循环荷载作用下单桩沉降的数值模拟研究
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摘要
随着世界船舶市场持续兴旺,中国船舶工业不断壮大发展。在船舶工业蒸蒸日上的格局之下,三大骨干造船基地上海长兴、广州龙穴、青岛海西湾需要兴建不少吊车吊装厂房。然而造船基地吊装厂房内运行的吊车自重与起吊重量之和少则数百吨,多则千吨。桩基础不仅在承受厂房以及吊车梁等本身的静荷载,而且同时也要承受吊车装卸运转所带来的循环荷载。该类厂房桩基础承受荷载的特点之一是循环荷载与占其承受的总荷载比例较高,另一个特点是具有一定的循环荷载的频率。且根据ISI、EI以及中国期刊库的检索结果,目前国内外尚无针对吊车荷载作用下桩基础沉降的研究成果可供参考。因此,迫切需要对吊车吊装厂房的基础承载沉降特性进行研究,提出合理的建设要求。
针对循环荷载作用下基础承载特性的研究,以往主要有三类。一是针对海洋平台桩基础的研究。与动力机器荷载相比较,该课题研究具有荷载频率低、加载时间短且桩循环位移幅值大等特点。二是针对高速公路、高速铁路等基础的研究。该课题研究具有加载时间短且加载量级较低等特点。三是针对承受风荷载的一些构筑物桩基础的研究,该研究的特点是结构上部承受的是水平向的循环荷载,对于下部基础,则是循环弯矩的作用。其中,针对海洋平台桩基础的研究与本试验研究相类似,区别在于荷载模式:前者主要是双向循环荷载,而我们仅进行单向循环荷载的研究。前人的模型试验、原型试验以及数值计算的相关研究表明,此类循环荷载对于桩基础沉降带来的影响与单纯的静载并不完全相同,影响桩沉降的因素除结构上部荷载水平外,循环荷载所占总荷载比例、循环周期以及循环振次的影响也是不容忽视的。
然而,在现行设计手册和规范中,并没有专门考虑该类循环荷载对基础沉降影响的相关内容,而且在计算基础沉降时一般也不将吊车等循环荷载考虑进去。针对目前造船基地等需要建设此类重、大、高、深基础的实际工程,若能够较好地解决该问题,有着降低建造成本,保证工程安全的重大意义。
本课题针对以上问题所提出,目的是为了研究吊车循环荷载作用下的桩的循环沉降特性。从该课题的科学本质上来讲,吊车荷载对厂房地基沉降的影响,实质上就是研究循环荷载作用下桩的沉降特性。
为了研究循环荷载下桩基础的沉降规律,首先进行了砂土中的单桩模型试验。然后通过有限元数值分析进行模拟与验证。在有限元分析中,采用了下负荷面t_(ij)弹塑性模型来描述土的本构特性。如不考虑长期作用,在较小循环荷载下的位移仍将达到一个有限的幅值。但是,如果循环荷载超过稳定容许值,桩顶有可能产生危害工程的明显沉降。这种数值分析方法的计算结果与循环荷载作用下的实测值吻合较好。
论文共分为以下几个部分。
1.介绍论文的研究背景、意义和主要内容:介绍循环荷载下桩基础的沉降进展,并进行综述分析。与常规动力机械桩基础相比较,这一课题的研究具有荷载频率较低、加载时间短等特点。然而该问题从本质上说仍属于桩—土动力相互作用的问题,因此仍需要从此处入手进行研究。桩—土动力相互作用研究是土力学与结构力学的交叉研究方向之一,土—结构相互作用研究大致经历了三个阶段。第一个阶段是二十世纪初到六十年代中期,这段时间是理论准备时期,主要研究循环载荷在不同基础情况下的解析解。第二个阶段是六十年代中期到八十年代中期,这一时期不但在理论方面进一步完善,而且在计算方面也得到了较大的提高,能够分析较为复杂的结构与基础之间的相互作用,考虑各种条件的分析方法相继出现,并且在各自的领域内得到合理的解释。第三个阶段是在八十年代中期以后,这一时期的研究进一步深化,各种更为精确更为实用的方法得到了发展,并逐渐向三维分析过渡,而且非线性分析逐渐成为研究的主流方向,同时各种试验及观测也得到了广泛的应用。
2.循环荷载下桩基础的试验:为了使模型试验的结果更切合实际,2006年9月28日、29日在上海某造船基地进行了为期两天的吊车工作荷载现场调查。实地考察的目的在于调查吊车日常工作荷载的特性,以确定模型试验加载的周期、大小等加载特性。
模型试验研究分别以干砂、饱和砂土以及饱和粘土这三种不同土性的土作为桩周土体进行了三组模型试验。每组土都通过静载试验确定单桩的承载力,并通过该值确定不同分组试验的循环荷载大小。每组试验都进行3组不同循环荷载比的加载,循环次数均在2000次左右或者达到破坏。
试验内容:针对吊车交变荷载作用下的桩基础沉降,主要研究桩在动力作用下与静载作用下的异同,以及影响桩动力特性的主要因素。采用快速加载法进行桩的静承载性能试验,采用动力循环加载进行桩动力循环性能试验。根据加载系统条件、研究目的以及实际情况所需,按照循环荷载比分级进行分组加载试验。为了便于确定动荷载作用下的桩极限承载力,并了解桩的行为特点,首先进行模型桩的静力试验。
3.室内试验的内容:在传统的岩土力学研究中,多数是对土样进行各种室内力学特性试验以确定其强度变形关系和力学参数,为数值计算做准备。本章对土体进行常规土工试验,三轴试验,循环三轴试验,并对试验结果进行分析。本次试验用砂取自上海市崇明岛处于河口、砂嘴、砂岛相的东滩地区。为了完成试验,砂土需要烘干并且重塑。另外,粘土取自上海市闵行区华翔路某工地的11m深基坑,为第三层灰色粉质粘土。粘土的制备过程较为繁琐,需要将粘土风干后碾碎,去掉土中夹杂物。模型试验后,从槽内直接取出原状饱和粘土。常规土工试验是分别对试验所用的砂土和粘土进行了常规物理试验、压缩试验、渗透试验、固结试验以及直剪试验等常规土工试验。使用国际先进的GDS三轴仪进行饱和土体的三轴试验研究,与模型试验相结合,从微观、宏观两方面入手,分析了影响桩的沉降的因素。
并将通过试验得到的曲线直接用来确定有限元的模型参数,用来进行模型试验以及原型桩的数值计算。用饱和砂土,对于回弹指数κ和压缩指数λ,进行各向同性下固结排水试验。然后,对于Rcs(排水三轴压缩时主应力比σ_1/σ_3在临界状态下的值)和β物理参量,进行三轴压缩排水试验。为了估计关于各向同性下循环的参数a(材料参量,用于控制ρ的发展速度),进行各向同性下固结排水循环三轴试验。为了估计关于循环的特性进行排水的循环三轴压缩试验。另外,为了评价砂土的密实性,进行了相对密实度试验。用饱和粘土,对于回弹指数κ和压缩指数λ,分别进行各向同性下固结排水试验和一维固结试验。为了估计关于等方性循环的参数排水的等方循环三轴加载试验行为了。然后,对于Rcs,进行三轴压缩不排水试验。通过GDS系统控制的循环三轴试验能够较好的反映土样在循环加卸载作用下的竖向应变、体积应变等参数,同时还能准确的记录加卸载带来的超孔隙水压力的变化。为了估计关于各向同性下循环的参数a,进行各向同性下固结排水循环三轴试验。为了估计循环特性,进行不排水的循环三轴压缩试验。
通过整理对比三轴试验得到的资料,分析了在循环作用下土体的特性。
4.下负荷面t_(ij)弹塑性模型基本概念:
岩土工程问题大体上可以分为两大类:变形问题和稳定问题。传统的岩土工程设计计算方法中,对于变形问题,大多采用先弹性模型;对于稳定问题,采用基于理想刚塑性模型的极限平衡分析方法。本质上来讲,岩土工程的变形和稳定问题并不是完全割裂的两个问题,岩土体的强度和变形间存在密切的联系,本构模型是描述其应力应变关系的数学模型,也即本构关系。岩土材料的真实应力应变关系特性非常复杂,不仅具有非线性、弹塑性、粘塑性,还具有各向异性、剪涨性等特性,同时应力路径、强度发挥以及土的组成、结构、状态和温度等因素均对其有着不同程度的影响。通常对这类问题有两种解决途径:一种是引入简化假设,使其达到能用解析法求解的地步,求得问题在简化状态下的近似解,这种方法并不总是可行,常导致不正确甚至错误的解答。另一种方法是保留问题的复杂性,利用数值计算方法来求得问题的近似数值解。随着计算机技术的飞速发展,已使得采用这种方法解决实际工程问题成为可能,并能得到令人满意的结果。有限元法把结构离散成有限个有限大小的单元,通过在结点互相联结而构成集合体,利用物理上的相似性,把求解偏微分方程的问题变成求解线性方程组的问题,从而利用计算机解线性方程组,可得到工程上满意的数值解。有限元方法是一种基于性能的计算方法,理论上来说有限元方法能够合理的预测结构受荷后的全过程,并且能够反映出试验难以详细测定的参数。随着计算机技术的发展,有限元方法日趋完善,能较好的描述土体的非线性特征。
目前在计算中粘弹性和弹塑性模型占主流,而不论选取何种模型都应该考虑其能否真实有效的反映给定环境下土的物理力学特征。下负荷面t_(ij)弹塑性模型的基本概念。该模型的最大特点就是能够准确地描述土在一般应力状态下的应力应变及剪胀特性。该模型开始于SMP概念。空间滑动面SMP在1974就由Matsuoka& Nakai提出来了,但真正将其融入到土的本构关系,则是在10年后的1984年,由Nakai & Mihara提出了t_(ij)的概念,并相继在1986及1989年,由Nakai提出了t_(ij)粘土模型(t_(ij)clay model,Nakai &Matsuoka,1986)及t_(ij)砂土模型(t_(ij)sandmodel,Nakai,1989)。一般应力状态下的力学特性,加入了由Nakai & Hinokio(2004)提出的下负荷面t_(ij)模型。
首先,介绍岩土类材料的特征面“空间滑动面(SMP面)”。与金属材料不同,土是一种摩擦性材料,经典的金属塑性理论难以解释土的变形特性。各种材料在三维应力作用下的变形和强度是工程学科中一个普遍的重要问题,吸引了不少研究者进行大量的试验和理论研究。在多轴应力状态下材料的变形和强度问题是非常复杂的,解决的基本思路是将复杂问题简单化,通过一个应力状态的函数将多维问题归一化,所提出的各种屈服准则和破坏准则就是其中代表性的研究成果。实践证明,对岩土类材料,SMP准则是最好的强度准则之一。Matsuoka和Nakai等提出,土颗粒在剪应力作用下的运动状态是由摩擦定律控制的,即土颗粒滑动最可能发生在剪应力与正应力之比达到最大的平面,即为空间滑动面的概念(Spatial Mobilized Plane,SMP)。即在三维应力状态下,破坏是沿着SMP面滑动的。SMP面的方向余弦用I_1,I_2,I_3(分别为第一应力不变量、第二应力不变量和第三应力不变量)来表示。Toyoura砂的三轴压缩和三轴拉伸试验得到的试验数据,用SMP面上的应力应变参量来整理,所得结果趋近于一条直线,说明岩土材料的应力比和应变增量比的关系(剪胀方程),在SMP面上具有归一性。另外,砂的真三轴试验得到的结果显示,SMP面上的应力比τ_(SMP)/σ_(SMP)与γ_(SMP),ε_(SMP)有唯一的、确定的关系,即岩土材料的面上应力比和应变具有归一性。SMP准则实际上是三维空间中的摩擦准则,也可以认为是在个主应力下平均化了的Mohr-Coulomb准则。在SMP面上,岩土材料的应力一应变及强度具有归一性。在三维应力空间中,通过SMP面可以唯一确定岩土材料的应力应变特性。
其次介绍,“变换应力张量t_(ij)”。在SMP面,沿应力Lode角θ(σ_1轴正方向的夹角)θ=15°,30°,45°的径向应力路径时,试验所得的粘土的应变,箭头代表应变增的大小和方向,对于岩土材料,与其塑性应变相比,弹性应变在总的应变中所占比例很小,所以也可以认为各箭头的方向基本反映了塑性应变增量的方向。Nakai通过试验研究得到了这种分叉现象。这是考虑了中间主应力的影响而得到的一个必然结果。修正后的三重屈服面应力t_(ij)-应变模型也可以反映土体的应力-应变分叉特性。修正后的模型很好的反映了一般应力状态下土体的应变分叉特性。变换应力张量t_(ij)用平面的法向矢量和SMP面的单位法向矢量。
其次将介绍下负荷面的概念。剑桥模型(Cam-Clay Model)对正常固结重塑粘土的三轴压缩试验能作出较为准确的描述,但对超固结粘土及自然土,即具有结构的土,则不能给出准确的描述。在经典土力学弹塑性理论(包括剑桥模型)中,在卸载及再加载过程中的土的应力应变关系是被假定为弹性的。Hashiguchi& Ueno(1977)提出的下负荷面概念的基本特征如下:连续平滑的弹塑性应力应变关系。下负荷面模型的卸载·再加载过程中的应力应变关系,经典弹塑性理论的应力应变关系明显不同。下负荷面是经过现有应力点并和正常屈服面几何相似的面。下负荷面必定经过现在应力状态,而且随应力变化而变化。也就是说,现在应力都存在于下负荷面上。因此加载准则比经典弹塑性理论的简单,不需要判断应力状态是否到达屈服面,并且可以简化程序编制。根据以上土的一般应力状态下的力学特性,加入了由Nakai & Hinokio(2004)提出的下负荷面t_(ij)模型。t_(ij)下负荷面模型不仅可以很好地描述单向加载试验,对交变载荷或逆反加载破坏实验,同样可以做出非常准确的描述。需要再次强调的是,所有理论模拟都使用同样的物理参量。还有,下负荷面t_(ij)模型内,Nakai等人(2004)提出的下负荷面t_(ij)模型中采用和修正剑桥模型类似的剪切应力比与塑性剪胀比之间的关系式,即剪应力比与塑性剪胀比之间存在一定的关系。其中物理参量β可由实验唯一确定。β=1时粗实线为一直线,就相当于原始剑桥模型的关系式了。另外,实际上是与剑桥模型中指出的塑性体积应变由等向固结及剪切变形两部分组成的概念是完全一致的。根据以上的推导,最后需要做的就是确定塑性应变增量的大小。
5.模型试验结果与数值分析结果比较:利用有限元程序建立竖向循环荷载作用下模型桩—土体系的轴对称有限元模型,并结合试验成果进行比较。本文以下负荷面t_(ij)弹塑性理论为依据,利用室内试验的参数,对循环荷载下桩基础的沉降规律进行研究,为循环荷载下的设计提供理论依据。通过对比模型试验结果与数值模拟计算结果,可以得到以下结论:对于单调载荷,数值计算得到的结果能够比较好地描述模型试验的特性。特别在加载初期阶段,可以很好地描述荷载-位移关系。但是,在后期加载阶段,数值计算得到的结果比模型试验的大一点。在循环载荷条件下,数值计算得到的结果,难以描述模型试验的特性。对于砂土,循环荷载比比较小的情况,计算结果相差较大。但是,对粘土的数值模拟结果表明,在较大循环荷载比条件下,计算结果与试验结果较为接近。另外,数值计算得到的结果,较好的反映了桩的沉降随着循环荷载比、循环振次变化的规律性。
6.通过以上研究工作,得出以下结论:基于有限元基本原理,通过使用下负荷面t_(ij)弹塑性模型结合室内试验数据得到的土工参数,对模型桩在循环荷载下的沉降特性进行模拟计算,并对计算的到的结果进行了比对分析。现将本部分内容总结如下:
1)基于室内试验所获参数,进行数值计算,通过数值计算的结果和模型试验的比较可知:(1)尽管材料不同,但是由于长期荷载的原因,小的循环荷载作用也可以使得累积位移到达一个极限值。然而,当循环荷载值超过其稳定承载值,桩头的位移将显著增长,最终将导致建筑物不利的影响。另外,数值结算在考虑土体的典型力学性能后能够很好地预测循环荷载作用下短桩的行为。(2)计算结果和实测数据的比较显示,数值分析定性地和定量地模拟桩在单向荷载作用下的承载能力。其结果适用于所用的情况。然后,在作用的后期阶段会出现一些差别。(3)模型桩的数值模拟沉降比曲线与实测沉降曲线发展趋势基本一致,而在循环荷载比较小的时候,计算得到的结果偏大。循环荷载比较高的时候,计算结果与试验得到的结果较为吻合。即数值模拟能够定性地描述模型试验结果,但是数值上总是超过其值。(4)室内试验的结果显示,上海粘土和砂的力学特性与日本Toyoura砂和Fujinomori粘土非常相似。
2)关于进一步工作的方向简要的讨论:目前本课题的数值模拟仍存在许多不足之处:(1)采用的参数不是很适当,而且这些参数难以用简单试验获得,因此数值分析方法有很大的不确定性;(2)数值分析方法所使用的物理模型或本构模型有局限性,难以反映实际情况。比如本研究中的模型,主要适用于描述土体在压缩和拉伸下的力学特性。而在本研究中,再加载过程中,塑性应变将会在屈服面内持续增长,不会到达一个稳定状态。因此本模型并不是很适用于该项研究。这些问题都有待进一步解决。
One of the most important problems in the field of geotechnical engineering is prediction of bearing capacity and settlement of pile foundations of structures, especially for port infrastructures which play a significant role in sustaining an economy. In a shipbuilding industry, pile structures, such as a foundation of overhead cranes, are subjected to a repeated loading under daily function. Many researches have already been conducted to investigate the effects of a daily workload on an overhead crane foundation located on the reclaimed Shanghai sand ground. However, the effect of repeated loading on a reclaimed Shanghai soils located has not been fully understood.
The overall objective of this research is to investigate the behavior of crane foundation under the crane load function. This includes experimental and analytical verification. Recently, the study for model test result on this repeat-loading settlement has been conducted. In this thesis, scope of research is mainly aimed at analysis to confirm these experiment results done before through elasto-plastic finite element method. The result of whole numerical analysis is grasped from the nonlinear analysis technique by two-dimensional finite element method using the subloading t_(ij) model (Nakai & Hinokio 2004) as an elastoplastic constitutive model. This model can describe typical stress deformation and strength characteristics of soils such as the influence of intermediate principal stress, the influence of stress path dependency of plastic flow and the influence of density and/or confining pressure. Finally comparisons of observed result and computed result are discussed.
The main contents in this thesis are as follows:
1. First chapter presents the general background of research. With the continuous prospering of the world ships market, Chinese ships industry unceasingly expands the development. In order to enhance the ships product technology content and the attachment value the State Commission of Science and Technology for National Defense Industry carried out "the High-tech Ships Scientific Research Plan", and also vigorously advances the innovation of ship shape and the implementation brand strategy. For these reason, recently three huge ship building bases are being under construction in China. In spite of these progresses day by day in the ships industry, ship factory still lacked crane facilities. To determine the weight caused by daily work experimental space was constructed in the shipbuilding base, and finally we got a result; minimum is several hundred ton; maximum is over one thousand. Pile foundation of crane is withstanding not only outside loading from daily work, but also itself static load. Moreover, it also must withstand the circulation load caused by the crane loading and unloading.
One of the most important considering points of bearing load characteristics is the repeated loading ratio, and another characteristic is the certain circulation load the frequency. According to the major results from recent studies, present research also still could not investigate the behavior of crane foundation under cyclic load function. Therefore, there are urgent needs to conduct a research for a crane foundation behavior under repeated loading. However, in the present design handbooks and the standards in china, there are no special considers of circulate loading leading to settlement problem, moreover in the computation method large number of circulations are not considered. During the actual project, there are huge demands to construct heavy, big, and high, pile foundation in view of the present shipbuilding base, if can be solved well, and it is possible to say that the construction cost will be reduced with the guarantee of project security and significant practical advance. Many researches have already been conducted to investigate the effects of a daily workload on an overhead crane foundation located on the reclaimed Shanghai sand ground. However, the effect of repeated loading on a reclaimed Shanghai soils located has not been fully understood.
In this chapter, recent researches were reviewed with specific focus on theoretical methods for pile-ground interaction and model tests under cyclic loading. During the last few decades, several researchers have studied the behavior of shaft piles using both laboratory tests and theoretical studies. From both reviews, it is clear that research history was divided into three parts. First section was stated in 1960s, investigation was focused on the pile type subjected to cyclic loading as preparation period. In the 1960's and 1970's, second stage was outgrowth period by numerical analysis, of which advancements have made complicated cases possible to calculate and also computational efforts required with analytical models described below are the least. In recent years, extensive researches and developments have been undertaken to predict more practical and complicated conditions, such as three dimensions, by using nonlinear constitutive model.
Soil-pile interaction is a very complicated phenomenon. This complexity is mostly attributed to the soil, rather than to the pile, and it also involves other phenomena such as soil nonlinearity, soil pile gapping, developing of excess pore pressure. Consequently, there are many analytical models which consider this phenomenon with varying levels of emphasis. In general, it is possible to classify the different analytical-numerical models in three groups (1) Continuum solution, (2) Finite element solution and (3) Discrete models. Finite Element Method was frequently used in engineering practice for solving stress analysis problems of which dimensions, mechanical behavior and constitutive model have been chosen by users. In this research, numerical analysis based on Finite Element Method with elastoplastic constitutive model was performed.
2. The second chapter presents outline of model tests where experimental method, equipment, and basic procedure are explained. In this research, model tests for a shaft pile are performed with sand and clay respectively. In advance, characteristic of overhead crane loading was investigated in the practical site research. The size of the model ground is 1.6m in width, 0.9m for sand in height, 1.2m for clay in height. The model pile of 1m in length, outer diameter of 16mm, inside diameter of 12mm (304 stainless steel piles) is set up in the Shanghai sand ground where the penetration depth of the pile is 60cm. Here, scale of tank and pile was decided based on the research Chen Zhu Chang (1989), where boundary affection was discussed deeply.
3. The third chapter describes results of laboratory test for investigating the characteristic of soil sample where laboratory test will describe physical and strength behavior of sand and clay used in model test. In the case of sand, the sample from Chongming Island was dried and disturbed for preparation, and then consolidated-drained triaxial test, cyclic triaxial test and isotropic test were performed by using the triaxial measurement system. In order to get a parameter of peak strength Rcs, consolidated-drained triaxial test have been carried out under consolidated drained condition with constant lateral stressσ_r, whereβis obtained from stress-strain relationship. As for compression index and swelling index, stress path of isotropic consolidation test was illustrated to assume normal consolidation line. After these procedures, finally, the density parameter a_(AF) was determined by Cyclic triaxial compress test with constant lateral stress and q/p amplitude. On the other hand, for clay, sample from experimental tank was prepared under saturated and undisturbed condition, and then consolidated-undrained triaxial test, cyclic triaxial test and isotropic test were performed by using triaxial measurement system. Isotropic consolidation test have been performed to determine compression index. As for the swelling index, one dimensional consolidation test, where clay was subjected to be unload-reload cycle for estimating of the recompression characteristics, were conducted. Moreover, another triaxial test have been carried out under consolidated undrained condition with constant lateral pressure so that a parameter of peak strength ratio was determined.
4. The fourth chapter presents the outline of numerical analyses in axi-symmetric condition. Numerical analysis was carried out to confirm the influence of repeated loading on the single pile where three types of soil ground, dry-sand, saturated-sand and clay with different ground depths and ground water lines were performed. This chapter covers the layout of numerical analyses and parameter of soil used in this research. Although model tests are carried out only for getting loading and settlement relations, in numerical analyses both loading and settlement relations and soil stresses in the vertical direction of ground elements are calculated. In this chapter, three types of soil have been used in these analyses for same diameter of apparatus. The scale of these apparatus is made with the similarity of real experiment. Solid elements are used as single pile in finite element analyses.
In order to predict properly the deformation and the failure of the ground, numerical analysis should be conducted using a simple and generalized constitutive model for soils. In this study, elastoplastic constitutive model for soils named subloading t_(ij) model (Nakai and Hinokio, 2004) is used. This model can describe properly the following typical characteristics of soils, in spite of its small numbers of parameters:(1) Influence of intermediate principal stress on the deformation and strength of soils.(2) Influence of stress path on the direction of plastic flow, and (3) Influence of density and/or confining pressure. To describe the whole characteristics, SMP (Spatially Mobilized Plane) concept was suggested in the first stage. Since the plastic strains are predominant in soil response, Matsuoka-Nakai has established a generalized flow rule, using the SMP, which is an almost independent of path. In the t_(ij) model, stress parameters are the functions of stress invariants but the strain increment parameters are the functions not only of the strain increments but also of the stress invariants. Nakai and Mihara proposed a modified stress tensor t_(ij) that is the function of ordinary stress and its invariants and whose principal directions are coaxial with the principal directions of ordinary stresses. For the next stage, constitutive model with modified t_(ij) was improved to rectify the problem, such as over prediction of volumetric strain and un-stabilization of strain during cyclic loading, the evolution rule of the rotational variable is modified and a subloading surface is introduced. Subloading surface always expands or contracts such that the current state of stress lies on it but can never go beyond the normal yield surface. Both normal yield surface and subloading surface move in the stress space keeping similarity in their shapes. As for the influence of stress path on the direction of plastic flow, it is considered by dividing the plastic strain increment into two components - the plastic strain increment dε_(ij)~(p(AF)) satisfying the associated flow rule in t_(ij)-space as mentioned above and the isotropic plastic strain increment dε_(ij)~(p(IC)) under increasing mean stress - in spite of employing just one yield function and one strain hardening parameter.
5. The fifth chapter represents the comparison of numerical analysis and model test where the influence of repeated load range is discussed. Finally, the sixth chapter summarizes the overview of the main conclusions. The comparisons of experimental and numerical result are summarized as follows: During the monotonic loading test, in spite of different soil ground, it is seen that the calculation result overestimates the displacement result of model test. However, initial condition of load-displacement response is totally matched with observed result. As for the cyclic loading test, through all comparison, it is possible to say that the calculation results overestimate the circulation settlement. Meanwhile, initial stiffness indicates an acceptable value for all cases. Consistently, those analysis results show very good agreement with the results of the model tests in qualitatively. In terms of the comparison of three different multiplied patterns, once the load is applied over specific value, the experiment result shows a significant plastic deformation, of which characteristic is properly illustrated by computed result. For this meaning, it is possible to say that appropriate numerical analysis, which is able to describe a one loading test result well, enable us to distinguish where the huge displacement is observed or not.
6. In this thesis, model tests and numerical analyses were carried out to examine the effects of a daily workload on an overhead crane foundation located on reclaimed sand ground in Shanghai.
The results of these researches are summarized as follows:
(1) In spite of different soil properties, it becomes clear through the experimental and numerical study that under smaller circulation load an accumulative displacement is still achieving the limit value, in spite of the long-term function. However, once the circulation load surpasses a stable tolerance, displacement of pile head will be significant large, which causes the construction adverse effect. Moreover, it is clear that the numerical analysis in which typical mechanical behavior of soils is appropriately taken into account, can predict well the behavior of shaft pile under cyclic loading condition.
(2) By comparing all calculated results with observed ones, it is clear that the numerical analyses can well simulate the observed behavior about bearing capacity under monotonic loading, qualitatively and quantitatively. The results are quite acceptable for all cases. There were, however, some small differences in the behavior during the later stage of loading.
(3) The analysis show very good agreement with the results of the model tests qualitatively. The calculation results, however, overestimate the observed circulation settlement quantitatively.
(4) As for the parameters and characteristics of sand and clay, laboratory tests strongly indicate that properties of Shanghai sand and clay are quite similar to those of Toyoura sand and Fujinomori clay.
For improvement of this research, the following points are indicated:
First, it is possible to say that parameters were not good enough to perform the numerical analysis and still there were many uncertain things in the numerical analysis. Second, it might be a cause of characteristic in constitutive models, having a tendency of plasticity displacement under the subloading surface during the reloading condition. For this reason, without expansion loading, plasticity displacement was continuously increasing whole analysis procedure by subloading t_(ij) model of which hardening rule was located as isotropic hardening rule. In order to overcome these issues, kinematic t_(ij) model following the kinematic hardening rule was suggested in 1999. This model allows the yield surface to rotate in the modified stress-space and hence expresses the stress-induced anisotropy in the deformation behavior of clay. A subloading surface has also been considered in this model for the smooth transition from elastic to fully elastoplastic state. Also it pertinently expresses the increase of strength and stabilization of strains due to over consolidation or cyclic loading. However, in this research, behavior of shaft pile settlement under the repeated loading was acceptable in spite of these issues.
针对循环荷载作用下基础承载特性的研究,以往主要有三类。一是针对海洋平台桩基础的研究。与动力机器荷载相比较,该课题研究具有荷载频率低、加载时间短且桩循环位移幅值大等特点。二是针对高速公路、高速铁路等基础的研究。该课题研究具有加载时间短且加载量级较低等特点。三是针对承受风荷载的一些构筑物桩基础的研究,该研究的特点是结构上部承受的是水平向的循环荷载,对于下部基础,则是循环弯矩的作用。其中,针对海洋平台桩基础的研究与本试验研究相类似,区别在于荷载模式:前者主要是双向循环荷载,而我们仅进行单向循环荷载的研究。前人的模型试验、原型试验以及数值计算的相关研究表明,此类循环荷载对于桩基础沉降带来的影响与单纯的静载并不完全相同,影响桩沉降的因素除结构上部荷载水平外,循环荷载所占总荷载比例、循环周期以及循环振次的影响也是不容忽视的。
然而,在现行设计手册和规范中,并没有专门考虑该类循环荷载对基础沉降影响的相关内容,而且在计算基础沉降时一般也不将吊车等循环荷载考虑进去。针对目前造船基地等需要建设此类重、大、高、深基础的实际工程,若能够较好地解决该问题,有着降低建造成本,保证工程安全的重大意义。
本课题针对以上问题所提出,目的是为了研究吊车循环荷载作用下的桩的循环沉降特性。从该课题的科学本质上来讲,吊车荷载对厂房地基沉降的影响,实质上就是研究循环荷载作用下桩的沉降特性。
为了研究循环荷载下桩基础的沉降规律,首先进行了砂土中的单桩模型试验。然后通过有限元数值分析进行模拟与验证。在有限元分析中,采用了下负荷面t_(ij)弹塑性模型来描述土的本构特性。如不考虑长期作用,在较小循环荷载下的位移仍将达到一个有限的幅值。但是,如果循环荷载超过稳定容许值,桩顶有可能产生危害工程的明显沉降。这种数值分析方法的计算结果与循环荷载作用下的实测值吻合较好。
论文共分为以下几个部分。
1.介绍论文的研究背景、意义和主要内容:介绍循环荷载下桩基础的沉降进展,并进行综述分析。与常规动力机械桩基础相比较,这一课题的研究具有荷载频率较低、加载时间短等特点。然而该问题从本质上说仍属于桩—土动力相互作用的问题,因此仍需要从此处入手进行研究。桩—土动力相互作用研究是土力学与结构力学的交叉研究方向之一,土—结构相互作用研究大致经历了三个阶段。第一个阶段是二十世纪初到六十年代中期,这段时间是理论准备时期,主要研究循环载荷在不同基础情况下的解析解。第二个阶段是六十年代中期到八十年代中期,这一时期不但在理论方面进一步完善,而且在计算方面也得到了较大的提高,能够分析较为复杂的结构与基础之间的相互作用,考虑各种条件的分析方法相继出现,并且在各自的领域内得到合理的解释。第三个阶段是在八十年代中期以后,这一时期的研究进一步深化,各种更为精确更为实用的方法得到了发展,并逐渐向三维分析过渡,而且非线性分析逐渐成为研究的主流方向,同时各种试验及观测也得到了广泛的应用。
2.循环荷载下桩基础的试验:为了使模型试验的结果更切合实际,2006年9月28日、29日在上海某造船基地进行了为期两天的吊车工作荷载现场调查。实地考察的目的在于调查吊车日常工作荷载的特性,以确定模型试验加载的周期、大小等加载特性。
模型试验研究分别以干砂、饱和砂土以及饱和粘土这三种不同土性的土作为桩周土体进行了三组模型试验。每组土都通过静载试验确定单桩的承载力,并通过该值确定不同分组试验的循环荷载大小。每组试验都进行3组不同循环荷载比的加载,循环次数均在2000次左右或者达到破坏。
试验内容:针对吊车交变荷载作用下的桩基础沉降,主要研究桩在动力作用下与静载作用下的异同,以及影响桩动力特性的主要因素。采用快速加载法进行桩的静承载性能试验,采用动力循环加载进行桩动力循环性能试验。根据加载系统条件、研究目的以及实际情况所需,按照循环荷载比分级进行分组加载试验。为了便于确定动荷载作用下的桩极限承载力,并了解桩的行为特点,首先进行模型桩的静力试验。
3.室内试验的内容:在传统的岩土力学研究中,多数是对土样进行各种室内力学特性试验以确定其强度变形关系和力学参数,为数值计算做准备。本章对土体进行常规土工试验,三轴试验,循环三轴试验,并对试验结果进行分析。本次试验用砂取自上海市崇明岛处于河口、砂嘴、砂岛相的东滩地区。为了完成试验,砂土需要烘干并且重塑。另外,粘土取自上海市闵行区华翔路某工地的11m深基坑,为第三层灰色粉质粘土。粘土的制备过程较为繁琐,需要将粘土风干后碾碎,去掉土中夹杂物。模型试验后,从槽内直接取出原状饱和粘土。常规土工试验是分别对试验所用的砂土和粘土进行了常规物理试验、压缩试验、渗透试验、固结试验以及直剪试验等常规土工试验。使用国际先进的GDS三轴仪进行饱和土体的三轴试验研究,与模型试验相结合,从微观、宏观两方面入手,分析了影响桩的沉降的因素。
并将通过试验得到的曲线直接用来确定有限元的模型参数,用来进行模型试验以及原型桩的数值计算。用饱和砂土,对于回弹指数κ和压缩指数λ,进行各向同性下固结排水试验。然后,对于Rcs(排水三轴压缩时主应力比σ_1/σ_3在临界状态下的值)和β物理参量,进行三轴压缩排水试验。为了估计关于各向同性下循环的参数a(材料参量,用于控制ρ的发展速度),进行各向同性下固结排水循环三轴试验。为了估计关于循环的特性进行排水的循环三轴压缩试验。另外,为了评价砂土的密实性,进行了相对密实度试验。用饱和粘土,对于回弹指数κ和压缩指数λ,分别进行各向同性下固结排水试验和一维固结试验。为了估计关于等方性循环的参数排水的等方循环三轴加载试验行为了。然后,对于Rcs,进行三轴压缩不排水试验。通过GDS系统控制的循环三轴试验能够较好的反映土样在循环加卸载作用下的竖向应变、体积应变等参数,同时还能准确的记录加卸载带来的超孔隙水压力的变化。为了估计关于各向同性下循环的参数a,进行各向同性下固结排水循环三轴试验。为了估计循环特性,进行不排水的循环三轴压缩试验。
通过整理对比三轴试验得到的资料,分析了在循环作用下土体的特性。
4.下负荷面t_(ij)弹塑性模型基本概念:
岩土工程问题大体上可以分为两大类:变形问题和稳定问题。传统的岩土工程设计计算方法中,对于变形问题,大多采用先弹性模型;对于稳定问题,采用基于理想刚塑性模型的极限平衡分析方法。本质上来讲,岩土工程的变形和稳定问题并不是完全割裂的两个问题,岩土体的强度和变形间存在密切的联系,本构模型是描述其应力应变关系的数学模型,也即本构关系。岩土材料的真实应力应变关系特性非常复杂,不仅具有非线性、弹塑性、粘塑性,还具有各向异性、剪涨性等特性,同时应力路径、强度发挥以及土的组成、结构、状态和温度等因素均对其有着不同程度的影响。通常对这类问题有两种解决途径:一种是引入简化假设,使其达到能用解析法求解的地步,求得问题在简化状态下的近似解,这种方法并不总是可行,常导致不正确甚至错误的解答。另一种方法是保留问题的复杂性,利用数值计算方法来求得问题的近似数值解。随着计算机技术的飞速发展,已使得采用这种方法解决实际工程问题成为可能,并能得到令人满意的结果。有限元法把结构离散成有限个有限大小的单元,通过在结点互相联结而构成集合体,利用物理上的相似性,把求解偏微分方程的问题变成求解线性方程组的问题,从而利用计算机解线性方程组,可得到工程上满意的数值解。有限元方法是一种基于性能的计算方法,理论上来说有限元方法能够合理的预测结构受荷后的全过程,并且能够反映出试验难以详细测定的参数。随着计算机技术的发展,有限元方法日趋完善,能较好的描述土体的非线性特征。
目前在计算中粘弹性和弹塑性模型占主流,而不论选取何种模型都应该考虑其能否真实有效的反映给定环境下土的物理力学特征。下负荷面t_(ij)弹塑性模型的基本概念。该模型的最大特点就是能够准确地描述土在一般应力状态下的应力应变及剪胀特性。该模型开始于SMP概念。空间滑动面SMP在1974就由Matsuoka& Nakai提出来了,但真正将其融入到土的本构关系,则是在10年后的1984年,由Nakai & Mihara提出了t_(ij)的概念,并相继在1986及1989年,由Nakai提出了t_(ij)粘土模型(t_(ij)clay model,Nakai &Matsuoka,1986)及t_(ij)砂土模型(t_(ij)sandmodel,Nakai,1989)。一般应力状态下的力学特性,加入了由Nakai & Hinokio(2004)提出的下负荷面t_(ij)模型。
首先,介绍岩土类材料的特征面“空间滑动面(SMP面)”。与金属材料不同,土是一种摩擦性材料,经典的金属塑性理论难以解释土的变形特性。各种材料在三维应力作用下的变形和强度是工程学科中一个普遍的重要问题,吸引了不少研究者进行大量的试验和理论研究。在多轴应力状态下材料的变形和强度问题是非常复杂的,解决的基本思路是将复杂问题简单化,通过一个应力状态的函数将多维问题归一化,所提出的各种屈服准则和破坏准则就是其中代表性的研究成果。实践证明,对岩土类材料,SMP准则是最好的强度准则之一。Matsuoka和Nakai等提出,土颗粒在剪应力作用下的运动状态是由摩擦定律控制的,即土颗粒滑动最可能发生在剪应力与正应力之比达到最大的平面,即为空间滑动面的概念(Spatial Mobilized Plane,SMP)。即在三维应力状态下,破坏是沿着SMP面滑动的。SMP面的方向余弦用I_1,I_2,I_3(分别为第一应力不变量、第二应力不变量和第三应力不变量)来表示。Toyoura砂的三轴压缩和三轴拉伸试验得到的试验数据,用SMP面上的应力应变参量来整理,所得结果趋近于一条直线,说明岩土材料的应力比和应变增量比的关系(剪胀方程),在SMP面上具有归一性。另外,砂的真三轴试验得到的结果显示,SMP面上的应力比τ_(SMP)/σ_(SMP)与γ_(SMP),ε_(SMP)有唯一的、确定的关系,即岩土材料的面上应力比和应变具有归一性。SMP准则实际上是三维空间中的摩擦准则,也可以认为是在个主应力下平均化了的Mohr-Coulomb准则。在SMP面上,岩土材料的应力一应变及强度具有归一性。在三维应力空间中,通过SMP面可以唯一确定岩土材料的应力应变特性。
其次介绍,“变换应力张量t_(ij)”。在SMP面,沿应力Lode角θ(σ_1轴正方向的夹角)θ=15°,30°,45°的径向应力路径时,试验所得的粘土的应变,箭头代表应变增的大小和方向,对于岩土材料,与其塑性应变相比,弹性应变在总的应变中所占比例很小,所以也可以认为各箭头的方向基本反映了塑性应变增量的方向。Nakai通过试验研究得到了这种分叉现象。这是考虑了中间主应力的影响而得到的一个必然结果。修正后的三重屈服面应力t_(ij)-应变模型也可以反映土体的应力-应变分叉特性。修正后的模型很好的反映了一般应力状态下土体的应变分叉特性。变换应力张量t_(ij)用平面的法向矢量和SMP面的单位法向矢量。
其次将介绍下负荷面的概念。剑桥模型(Cam-Clay Model)对正常固结重塑粘土的三轴压缩试验能作出较为准确的描述,但对超固结粘土及自然土,即具有结构的土,则不能给出准确的描述。在经典土力学弹塑性理论(包括剑桥模型)中,在卸载及再加载过程中的土的应力应变关系是被假定为弹性的。Hashiguchi& Ueno(1977)提出的下负荷面概念的基本特征如下:连续平滑的弹塑性应力应变关系。下负荷面模型的卸载·再加载过程中的应力应变关系,经典弹塑性理论的应力应变关系明显不同。下负荷面是经过现有应力点并和正常屈服面几何相似的面。下负荷面必定经过现在应力状态,而且随应力变化而变化。也就是说,现在应力都存在于下负荷面上。因此加载准则比经典弹塑性理论的简单,不需要判断应力状态是否到达屈服面,并且可以简化程序编制。根据以上土的一般应力状态下的力学特性,加入了由Nakai & Hinokio(2004)提出的下负荷面t_(ij)模型。t_(ij)下负荷面模型不仅可以很好地描述单向加载试验,对交变载荷或逆反加载破坏实验,同样可以做出非常准确的描述。需要再次强调的是,所有理论模拟都使用同样的物理参量。还有,下负荷面t_(ij)模型内,Nakai等人(2004)提出的下负荷面t_(ij)模型中采用和修正剑桥模型类似的剪切应力比与塑性剪胀比之间的关系式,即剪应力比与塑性剪胀比之间存在一定的关系。其中物理参量β可由实验唯一确定。β=1时粗实线为一直线,就相当于原始剑桥模型的关系式了。另外,实际上是与剑桥模型中指出的塑性体积应变由等向固结及剪切变形两部分组成的概念是完全一致的。根据以上的推导,最后需要做的就是确定塑性应变增量的大小。
5.模型试验结果与数值分析结果比较:利用有限元程序建立竖向循环荷载作用下模型桩—土体系的轴对称有限元模型,并结合试验成果进行比较。本文以下负荷面t_(ij)弹塑性理论为依据,利用室内试验的参数,对循环荷载下桩基础的沉降规律进行研究,为循环荷载下的设计提供理论依据。通过对比模型试验结果与数值模拟计算结果,可以得到以下结论:对于单调载荷,数值计算得到的结果能够比较好地描述模型试验的特性。特别在加载初期阶段,可以很好地描述荷载-位移关系。但是,在后期加载阶段,数值计算得到的结果比模型试验的大一点。在循环载荷条件下,数值计算得到的结果,难以描述模型试验的特性。对于砂土,循环荷载比比较小的情况,计算结果相差较大。但是,对粘土的数值模拟结果表明,在较大循环荷载比条件下,计算结果与试验结果较为接近。另外,数值计算得到的结果,较好的反映了桩的沉降随着循环荷载比、循环振次变化的规律性。
6.通过以上研究工作,得出以下结论:基于有限元基本原理,通过使用下负荷面t_(ij)弹塑性模型结合室内试验数据得到的土工参数,对模型桩在循环荷载下的沉降特性进行模拟计算,并对计算的到的结果进行了比对分析。现将本部分内容总结如下:
1)基于室内试验所获参数,进行数值计算,通过数值计算的结果和模型试验的比较可知:(1)尽管材料不同,但是由于长期荷载的原因,小的循环荷载作用也可以使得累积位移到达一个极限值。然而,当循环荷载值超过其稳定承载值,桩头的位移将显著增长,最终将导致建筑物不利的影响。另外,数值结算在考虑土体的典型力学性能后能够很好地预测循环荷载作用下短桩的行为。(2)计算结果和实测数据的比较显示,数值分析定性地和定量地模拟桩在单向荷载作用下的承载能力。其结果适用于所用的情况。然后,在作用的后期阶段会出现一些差别。(3)模型桩的数值模拟沉降比曲线与实测沉降曲线发展趋势基本一致,而在循环荷载比较小的时候,计算得到的结果偏大。循环荷载比较高的时候,计算结果与试验得到的结果较为吻合。即数值模拟能够定性地描述模型试验结果,但是数值上总是超过其值。(4)室内试验的结果显示,上海粘土和砂的力学特性与日本Toyoura砂和Fujinomori粘土非常相似。
2)关于进一步工作的方向简要的讨论:目前本课题的数值模拟仍存在许多不足之处:(1)采用的参数不是很适当,而且这些参数难以用简单试验获得,因此数值分析方法有很大的不确定性;(2)数值分析方法所使用的物理模型或本构模型有局限性,难以反映实际情况。比如本研究中的模型,主要适用于描述土体在压缩和拉伸下的力学特性。而在本研究中,再加载过程中,塑性应变将会在屈服面内持续增长,不会到达一个稳定状态。因此本模型并不是很适用于该项研究。这些问题都有待进一步解决。
One of the most important problems in the field of geotechnical engineering is prediction of bearing capacity and settlement of pile foundations of structures, especially for port infrastructures which play a significant role in sustaining an economy. In a shipbuilding industry, pile structures, such as a foundation of overhead cranes, are subjected to a repeated loading under daily function. Many researches have already been conducted to investigate the effects of a daily workload on an overhead crane foundation located on the reclaimed Shanghai sand ground. However, the effect of repeated loading on a reclaimed Shanghai soils located has not been fully understood.
The overall objective of this research is to investigate the behavior of crane foundation under the crane load function. This includes experimental and analytical verification. Recently, the study for model test result on this repeat-loading settlement has been conducted. In this thesis, scope of research is mainly aimed at analysis to confirm these experiment results done before through elasto-plastic finite element method. The result of whole numerical analysis is grasped from the nonlinear analysis technique by two-dimensional finite element method using the subloading t_(ij) model (Nakai & Hinokio 2004) as an elastoplastic constitutive model. This model can describe typical stress deformation and strength characteristics of soils such as the influence of intermediate principal stress, the influence of stress path dependency of plastic flow and the influence of density and/or confining pressure. Finally comparisons of observed result and computed result are discussed.
The main contents in this thesis are as follows:
1. First chapter presents the general background of research. With the continuous prospering of the world ships market, Chinese ships industry unceasingly expands the development. In order to enhance the ships product technology content and the attachment value the State Commission of Science and Technology for National Defense Industry carried out "the High-tech Ships Scientific Research Plan", and also vigorously advances the innovation of ship shape and the implementation brand strategy. For these reason, recently three huge ship building bases are being under construction in China. In spite of these progresses day by day in the ships industry, ship factory still lacked crane facilities. To determine the weight caused by daily work experimental space was constructed in the shipbuilding base, and finally we got a result; minimum is several hundred ton; maximum is over one thousand. Pile foundation of crane is withstanding not only outside loading from daily work, but also itself static load. Moreover, it also must withstand the circulation load caused by the crane loading and unloading.
One of the most important considering points of bearing load characteristics is the repeated loading ratio, and another characteristic is the certain circulation load the frequency. According to the major results from recent studies, present research also still could not investigate the behavior of crane foundation under cyclic load function. Therefore, there are urgent needs to conduct a research for a crane foundation behavior under repeated loading. However, in the present design handbooks and the standards in china, there are no special considers of circulate loading leading to settlement problem, moreover in the computation method large number of circulations are not considered. During the actual project, there are huge demands to construct heavy, big, and high, pile foundation in view of the present shipbuilding base, if can be solved well, and it is possible to say that the construction cost will be reduced with the guarantee of project security and significant practical advance. Many researches have already been conducted to investigate the effects of a daily workload on an overhead crane foundation located on the reclaimed Shanghai sand ground. However, the effect of repeated loading on a reclaimed Shanghai soils located has not been fully understood.
In this chapter, recent researches were reviewed with specific focus on theoretical methods for pile-ground interaction and model tests under cyclic loading. During the last few decades, several researchers have studied the behavior of shaft piles using both laboratory tests and theoretical studies. From both reviews, it is clear that research history was divided into three parts. First section was stated in 1960s, investigation was focused on the pile type subjected to cyclic loading as preparation period. In the 1960's and 1970's, second stage was outgrowth period by numerical analysis, of which advancements have made complicated cases possible to calculate and also computational efforts required with analytical models described below are the least. In recent years, extensive researches and developments have been undertaken to predict more practical and complicated conditions, such as three dimensions, by using nonlinear constitutive model.
Soil-pile interaction is a very complicated phenomenon. This complexity is mostly attributed to the soil, rather than to the pile, and it also involves other phenomena such as soil nonlinearity, soil pile gapping, developing of excess pore pressure. Consequently, there are many analytical models which consider this phenomenon with varying levels of emphasis. In general, it is possible to classify the different analytical-numerical models in three groups (1) Continuum solution, (2) Finite element solution and (3) Discrete models. Finite Element Method was frequently used in engineering practice for solving stress analysis problems of which dimensions, mechanical behavior and constitutive model have been chosen by users. In this research, numerical analysis based on Finite Element Method with elastoplastic constitutive model was performed.
2. The second chapter presents outline of model tests where experimental method, equipment, and basic procedure are explained. In this research, model tests for a shaft pile are performed with sand and clay respectively. In advance, characteristic of overhead crane loading was investigated in the practical site research. The size of the model ground is 1.6m in width, 0.9m for sand in height, 1.2m for clay in height. The model pile of 1m in length, outer diameter of 16mm, inside diameter of 12mm (304 stainless steel piles) is set up in the Shanghai sand ground where the penetration depth of the pile is 60cm. Here, scale of tank and pile was decided based on the research Chen Zhu Chang (1989), where boundary affection was discussed deeply.
3. The third chapter describes results of laboratory test for investigating the characteristic of soil sample where laboratory test will describe physical and strength behavior of sand and clay used in model test. In the case of sand, the sample from Chongming Island was dried and disturbed for preparation, and then consolidated-drained triaxial test, cyclic triaxial test and isotropic test were performed by using the triaxial measurement system. In order to get a parameter of peak strength Rcs, consolidated-drained triaxial test have been carried out under consolidated drained condition with constant lateral stressσ_r, whereβis obtained from stress-strain relationship. As for compression index and swelling index, stress path of isotropic consolidation test was illustrated to assume normal consolidation line. After these procedures, finally, the density parameter a_(AF) was determined by Cyclic triaxial compress test with constant lateral stress and q/p amplitude. On the other hand, for clay, sample from experimental tank was prepared under saturated and undisturbed condition, and then consolidated-undrained triaxial test, cyclic triaxial test and isotropic test were performed by using triaxial measurement system. Isotropic consolidation test have been performed to determine compression index. As for the swelling index, one dimensional consolidation test, where clay was subjected to be unload-reload cycle for estimating of the recompression characteristics, were conducted. Moreover, another triaxial test have been carried out under consolidated undrained condition with constant lateral pressure so that a parameter of peak strength ratio was determined.
4. The fourth chapter presents the outline of numerical analyses in axi-symmetric condition. Numerical analysis was carried out to confirm the influence of repeated loading on the single pile where three types of soil ground, dry-sand, saturated-sand and clay with different ground depths and ground water lines were performed. This chapter covers the layout of numerical analyses and parameter of soil used in this research. Although model tests are carried out only for getting loading and settlement relations, in numerical analyses both loading and settlement relations and soil stresses in the vertical direction of ground elements are calculated. In this chapter, three types of soil have been used in these analyses for same diameter of apparatus. The scale of these apparatus is made with the similarity of real experiment. Solid elements are used as single pile in finite element analyses.
In order to predict properly the deformation and the failure of the ground, numerical analysis should be conducted using a simple and generalized constitutive model for soils. In this study, elastoplastic constitutive model for soils named subloading t_(ij) model (Nakai and Hinokio, 2004) is used. This model can describe properly the following typical characteristics of soils, in spite of its small numbers of parameters:(1) Influence of intermediate principal stress on the deformation and strength of soils.(2) Influence of stress path on the direction of plastic flow, and (3) Influence of density and/or confining pressure. To describe the whole characteristics, SMP (Spatially Mobilized Plane) concept was suggested in the first stage. Since the plastic strains are predominant in soil response, Matsuoka-Nakai has established a generalized flow rule, using the SMP, which is an almost independent of path. In the t_(ij) model, stress parameters are the functions of stress invariants but the strain increment parameters are the functions not only of the strain increments but also of the stress invariants. Nakai and Mihara proposed a modified stress tensor t_(ij) that is the function of ordinary stress and its invariants and whose principal directions are coaxial with the principal directions of ordinary stresses. For the next stage, constitutive model with modified t_(ij) was improved to rectify the problem, such as over prediction of volumetric strain and un-stabilization of strain during cyclic loading, the evolution rule of the rotational variable is modified and a subloading surface is introduced. Subloading surface always expands or contracts such that the current state of stress lies on it but can never go beyond the normal yield surface. Both normal yield surface and subloading surface move in the stress space keeping similarity in their shapes. As for the influence of stress path on the direction of plastic flow, it is considered by dividing the plastic strain increment into two components - the plastic strain increment dε_(ij)~(p(AF)) satisfying the associated flow rule in t_(ij)-space as mentioned above and the isotropic plastic strain increment dε_(ij)~(p(IC)) under increasing mean stress - in spite of employing just one yield function and one strain hardening parameter.
5. The fifth chapter represents the comparison of numerical analysis and model test where the influence of repeated load range is discussed. Finally, the sixth chapter summarizes the overview of the main conclusions. The comparisons of experimental and numerical result are summarized as follows: During the monotonic loading test, in spite of different soil ground, it is seen that the calculation result overestimates the displacement result of model test. However, initial condition of load-displacement response is totally matched with observed result. As for the cyclic loading test, through all comparison, it is possible to say that the calculation results overestimate the circulation settlement. Meanwhile, initial stiffness indicates an acceptable value for all cases. Consistently, those analysis results show very good agreement with the results of the model tests in qualitatively. In terms of the comparison of three different multiplied patterns, once the load is applied over specific value, the experiment result shows a significant plastic deformation, of which characteristic is properly illustrated by computed result. For this meaning, it is possible to say that appropriate numerical analysis, which is able to describe a one loading test result well, enable us to distinguish where the huge displacement is observed or not.
6. In this thesis, model tests and numerical analyses were carried out to examine the effects of a daily workload on an overhead crane foundation located on reclaimed sand ground in Shanghai.
The results of these researches are summarized as follows:
(1) In spite of different soil properties, it becomes clear through the experimental and numerical study that under smaller circulation load an accumulative displacement is still achieving the limit value, in spite of the long-term function. However, once the circulation load surpasses a stable tolerance, displacement of pile head will be significant large, which causes the construction adverse effect. Moreover, it is clear that the numerical analysis in which typical mechanical behavior of soils is appropriately taken into account, can predict well the behavior of shaft pile under cyclic loading condition.
(2) By comparing all calculated results with observed ones, it is clear that the numerical analyses can well simulate the observed behavior about bearing capacity under monotonic loading, qualitatively and quantitatively. The results are quite acceptable for all cases. There were, however, some small differences in the behavior during the later stage of loading.
(3) The analysis show very good agreement with the results of the model tests qualitatively. The calculation results, however, overestimate the observed circulation settlement quantitatively.
(4) As for the parameters and characteristics of sand and clay, laboratory tests strongly indicate that properties of Shanghai sand and clay are quite similar to those of Toyoura sand and Fujinomori clay.
For improvement of this research, the following points are indicated:
First, it is possible to say that parameters were not good enough to perform the numerical analysis and still there were many uncertain things in the numerical analysis. Second, it might be a cause of characteristic in constitutive models, having a tendency of plasticity displacement under the subloading surface during the reloading condition. For this reason, without expansion loading, plasticity displacement was continuously increasing whole analysis procedure by subloading t_(ij) model of which hardening rule was located as isotropic hardening rule. In order to overcome these issues, kinematic t_(ij) model following the kinematic hardening rule was suggested in 1999. This model allows the yield surface to rotate in the modified stress-space and hence expresses the stress-induced anisotropy in the deformation behavior of clay. A subloading surface has also been considered in this model for the smooth transition from elastic to fully elastoplastic state. Also it pertinently expresses the increase of strength and stabilization of strains due to over consolidation or cyclic loading. However, in this research, behavior of shaft pile settlement under the repeated loading was acceptable in spite of these issues.
引文
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[5].徐和,陈竹昌,任陈宝.在竖向循环荷载下砂土中模型桩的试验研究.岩土工程学报.1989,11(4):64-71
[6].华南理工大学,东南大学,浙江大学等地基及基础(第三版)北京:中国建筑工业出版社1998
[7].桩基工程手册编写委员会 桩基工程手册 北京:中国建筑工业出版社,1995
[8].中华人民共和国国家标准,起重机设计规范,GB3811-83
[9].中华人民共和国行业标准,建筑桩基技术规范,JTJ94-94
[10].中华人民共和国行业标准,公路桥涵地基与基础设计规范,JTJ024-85
[11].Matsuoka,H.and Nakai,T.Stress deformation and strength characteristics of soil under three different principal stresses,proc.Japan Society of Civil Engineering(JSCE):1974,No 232,pp.59-70.
[12].Nakai,T.& Matsuoka,H.Constitutive equation for soils based on the extended concept of "Spatial Mobilized Plane" and its application to finite element analysis,Soil and Foundations,1983,Vol.12,No2,pp.1-18.
[13].Nakai,T.& Mihara,Y.A New Quantity for Soils and lts application to Elastoplastic Constitutive Models.Soil and Foundations,1984,Vol.24 No.2,pp.82-94.
[14].Nakai,T.and Hinokio,M.A simple elastoplastic model for normally and over consolidated soils with unified material parameters.Soils and Foundations,2004,Vol.44,No.2
[15].Broms,B.B.Lateral Resistance of Piles in Cohesionless Soils,Journal of Soil Mechanics and Foundations Division,ASCE,1964,Vol.90(3):pp.123-156.
[16].Broms,B.B.Design of Laterally Loaded Piles,Journal of Soil Mechanics and Foundations Division.ASCE,1965,Vol.91(3):pp.79-99.
[17].Finn,W.D.L.and Fujita,N.Piles in Liquefiable Soils:Seismic Analysis and Design Issues,Soil Dynamics and Earthquake Engineering,2002,22:pp.731-742.
[18].Hetenyi,Beams on Elastic Foundation,University of Michigan Press,1946
[19].Ishibashi,I.and Zhange,X.Unified Dynamic Shear Moduli and Damping Ratios of Sand and Clay, Soil and Foundation, 1993, Vol 33. No. 1: pp. 182-191
[20].Kagawa, T. Effect of Liquefaction on Lateral Pile response, ASCE, Geotechnical Special Publication, 1992, No. 34, pp. 207-223.
[21].Kagawa, T. and Kraft, L.M. Lateral Pile Response during Earthquakes, Geotechnical Engineering, 1981, Vol. 107(12): pp. 1713-1731.
[22].Kagawa, T., Minowa, C, Abe, A. and Oda. S. Shaking table Tests on and analyses of piles in liquefying sands, Earthquake Geotechnical Engineering Proceedings of the first international conference, IS-Tokyo, 1995, pp. 699-705
[23].Liyanathirana, D. S. and Poulos, H.G A Numerical Model for Dynamic Soil Liquefaction Analysis, Soil Dynamics and Earthquake Engineering, 2002, 22: pp. 1007-101
[24].Maheshwari, B.K., Truman, K.Z., Gould, P, L. and EI Naggar, M.H.Three Dimensional Nonlinear Seismic Analysis of Single Piles Using Finite Element Model: Effects of Plasticity of Soil, ASCE, International Journal of Geomechanics, 2005, Vol. 5,No. 1: pp. 35-44.
[25].Martin, G.R., Finn, L.W.D. and Seed, H.B. Fundamentals of Liquefaction under Cyclic Loading, J. of Geotechnical Engineering, 1975, Vol. 101(5): pp. 423-438.
[26].Martin, P. P. and Seed, H. B. Simplified Procedure for Effective Stress Analysis of Ground Response, J. of Geotechnical Engineering division, 1979, Vol. 105: No. GT6, pp. 739-758.
[27].Matlock, H., Foo, S.H.C. and Bryant, L.M. Simulation of Lateral Pile Behavior under Earthquake Motion, Proc, Earthquake Engineering and Soil Dynamic, Pasadena, California, 1978, pp. 600-619.
[28].Miwa, S., Ikeda, T. and Sato, T. Damage Process of Pile Foundation in Liquefied Ground during Strong Ground Motion, 2005, Soil Dynamics and Earthquake Engineering, (Article in Press): pp. 1-12.
[29].Naggar, M. H. E. and Novak, M. Nonlinear Lateral interaction in Pile Dynamics, Soil Dynamics and Earthquake Engineering, 1995,14, pp. 141 - 157.
[30].Naggar, M. H. E. and Novak, M. Nonlinear Analysis for Dynamic Lateral Pile Response, Soil Dynamics and Earthquake Engineering, 1996,15: pp. 233-244.
[31].Nogami, T. and Konagai, K. Time Domain Axial Response of Dynamically Loaded Single Piles, J. of Engineering Mechanics, ASCE, 1986, Vol. 112 No. 11: pp.1512-1525.
[32].Nogami, T. and Konagai, K. Time Domain Flexural Response of Dynamically Loaded Single Piles, J. of Engineering Mechanics, ASCE, 1998, Vol. 144(9): pp.1512-1525.
[33].Nogami, T., Otani, J., Konagai, K. and Chen, H.L. Nonlinear Soil Pile Interaction Model for Dynamic Lateral Motion, J. Geotechnical Engineering, 1992, Vol. 118(1): pp. 89-106.
[34].Nogami, T., Zhu, J.X. and Ito, T. First and Second Order Dynamic Subgrade Models for Soil Pile Interaction, ASCE, Geotechnical Special Publication .No. 34 Piles Under Dynamic Loads, 1992, pp. 187-206
[35].Novak, M. Dynamic Stiffness and Damping of Piles, Canadian Geotechnical J. 1974, Vol. 11: pp. 574-598.
[36]. Novak, M., Nogami, T. and Aboul Ella, F. Dynamic Soil Reaction for Plane Strain Case, J. Engineering. Mechanics, ASCE, 1978, Vol. 104(4): pp. 953-595
[37]. Novak, M. and Sheta, M. Approximate Approach to Contact Effects of Piles, ASCE, Proceeding, Dynamic Response of Pile Foundation: Analytical Aspects, 1980, pp. 53-79.
[38]. Novak, M., Nogami, T. and Aboul Ella, F. Dynamic Soil Reaction for Plane Strain Case, J. of Engg. Mechanics, ASCE, 1978, Vol. 104(4): pp. 953-595
[39].Briaud, J.-L, and Garland, E., Influence of loading rate on axially loaded piles in clay. PRAC 1984, pp. 82-42
[40].Dunnavant, T. W., Clukey, E. C , and Murff, J. D. Effects of cyclic loading and pile flexibility on axial pile capacities in clay. Proc. Offshore Tech. Conf., Society of Petroleum Engineers, 1990, OTC 6378.
[41].Gallagher, K. A., and St. John, H. D. Field scale model studies of piles as anchorages for buoyant platforms. Proc. European Offshore Petroleum Conf., Society of Petroleum Engineers, 1980, pp.334-360.
[42].Karlsrud, K., and Kaugen, T. Behavior of piles in clay under cyclic axial, 1985
[43].Karlsrud, K., Nadim, F., and Haugen, T. Pile in clay under cyclic axial loading field tests and computational modeling. Proc. 3rd Int. Conf, on Numerical Methods in Offshore Piling, French Petroleum Institute, Nates, France, 1986, pp.145-160
[44]. Kraft, L. M., Jr., Cox, W. R., and Verner, E. A., Pile load tests: Cyclic loads and varying load rates. J. Geotech. Engrg. Div., ASCE, 1981,107(1): pp.233-245.
[45]. Kraft, L. M., Jr., Ray, R. P., and Kagawa, T. Theoretical T-Z Curves. I. Geotech. Engrg. Div., ASCE, 1981,107(11): 110-121.
[46].Matlock, H., and Foo, S. H. C. Axial analysis of piles using a hysteretic and degrading soil model. Proc. Conf, on Numerical Methods in Offshore Piling, Inst, of Civ. Engrs. 1979, pp.276-291.
[47].McAnoy, R. P. L, Cashman, A. C , and Purvis, O. Cyclic tensile testing of a pile in glacial till. Proc. 2nd Int. Conf, on Numerical Methods in Offshore Piling, University of Texas, 1982, pp.121-133.
[48].McClelland, B., and Ehlers, C. J. Offshore geotechnical site investigations. Planning and design of fixed offshore platforms, Bramlette McClelland, and Michael D. Reifel, eds., Van Nostrand Reinhold Co., New York, N.Y. 1986, pp.224-284.
[49]. Pelletier, J. H., and Doyle, E. H. Tension capacity in silty clays-Beta pile test. Proc. 2nd Int. Conf, on Numerical Methods in Offshore Piling, University of Texas, 1982, pp.334-420.
[50].Pelletier, J. H., and Sgouros, G E. Shear transfer behavior of a 30-inch pile in silty clay. Proc. Offshore Tech. Conf., OTC 5407, Houston, Texas, 1987, pp.455-470.
[51].Poulos, H. G Cyclic axial pile response-Alternative analyses. Proc. Conf, on Geotech. Practice in Offshore Engrg., ASCE, 1983, pp.455-490.
[52]. Randolph, M. F., and Wroth, P. C. Analysis and deformation of vertically loaded piles. Geotech. Eng. Div., ASCE, 1978,104(12): pp.55-69
[53].CHOWDHURY E Q(Nagoya Inst. Technol.), NAKAI T(Nagoya Inst. Technol.) A model for cyclic behavior of clay. Proceedings of Japan National Conference on Geotechnical Engineering, 1999, VOL. 34th;NO.;pp..71-72
[54].Yasufuku, N., Hyde, A.F.L.: Pile end bearing capacity in crushable sands. Geotechnique, 1995,45(4): pp.663-676
[55].Shahin, M. D. Behavior of soils during shallow tunneling. PhD dissertation, Nagoya Institute of Thechnology. 2003
[2].陈竹昌,徐和.土类对竖向循环荷载下桩性状的影响.同济大学学报.1989,17(3):329-336
[3].陈竹昌,徐和.桩和桩基的试验与分析.见:高大钊主编.软土地基理论与实践.北京:中国建筑工业出版社,1992:117-124
[4].陈竹昌.国外土动力学研究的动向.见:汪闻韶主编.第三节全国土动力学学术会议论文集.上海:同济大学出版社,1990:71-90
[5].徐和,陈竹昌,任陈宝.在竖向循环荷载下砂土中模型桩的试验研究.岩土工程学报.1989,11(4):64-71
[6].华南理工大学,东南大学,浙江大学等地基及基础(第三版)北京:中国建筑工业出版社1998
[7].桩基工程手册编写委员会 桩基工程手册 北京:中国建筑工业出版社,1995
[8].中华人民共和国国家标准,起重机设计规范,GB3811-83
[9].中华人民共和国行业标准,建筑桩基技术规范,JTJ94-94
[10].中华人民共和国行业标准,公路桥涵地基与基础设计规范,JTJ024-85
[11].Matsuoka,H.and Nakai,T.Stress deformation and strength characteristics of soil under three different principal stresses,proc.Japan Society of Civil Engineering(JSCE):1974,No 232,pp.59-70.
[12].Nakai,T.& Matsuoka,H.Constitutive equation for soils based on the extended concept of "Spatial Mobilized Plane" and its application to finite element analysis,Soil and Foundations,1983,Vol.12,No2,pp.1-18.
[13].Nakai,T.& Mihara,Y.A New Quantity for Soils and lts application to Elastoplastic Constitutive Models.Soil and Foundations,1984,Vol.24 No.2,pp.82-94.
[14].Nakai,T.and Hinokio,M.A simple elastoplastic model for normally and over consolidated soils with unified material parameters.Soils and Foundations,2004,Vol.44,No.2
[15].Broms,B.B.Lateral Resistance of Piles in Cohesionless Soils,Journal of Soil Mechanics and Foundations Division,ASCE,1964,Vol.90(3):pp.123-156.
[16].Broms,B.B.Design of Laterally Loaded Piles,Journal of Soil Mechanics and Foundations Division.ASCE,1965,Vol.91(3):pp.79-99.
[17].Finn,W.D.L.and Fujita,N.Piles in Liquefiable Soils:Seismic Analysis and Design Issues,Soil Dynamics and Earthquake Engineering,2002,22:pp.731-742.
[18].Hetenyi,Beams on Elastic Foundation,University of Michigan Press,1946
[19].Ishibashi,I.and Zhange,X.Unified Dynamic Shear Moduli and Damping Ratios of Sand and Clay, Soil and Foundation, 1993, Vol 33. No. 1: pp. 182-191
[20].Kagawa, T. Effect of Liquefaction on Lateral Pile response, ASCE, Geotechnical Special Publication, 1992, No. 34, pp. 207-223.
[21].Kagawa, T. and Kraft, L.M. Lateral Pile Response during Earthquakes, Geotechnical Engineering, 1981, Vol. 107(12): pp. 1713-1731.
[22].Kagawa, T., Minowa, C, Abe, A. and Oda. S. Shaking table Tests on and analyses of piles in liquefying sands, Earthquake Geotechnical Engineering Proceedings of the first international conference, IS-Tokyo, 1995, pp. 699-705
[23].Liyanathirana, D. S. and Poulos, H.G A Numerical Model for Dynamic Soil Liquefaction Analysis, Soil Dynamics and Earthquake Engineering, 2002, 22: pp. 1007-101
[24].Maheshwari, B.K., Truman, K.Z., Gould, P, L. and EI Naggar, M.H.Three Dimensional Nonlinear Seismic Analysis of Single Piles Using Finite Element Model: Effects of Plasticity of Soil, ASCE, International Journal of Geomechanics, 2005, Vol. 5,No. 1: pp. 35-44.
[25].Martin, G.R., Finn, L.W.D. and Seed, H.B. Fundamentals of Liquefaction under Cyclic Loading, J. of Geotechnical Engineering, 1975, Vol. 101(5): pp. 423-438.
[26].Martin, P. P. and Seed, H. B. Simplified Procedure for Effective Stress Analysis of Ground Response, J. of Geotechnical Engineering division, 1979, Vol. 105: No. GT6, pp. 739-758.
[27].Matlock, H., Foo, S.H.C. and Bryant, L.M. Simulation of Lateral Pile Behavior under Earthquake Motion, Proc, Earthquake Engineering and Soil Dynamic, Pasadena, California, 1978, pp. 600-619.
[28].Miwa, S., Ikeda, T. and Sato, T. Damage Process of Pile Foundation in Liquefied Ground during Strong Ground Motion, 2005, Soil Dynamics and Earthquake Engineering, (Article in Press): pp. 1-12.
[29].Naggar, M. H. E. and Novak, M. Nonlinear Lateral interaction in Pile Dynamics, Soil Dynamics and Earthquake Engineering, 1995,14, pp. 141 - 157.
[30].Naggar, M. H. E. and Novak, M. Nonlinear Analysis for Dynamic Lateral Pile Response, Soil Dynamics and Earthquake Engineering, 1996,15: pp. 233-244.
[31].Nogami, T. and Konagai, K. Time Domain Axial Response of Dynamically Loaded Single Piles, J. of Engineering Mechanics, ASCE, 1986, Vol. 112 No. 11: pp.1512-1525.
[32].Nogami, T. and Konagai, K. Time Domain Flexural Response of Dynamically Loaded Single Piles, J. of Engineering Mechanics, ASCE, 1998, Vol. 144(9): pp.1512-1525.
[33].Nogami, T., Otani, J., Konagai, K. and Chen, H.L. Nonlinear Soil Pile Interaction Model for Dynamic Lateral Motion, J. Geotechnical Engineering, 1992, Vol. 118(1): pp. 89-106.
[34].Nogami, T., Zhu, J.X. and Ito, T. First and Second Order Dynamic Subgrade Models for Soil Pile Interaction, ASCE, Geotechnical Special Publication .No. 34 Piles Under Dynamic Loads, 1992, pp. 187-206
[35].Novak, M. Dynamic Stiffness and Damping of Piles, Canadian Geotechnical J. 1974, Vol. 11: pp. 574-598.
[36]. Novak, M., Nogami, T. and Aboul Ella, F. Dynamic Soil Reaction for Plane Strain Case, J. Engineering. Mechanics, ASCE, 1978, Vol. 104(4): pp. 953-595
[37]. Novak, M. and Sheta, M. Approximate Approach to Contact Effects of Piles, ASCE, Proceeding, Dynamic Response of Pile Foundation: Analytical Aspects, 1980, pp. 53-79.
[38]. Novak, M., Nogami, T. and Aboul Ella, F. Dynamic Soil Reaction for Plane Strain Case, J. of Engg. Mechanics, ASCE, 1978, Vol. 104(4): pp. 953-595
[39].Briaud, J.-L, and Garland, E., Influence of loading rate on axially loaded piles in clay. PRAC 1984, pp. 82-42
[40].Dunnavant, T. W., Clukey, E. C , and Murff, J. D. Effects of cyclic loading and pile flexibility on axial pile capacities in clay. Proc. Offshore Tech. Conf., Society of Petroleum Engineers, 1990, OTC 6378.
[41].Gallagher, K. A., and St. John, H. D. Field scale model studies of piles as anchorages for buoyant platforms. Proc. European Offshore Petroleum Conf., Society of Petroleum Engineers, 1980, pp.334-360.
[42].Karlsrud, K., and Kaugen, T. Behavior of piles in clay under cyclic axial, 1985
[43].Karlsrud, K., Nadim, F., and Haugen, T. Pile in clay under cyclic axial loading field tests and computational modeling. Proc. 3rd Int. Conf, on Numerical Methods in Offshore Piling, French Petroleum Institute, Nates, France, 1986, pp.145-160
[44]. Kraft, L. M., Jr., Cox, W. R., and Verner, E. A., Pile load tests: Cyclic loads and varying load rates. J. Geotech. Engrg. Div., ASCE, 1981,107(1): pp.233-245.
[45]. Kraft, L. M., Jr., Ray, R. P., and Kagawa, T. Theoretical T-Z Curves. I. Geotech. Engrg. Div., ASCE, 1981,107(11): 110-121.
[46].Matlock, H., and Foo, S. H. C. Axial analysis of piles using a hysteretic and degrading soil model. Proc. Conf, on Numerical Methods in Offshore Piling, Inst, of Civ. Engrs. 1979, pp.276-291.
[47].McAnoy, R. P. L, Cashman, A. C , and Purvis, O. Cyclic tensile testing of a pile in glacial till. Proc. 2nd Int. Conf, on Numerical Methods in Offshore Piling, University of Texas, 1982, pp.121-133.
[48].McClelland, B., and Ehlers, C. J. Offshore geotechnical site investigations. Planning and design of fixed offshore platforms, Bramlette McClelland, and Michael D. Reifel, eds., Van Nostrand Reinhold Co., New York, N.Y. 1986, pp.224-284.
[49]. Pelletier, J. H., and Doyle, E. H. Tension capacity in silty clays-Beta pile test. Proc. 2nd Int. Conf, on Numerical Methods in Offshore Piling, University of Texas, 1982, pp.334-420.
[50].Pelletier, J. H., and Sgouros, G E. Shear transfer behavior of a 30-inch pile in silty clay. Proc. Offshore Tech. Conf., OTC 5407, Houston, Texas, 1987, pp.455-470.
[51].Poulos, H. G Cyclic axial pile response-Alternative analyses. Proc. Conf, on Geotech. Practice in Offshore Engrg., ASCE, 1983, pp.455-490.
[52]. Randolph, M. F., and Wroth, P. C. Analysis and deformation of vertically loaded piles. Geotech. Eng. Div., ASCE, 1978,104(12): pp.55-69
[53].CHOWDHURY E Q(Nagoya Inst. Technol.), NAKAI T(Nagoya Inst. Technol.) A model for cyclic behavior of clay. Proceedings of Japan National Conference on Geotechnical Engineering, 1999, VOL. 34th;NO.;pp..71-72
[54].Yasufuku, N., Hyde, A.F.L.: Pile end bearing capacity in crushable sands. Geotechnique, 1995,45(4): pp.663-676
[55].Shahin, M. D. Behavior of soils during shallow tunneling. PhD dissertation, Nagoya Institute of Thechnology. 2003