件ABAQUS对刚性桩加固软土路基的失稳破坏模式进行分析,相较于传统的数值模拟方法,体现了路堤荷载作用下,刚性桩的渐次失稳破坏过程。在此基础上,考虑桩体可能优先发生的弯曲破坏,提出将临界比例n作为判断桩体优先发生剪切破坏或弯曲破坏的临界值,并将其作为本文桩体断开机制的终止判别条件,合理地规避了数值模拟软件定量计算存在的较大误差。最后,将本文数值模拟与传统的数值模拟、等效砂桩法的数值模拟进行对比,结果反应出本文数值模拟方法的合理性与可靠性,工程上可通过增大前排桩的抗弯强度或限制桩体的水平位移,提高路堤的整体稳定性。     

Finite element analyses of layered visco‐elastic system under vertical circular loading

Analyses for the response of a linear visco‐elastic system subjected to axi‐symmetric vertical circular loading are presented. Hankel transforms with respect to the radial spatial coordinate are used to reduce the three‐dimensional problem to that involving only a single spatial dimension, which is then discretized using the finite element method. Three techniques are employed to handle the time factor in the visco‐elastic material: (i) direct time integration; (ii) Fourier transforms; and (iii) Laplace transforms. These methods are compared and evaluated through their numerical results. Copyright © 2007 John Wiley & Sons, Ltd.     

加筋材料动态松弛有限元模型的建立及应用

为分析加筋材料的抗弯刚度对加筋性能的影响,加筋材料采用梁单元形式。基于动态松弛法,通过定义梁单元的刚度矩阵,求解内力矢量,随后定义虚拟质量密度而建立总质量矩阵,将加筋材料的梁单元有限元模型嵌入到已有的动态松弛法求解程序中。通过对简支梁的简单加载模拟验证了该梁单元模型的准确性能。随后,将该有限元模型与已有的动态松弛法计算程序结合（含砂土本构及弱面单元模型）,对加筋砂土地基室内模型试验进行了数值模拟。将梁单元的模拟结果与杆单元（梁单元的特例）模拟结果进行了比较,并分别探讨了抗拉刚度和抗弯刚度对加筋砂土地基承载性能的影响。结果表明：抗拉刚度对承载能力的影响较小;抗弯刚度对承载力的影响程度与加筋材料的布置形式有关,特别是当加筋砂土中出现剪切带以后,其影响逐渐增大。因此,在分析加筋砂土结构的增强机制时,建议采用梁单元（具有一定的抗弯刚度）对加筋材料进行模拟。     

四节点矩形弹簧元及其特性研究

弹簧元法是一种将单元离散为一系列弹簧的数值计算方法。不同的单元具有不同的离散方式,确定相应的离散弹簧的刚度系数表达式是弹簧元法的关键。将四节点矩形单元离散为6个基本弹簧,每个基本弹簧包括法向弹簧和切向弹簧两个派生弹簧,并用泊松弹簧和纯剪弹簧描述单元的泊松效应和剪切效应,用有限元的单元刚度矩阵标定各弹簧的刚度系数,实现了一种四节点矩形弹簧元的构造形式。该单元的同类弹簧具有相同的表达形式。法向与切向弹簧的刚度表达式中分别含有法向和切向弹簧刚度待定系数。通过改变待定系数的值可使该单元分别对应于有限元的常应变、双线性及Wilson非协调单元。将上述弹簧元方法进行理论推导,并应用于基于连续介质的离散单元法（CDEM）的核心计算进行简单算例验证,证明了提出方法的正确性。通过以上研究发现,四节点矩形弹簧元有以下特点：对于相同问题,不同单元有不同的计算精度;对于梁弯曲问题,应用该单元可显著提高离散单元法的求解精度;改变待定系数的值,可得到更高或者更低精度的单元。     

The ultimate uplift capacity of multi-plate strip anchors in undrained clay

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. Anchors commonly have more than one plate or bearing element and therefore there is a complex interaction between adjacent plates due to overlapping stress zones. This interaction will affect the failure mode and ultimate capacity. However, no thorough numerical analyses have been performed to determine the ultimate pullout loads of multi-plate anchors. By far the majority of the research has been directed toward the tensile uplift behaviour of single anchors (only one plate). The primary aim of this research paper is to use numerical modelling techniques to better understand plane strain multi-plate anchor foundation behaviour in clay soils. A practical design framework for multi-plate anchor foundations will be established to replace existing semi-empirical design methods that are inadequate and have been found to be excessively under or over conservative. This framework can then be used by design engineers to more confidently estimate the pullout capacity of multi-plate anchors under tension loading.