饱和土体中空沟对移动荷载被动隔振的 2.5D边界元法分析

根据饱和土Biot理论及移动荷载特性,采用积分变换方法,推导了半无限饱和土体频域-波数内的边界积分方程,讨论了2.5D边界积分方程中Cauchy的奇异性,并分析了空沟对移动荷载引起饱和土体振动的被动隔振效果。通过与已知文献结果比较,验证了算法的正确性。数值结果表明,采用2.5D BEM不仅可以解决具有复杂表面的移动荷载作用下动力响应问题,而且可极大减小计算工作量。对于饱和土体受高速移动荷载作用,空沟更能有效减小土体孔压、竖向位移的振幅;当荷载速度较小时,空沟对土体表面的水平向位移几乎不起衰减作用,甚至有放大效应。另外,随空沟距振源的距离增大,空沟能够更好阻隔土体表面波传播。     

上部结构－桩基—地基共同作用数值分析及桩基变刚度调平优化设计

本文采用有限元法对高层建筑上部结构—桩筏基础—地基共同作用及相互影响进行了研究。研究表明:高层建筑上部结构—桩筏基础—地基共同作用及相互影响时,基础总体沉降和差异沉降随楼层的增加呈非线性变化趋势,上部结构中存在次应力,弯矩和轴力比常规法设计偏大;随楼层的增加,桩体对荷载的分担比在减少,土体分担比在增加;随着上部结构刚度的增加,荷载向角桩、边桩集中;增加筏板厚度,能减少一定的差异沉降和基础平均沉降,从而减少上部结构的次应力,提高地基土的荷载分担比,同时筏板下桩顶反力分布更不均匀,因此需要从筏板受力,以及考虑筏下桩、土的受力来综合确定一个合理的筏板厚度,使设计安全经济;随着地基土变形模量的提高,地基土分担的上部荷载增加,桩顶反力趋向平均,筏板最大弯矩逐渐减小。桩筏基础在均匀布桩条件下呈中间大边缘小的“碟型”分布。差异沉降是由于上部结构次生应力和筏板内力产生的。通过对地基土刚度以及桩长、桩径、桩距等五种桩基刚度的调整,并分析不同刚度对基础差异沉降影响可知:改变桩长的布桩形式并结合地基土刚度调整的中心布桩形式是高层建筑桩筏基础最佳设计方案。     

矩形移动荷载作用下路面-双层地基系统三维振动分析

考虑路面和地基之间的相互作用,建立了路面-双层地基的三维模型,将车辆荷载模拟成矩形移动荷载,利用Fourier变换方法对车辆荷载作用下路面-双层地基系统的三维振动问题进行了研究。假设地基为上部弹性土体和下部为饱和土体组成的双层混合结构,整个系统置于刚性基岩上。通过引入势函数,利用Lame分解理论和积分变换方法分别对弹性土层和饱和土层进行求解。在Fourier变换域内,联立路面和下卧双层地基系统的的运动方程,获得了车辆荷载作用下路面-双层地基系统三维振动的位移和孔压响应的积分形式解,并利用IFFT算法和自适应数值积分算法得到了数值计算结果。研究结果可为路基动力响应分析提供参考。     

饱和土体中排桩对移动荷载的被动隔振效果分析

利用Muki和Sternberg的虚拟桩法,研究了饱和土体地基中排桩对移动荷载引起振动的被动隔振效果。隔振桩作为一维杆,饱和土体满足Biot理论。利用已有的移动荷载作用下的饱和土体的自由波场解及饱和土体内部受竖向圆形分布荷载作用下的基本解,建立了频域内土-桩的第2类Fredholm积分方程。通过Fourier逆变换得到时间域内评价隔振效果的振幅比。与已知文献结果相比较,验证了方法的正确性。数值结果表明,荷载速度对排桩的隔振效果有一定影响,即在相同隔振系统情况下,单排桩对低速荷载引起振动的隔振效果比高速移动荷载效果好。同时,较高速时的最佳桩长比低速时要短。     

移动荷载作用下非均匀地基的动力响应分析

基于线弹性动力学理论,结合坐标变换,建立了移动荷载作用下非均匀弹性半平面地基的动力控制方程,利用半解析法研究了移动荷载作用下二维非均匀地基的动力响应问题。采用傅里叶（Fourier）级数展开,假设了响应函数的级数形式,通过理论推导获得了剪切模量随深度任意变化的非均匀地基在移动荷载作用下各物理量的解析表达式。考虑土体的剪切模量沿厚度方向按幂函数梯度变化,通过数值算例分析并讨论了地基非均匀参数、荷载移动速度以及地基表面的剪切模量等对地基力学响应的影响规律,并与均质地基的计算结果进行了比较。数值结果表明：地基中各点的竖向位移随着土体表面剪切模量和表征土体非均匀性的梯度因子的增大而减小,随着荷载移动速度的增大而增大。在移动荷载作用下,非均匀地基与均匀地基的动力响应有着显著的区别。     

大型桩-筏基础筏板竖向位移及位移差变化特征

采用桩筏土共同作用分析法对筏板竖向位移及位移差随板厚变化特征进行分析,并指出:随板厚变化,筏板位移具有分区性,板心位移及板边位移在各自的特征厚度附近较小的厚度范围内变化最快,荷载水平对特征厚度基本没有影响。      

土体饱和度对移动荷载引起多层非饱和铁路地基振动的影响

采用半解析法研究了移动荷载作用下多层非饱和铁路地基的共振问题,分析了土体饱和度对非饱和地基振动的影响。采用分层非饱和多孔介质描述铁路地基;基于非饱和多孔介质的控制方程,采用多重傅里叶变换和土层界面位移、应力条件,推导了频率-波速域分层非饱和地基总体刚度矩阵。结合包括钢轨、轨垫、轨枕和道砟的轨道模型,建立耦合轨道-地基半解析模型。研究了移动简谐荷载作用在轨道上的多层非饱和地基的动力响应;考虑饱和度对土体剪切模量的影响,讨论了地基首层土和夹层土饱和度变化对地面振动的影响。采用频散曲线研究了地基共振模态。研究发现土体饱和度变化对振动位移的影响规律,与地基分层、荷载速度和频率有关。随饱和度减小,地基共振模态出现频率增大,地基关键速度增大。     

上部结构与基础、地基共同作用的仿真分析

利用有限元方法对上部结构、筏板基础与地基共同作用下应力、应变的一般规律进行分析,得出了在竖向与水平荷载作用下应力、应变的基本规律。     

交通荷载作用下Kelvin地基上不平整路面的动力响应分析

为了评价不平整路面在交通荷载作用下的动态响应,从路面几何不平整出发,假设路面不平整服从正弦函数曲线,并把1/4车身结构简化为2个自由度振动体系,得到了不平整路面上的动荷载表达式。又将此荷载模式看成是作用在Kelvin地基上无限大路面板表面的移动矩形荷载,采用双重Fourier变换方法得到了不平整无限大路面板竖向位移的积分形式解,此解析解可以退化为静荷载作用下的经典解答。并利用快速傅立叶变换(FFT)方法得到了数值计算结果。分析了荷载速度,路面不平整波长、不平整幅值以及地基阻尼和地基刚度对板的动力响应的影响。结果表明,板竖向位移的分布受荷载移动速度的影响;位移幅值随着路面不平整波长和荷载速度的变化出现2个峰值;路面不平整使得位移峰值出现滞后现象,且不平整波长越小或不平整幅值越大,滞后现象越明显。     

矩形运动荷载作用下软土地基的三维振动研究

通过引入势函数,并利用Helmholtz原理和Fourier变换技术,研究了运动荷载作用下有限层厚软土地基的振动,考虑了矩形分布荷载作用下振动的三维特性,使得分析更符合工程实际,给出了运动荷载作用下饱和黏弹性地基三维振动的应力、位移和孔隙水压力响应的积分形式解答。利用Fourier数值逆变换进行算例分析,讨论了荷载速度对位移及孔隙水压力分布的影响。结果表明,位移幅值随荷载速度的增加而增大,荷载不同位置处孔隙水压力的分布有很大差异。     

建筑边距对岩坡地基及上部结构影响数值分析

为节约用地,山地城镇建设中有些建筑建于岩坡地基上,岩坡地基与上部建筑结构之间的共同作用分析成为山区岩土工程实践中的一个课题。基于有限元分析的数值方法,对均质岩坡上建筑边距(建筑距坡顶边缘的距离)对上部建筑结构与地基基础相互作用的影响进行了计算分析,其中边坡地基为10 m高的直立岩坡,基础为平板式筏基,建筑边距分别考虑了2、5、8 m的3种情况。研究了3种建筑边距情况下边坡地基的强度变形情况及上部框架结构、筏板基础的内力和变形情况,分析中上部结构、基础与边坡地基满足三者的受力平衡和变形协调条件。得出了相关结论,对工程实践有一定参考意义     

Non-linear soil–structure interaction in disconnected piled raft foundations

Disconnected piled raft foundations are characterised by no structural connection between the upper raft and the underlying piles, mostly playing the role of settlement-reducers. The resulting raft–pile gap is usually filled with a granular interlayer, through which the loads from the superstructure are transferred to the piles.In this paper, the complex interaction mechanisms involving the foundational components (raft, piles and soil) are numerically investigated by means of 3D finite elements analyses, accounting for soil non-linearity. The main features of the soil–structure interaction mechanisms under purely vertical external loads are explored over a realistic range of raft–soil gaps for different pile configurations, in which the number of piles – i.e. their spacing – is varied. Special attention is also devoted to the structural response of the piles in terms of axial and bending internal stress resultants. In particular, while disconnection beneficially affects the structural pile response, increasing the raft–pile gap tends to reduce the overall settlement/stiffness efficiencies.The numerical results being presented are in substantial agreement with the outcomes from literature small-scale experiments and suggest a number of relevant theoretical inferences.     

Vertical harmonic vibration of piled raft foundations in layered soils

This paper develops a method to analyze the piled raft foundation under vertical harmonic load. This method takes into account the interactions among the piles, soil, and raft. The responses of the piles and raft are formulated as a series of equations in a suitable way and that of layered soils is simulated with the use of the analytical layer‐element method. Then, according to the equilibrium and continuity conditions at the piles–soil–raft interface, solutions for the piled raft systems are obtained and further demonstrated to be correct through comparing with the existing results. Finally, some examples are given to investigate the influence of the raft, pile length‐diameter ratio, and layering on the response of the piled raft foundations. Copyright © 2017 John Wiley & Sons, Ltd.     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of pile‐raft foundations under complex loads in layered soils

Considering there is hardly any concerted effort to analyze the pile‐raft foundations under complex loads (combined with vertical loads, horizontal loads and moments), an analysis method is proposed in this paper to estimate the responses of pile‐raft foundations which are subjected to vertical loads, horizontal loads and moments in layered soils based on solutions for stresses and displacements in layered elastic half space. Pile to pile, pile to soil surface, soil surface to pile and soil surface to soil surface interactions are key ingredients for calculating the responses of pile‐raft foundations accurately. Those interactions are fully taken into account to estimate the responses of pile‐raft foundations subject to vertical loads, horizontal loads and moments in layered soils. The constraints of the raft on vertical movements, horizontal movements and rotations of the piles as well as the constraints of the raft on vertical movements and horizontal movements of the soils are considered to reflect the coupled effect on the raft. The method is verified through comparisons with the published methods and FEM. Then, the method is adopted to investigate the influence of soil stratigraphy on pile responses. The study shows that it is necessary to consider the soil non‐homogeneity when estimating the responses of pile‐raft foundations in layered soils, especially when estimating the horizontal responses of pile‐raft foundations. The horizontal loads and the moments have a significant impact on vertical responses of piles in pile‐raft foundations, while vertical loads have little influence on horizontal responses of piles in pile‐raft foundations in the cases of small deformations. The proposed method can provide a simple and useful tool for engineering design. Copyright © 2013 John Wiley & Sons, Ltd.     

Three-dimensional analysis of bearing behavior of piled raft on soft clay

The piled raft has proved to be an economical foundation type compared to conventional pile foundations. However, there is a reluctance to consider the use of piled rafts on soft clay because of concerns about excessive settlement and insufficient bearing capacity. Despite these reasons, applications of piled rafts on soft clay have been increased recently. Current analysis methods for piled rafts on soft clay, however, are insufficient, especially for calculating the overall bearing capacity of the piled raft. This study describes the three-dimensional behavior of a piled raft on soft clay based on a numerical study using a 3D finite element method. The analysis includes a pile–soil slip interface model. A series of numerical analyses was performed for various pile lengths and pile configurations for a square raft subjected to vertical loading. Relatively stiff soil properties and different loading types were also used for estimating the bearing behavior of the piled raft. Based on the results, the effect of pile–soil slip on the bearing behavior of a piled raft was investigated. Furthermore, the proportion of load sharing of the raft and piles at the ultimate state and the relationship between the settlement and overall factor of safety was evaluated. The results show that the use of a limited number of piles, strategically located, might improve both bearing capacity and the settlement performance of the raft.     

Vertical response of pile raft foundations subjected to tunneling‐induced ground movements in layered soil

A simplified analysis method has been developed to estimate the vertical movement and load distribution of pile raft foundations subjected to ground movements induced by tunneling based on a two‐stage method. In this method, the Loganathan–Polous analytical solution is used to estimate the free soil movement induced by tunneling in the first stage. In the second stage, composing the soil movement to the pile, the governing equilibrium equations of piles are solved by the finite difference method. The interactions between structural members (such as pile–soil, pile–raft, raft–soil, and pile–pile) are modeled based on the elastic theory method of a layered half‐space. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups, and pile rafts subjected to ground movements induced by tunneling. Good agreements between these solutions are demonstrated. The method is also used for a parametric study to develop a better understanding of the behavior of pile rafts influenced by tunneling operation in layered soil foundations. Copyright © 2011 John Wiley & Sons, Ltd.     

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。     

软土地区深埋桩筏基础沉降实测与反分析

对上海环球金融中心（Shanghai World Financial Center,简称SWFC）实测沉降结果进行研究,分析坑底的回弹、沉降随时间的发展规律,并通过沉降推测上部结构刚度的变化情况。软土地区深埋桩筏基础沉降与加荷速率、基坑回弹、附加应力在桩长及桩下土中的传递、基坑降水与停止降水等多种因素有关。基础沉降-时间关系曲线并非理想的双曲线,即使是施工加荷速率相对稳定时。建筑物施工初始阶段沉降速率较小,与深基坑回弹密切相关,建筑物接近封顶时往往沉降速率较大,可能与附加应力传至桩端以下土中有关。沉降过程反映4.5 m的厚筏为弹性体,上部结构刚度对筏板刚度具有贡献性和有限性,上部刚度是随着施工的进程逐步形成。采用3种方法对SWFC进行沉降计算反分析,通过计算结果与实测数沉降数据进行对比得出,运用上海规范采取合适的经验系数（0.40～0.55）、考虑70%的水浮力,利用明德林解得出的计算结果与实测值吻合很好;深埋桩筏基础共同作用分析计算中不能过大考虑上部结构刚度的贡献。     

A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.