摘要
岩土工程有限元计算一般采用增量塑性本构模型来考虑材料非线性,对几何非线性即大变形问题考虑较少。而对于基础连续贯入或拔出、静力触探、边坡滑移和固结沉降等问题,土体失稳过程都是局部化变形形成和发展的结果,其累积塑性应变已超过小应变的界限,土体变形或结构位移对计算结果影响较大。对于这些问题,工程中还往往要求了解土体或结构连续变形直至破坏的灾变全过程,这就需要采用考虑几何非线性的大变形数值方法进行分析。
近年来,一些学者分别采用TL、UL和ALE大变形有限元方法,分析了各种土工大变形问题。其中,属于ALE范畴的RITSS方法是一种简便实用的大变形有限元方法,它在小变形有限元模型的基础上通过网格重剖分和应力插值技术实现大变形分析,目前已被广泛应用于模拟基础连续变形过程并取得了很好的成果。但现有大变形数值分析相关文献多为平面应变或轴对称的二维问题,三维土工大变形分析成果报道很少。这是因为三维大变形分析有限元实现比较复杂,比如考虑几何大变形的有限元列式推导繁琐,三维计算网格自动剖分与控制、边界变形追踪困难,以及计算规模过大导致效率低下等。而一些实际工程问题用二维模拟难以得到精确解答,比如方形和矩形基础贯入问题、倾斜圆形和方形锚板的承载力问题以及三维锚板的上拔调节旋转问题等,都需要采用三维大变形数值方法进行分析。
因此,本文在二维RITSS大变形有限元方法的基础上,提出了一种稳定可靠的三维应力插值方法,实现了三维网格的全自动剖分,从而开发了一种能在普通微机上执行的适用于土工分析的三维大变形有限元方法3D-RITSS,并采用该方法深入分析了双层地基方形基础刺入破坏和三维锚板旋转调节这两种三维土工大变形问题,以期为工程设计提供一定依据。另外,对于锚板承载力问题,多数文献都是针对均质土中的水平或竖直的锚板,研究锚板倾角和正常固结土非均质性对承载力影响的相关工作还不多,因此本文通过大量二维和三维小变形有限元计算分析了各种因素对倾斜锚板抗拔承载力的影响。本文主要工作包括:
1)将二维RITSS大变形有限元方法推广到三维情况,主要贡献包括:对多种单元类型进行了详细的比较与分析,找到了适用于三维大变形土工分析的单元类型——20结点非结构化六面体单元,它不但适于网格自动剖分,而且在模拟饱和黏土地基(三维不可压缩材料)时能够给出较准确的极限承载力;针对该单元类型提出了一种稳定高效的应力插值方法UED;开发了一种简便的三维结点节理单元模拟基础与土的相互作用;采用B样条曲线簇拟合变形后的边界自由面,实现了大变形计算的全自动运行;最后通过算例验证了3D-RITSS方法的可靠性和稳定性。
2)采用3D-RITSS大变形有限元法模拟了方形基础连续贯入上强下弱双层黏土地基的过程,分析了上层土厚度和上下土层强度比对基础发生刺入破坏时的临界承载力系数和临界深度的影响。贯入过程的承载力系数-沉降曲线以图表形式给出,并给出了近似公式以便于工程设计应用。给出了贯入过程中土体滑裂面形状和塑性区的发展情况,为解析和半解析计算提供一定依据。
3)采用二维小变形有限元法分析了倾斜条形锚板在均质和正常固结黏土中的承载力,着重探讨了锚-土黏结方式(始终黏结或立即分开)、锚板倾角、土体自重以及正常固结土非均质度等因素对承载力的影响。分析了土重叠加方法对正常固结黏土中立即分开形式锚板的适用性,并给出了不同埋深和倾角情况下锚板的极限承载力系数N_c~*。分析了土体非均质度对正常固结土中锚板承载力系数N_(ck)和极限承载力系数N_(ck)~*的影响。提出了任意正常固结黏土中任意角度条形锚板承载力系数的计算步骤和公式,为工程设计提供依据。采用2D-RITSS大变形有限元方法分析了考虑土重情况下锚-土分离的条件,结果表明γH/c是决定锚-土是否分离的重要标尺。
4)采用三维小变形有限元法分析了倾斜圆形和方形锚板在均质黏土中的承载力,探讨了倾角对承载力和土体流动机制的影响,并验证了利用已知水平和竖直锚板承载力计算任意倾斜角度锚板承载力的经验公式对圆形和方形锚板的适用性,验证了浅埋水平锚板的简化计算公式。
5)采用3D-RITSS大变形有限元法分析了三维条形和方形锚板在正常固结黏土中的旋转调节过程,着重分析了锚板加载偏心率、上拔倾角和几何形状(长宽比)对旋转调节过程中埋深损失的影响。分析了锚板旋转调节过程中承载力和土体流动机制的变化过程。计算结果表明加载偏心率e/B对埋深损失有重要影响,上拔倾角对埋深损失也有一定影响。在旋转调节过程中,方形锚板同条形锚板的上拔过程以及最终埋深损失都十分接近。方形锚板的最大承载力系数约为条形锚板的1.10～1.19倍。
本论文工作得到国家自然科学基金(编号:50679093,50538080,50578029)、教育部留学归国人员科研启动基金以及教育部创新团队发展计划(编号:IRT0518)的资助,在此一并表示感谢。
In soil mechanics,many incremental plasticity models have been proposed in attempts to deal with the issue of material nonlinearity.But little result has been reported regarding the effect of geometrical nonlinearity,i.e.,large deformation/displacement.However,the large deformation behaviors are involved in many geotechnical problems,such as the penetration/pullout of piles,cone penetrometer,soil slope failure,and large strain soil consolidation,et al.In these cases the soil failures may be due to the development and accumulation of localized soil deformation.The large deformation upon the overall geometry of the structure has great effect on the structure bearing capacity and should not be ignored. Moreover,the deformation or failure processes also need to be investigated for some engineering practices.Therefore,large deformation numerical procedures considering the effect of geometrical nonlinearity are required for these problems.
In recent years,TL,UL or ALE large strain finite element methods have been ultilized to study many geotechnical problems involving large deformation.Among these large strain FE methods,RITSS is a convenient and robust one.It falls essentially within the ALE category, in which,conventional small strain FE analysis is combined with fully automatic mesh genetration and plane linear stress interpolation techniques to deal with large deformation problems in soil.RITSS method has already been applied to simulate the continuous deforming process of various foundations in soil.And many valuable results have been obtained.However,most of the available publications focus on plane strain or axisymmetric 2-D problems,and the implementations of the 3-D large deformation analyses into the problems of practical geotechnical engineering are relatively rare.The reasons may include the difficulties in deriving the 3-D large deformation FE formulations,generating and controlling the 3-D mesh automatically,tracing the deformed boundary in 3-D space,and include the unacceptable time consuming in calculation.On the other hand,2-D numerical analyses would not be accurate enough for some practical problems,such as the penetration of square/rectangular footings,the uplift resistance of the inclined circular and square anchors, and the keying behavior of 3-D anchors,et al.3-D large deformation analyses are essential for these problems.
In order to deal with the above 3-D problems,an efficient and robust 3-D large deformation numerical method,which can be implemented on personal computers,was proposed in the present thesis.Based on the 2D-RITSS method,a convenient and robust 3-D stress interpolation method and an automatically 3-D mesh generation approach were presented.Thus a procedure of 3-D large deformation FE analysis was proposed.Furthermore, the present 3D-RITSS method was applied to investigate the behaviors of punch:through failures of square footings on double layered clays.This method was also applied to simulate the keying processes of 3-D plate anchors.Some conclusions of these two problems were obtained,which may be valuable to the engineering practice.In addition,the emphasis of most of the published researches about the anchor uplift resistance problems was on vertical or horizontal plate anchors in uniform clay,the results related to inclined anchors in normally consolidated(NC)clay were relatively rare.So in the present thesis a large amount of 2-D and 3-D small strain FE analyses were implemented to calculate the uplift resistance of inclined palte anchors in NC clay.The research work carried out in the present thesis could be summarized as follows:
1)The 2D-RITSS approach is developed to deal with 3-D geotechnical problems.Several types of elements are tested and the unstructured 20-node hexahedral element is found to work well both for generating mesh automatically.and for predicting collapse loads accurately for 3-D undrained geotechnical problems involving material incompressibility. A convenient method named UED is proposed to interpolate the stress variables of the new elements after each remeshing.A 3-D nodal joint element is developed to simulate the soil-structure interface.Aseries of B-spline lines are used to fit the deformed surface boundary.Thus the 3-D RITSS large deformation FE procedure can be run automatically. Finally the 3-D RITSS method is proved to be efficient and robust by several numerical examples.
2)The present 3D-RITSS method is used to simulate the continuous penetration processes of square footings into double layered clays with a strong layer overlying a weak one. The effects of the relative thickness of the top layer and the shear,strength ratio of the bottom layer to the top layer soil on the punch-through critical be,aring capacity factors and critical depths are investigated.The load-displacement curves during penetration of various cases are presented in chart form and are also fitted by approximate equations, which may be convenient for practical design.The developments of soil flow mechanisms and plastic zone distributions during penetration,which may be useful for analytical and semi-analytical calculations,are also presented:
3)2-D small strain FE analyses are implemented to investigate the uplift resistances of strip anchors in uniform and normally consolicated clay.The effects of the soil-structure interface(attached or vented),anchor inclination,the soil self-weight,and the soil nonhomogeneity on the anchor bearing capacity are analyzed in detail.For the vented plate anchors in NC clay considering soil weight,the bearing capacity factor N_c can also be calculated from the weightless result N_(c0)plus the dimensionless parameterγH/c,but remaining not larger than the limit uplift resistance factor N_c~*.The inclination angleβhas great effect on the N_c~* for shallow anchors.The larger is theβ,the lower is the N_c~*.The effects of the soil nonhomogeneity on the bearing capacity factor N_(ck)and limit bearing capacity factor N_(ck)~* of plate anchots in NC clay are both investigated.A systematic design procedure and approximate equations are proposed for the bearing capacity factors of plate anchors with any inclinations in uniform or NC clay.The 2-D RITSS approach is used to investigate the breakaway behavior of the soil beneath,the anchor.The results show that the dimensionless parameterγH/c is an important factor which determines whether the bottom soil would break away from the anchor or,not.
4)3-D small strain FE analyses are implemented to investigate the uplift resistances of inclined circular and square plate anchors.And the effects of anchor inclination on the uplift resistance and on the soil flow mechanisms are analyzed in detail.An equation which is to calculate the N_c of an inclined anchor from the N_c of vertical and horizontal anchors,is verified to be suitable for 3-D circular and square plate anchors.A simplified equation is proposed and is proved to be accurate for shallow horizontal anchors.
5)The 3D-RITSS method is also used to simulate the keying processes of 3-D strip and square anchors in NC clay.The effects of loading eccentricity,pullout angle and anchor aspect ratio(length/width)on the embedment loss during keying are investigated.The developments of the uplift resistance and the soil flow mechanisms are both presented. The numerical results show that the loading eccentricity e/B has a great effect on the value of embedment loss.The pullout angle has also a little effect on the embedment loss. The keying process and embedment loss of square anchors are almost the same as those of the strip anchors.The maximum uplift resistance factors of square anchors are about 1.10 to 1.19 times of those of strip anchors.
The work in this thesis is surported by the National Natural Science Foundation of China (Grant Nos:50679093,50538080,50578029),the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry and the Program for Changjiang Schorlars and Innovative Research Team in-University (IRT0518).These supports are gratefully acknowledged.
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