基于微结构指标主成分分析的沉桩挤土效应研究

前期研究已认识到,土的宏观力学性质及其表现从本质上应取决于土的微观结构。在结构性较强的软土中沉桩,桩周土体内部结构会发生显著变化,土体的强度与变形性质是这种内在变化的宏观表现,研究土体微观结构与宏观力学行为变化之间的关系,对认知土体的力学性质,从微观出发去认识沉桩挤土效应的机理,指导工程实践具有重要地理论和现实意义。本文基于天津滨海地基土实际静压桩工程,在沉桩的不同时刻、沿桩身的不同位置取桩周土体原状土样进行室内三轴固结不排水剪切试验,得到土体强度指标参数,同时进行对应的微观结构试验,得到垂直与水平方向的10个微结构指标。采用主成分分析方法,在微结构指标中提取3个主成分,较好地分析了土体微结构特征。研究表明: 3个主成分与黏聚力之间存在较好的相关关系,而与内摩擦角之间的相关性相对较弱; 第一主成分对各微结构信息的提取比较充分,第二、第三主成分是对第一主成分未反映信息的进一步补充。同时主成分分析表明,土体微结构性质对强度性质起控制作用,在沉桩过程中,近地表和下部土层宏观力学指标表现出了相反的变化规律。主成分分析方法较好地表述了土体的微结构性质,为进一步从微观入手解释沉桩挤土效应机理提供了有力依据。     

沉桩挤土位移应力变分解和积分泛函收敛性分析

静压桩是一种挤土桩,沉桩挤土作用将引发很多工程问题. 实际的贯桩过程发生在半无限成层土体中,且单桩具有空间轴对称性,桩的形状和长度也各不相同,因此需要研究半无限土体中一般桩孔扩张的特性和解. 通过对沉桩挤土的研究现状和实际存在问题的分析,建立沉桩挤土三维模型、设定符合变分约束条件的位移函数. 根据研究区域的积分泛函得到问题的位移和应力解. 由于能量泛函涉及三维广义积分问题,所以重点对积分和解的收敛性进行了分析,并应用经典土压力理论、小孔扩张理论和Ansys计算结果对计算和分析结果进行验证.      

基于有限元强度折减法的复式抗滑桩内力计算及桩土作用机理分析

在边坡、滑坡防治工程中已得到广泛应用的“П”形、“h”形等复合式抗滑桩,由于其多属于复杂的超静定结构,受力形式或荷载分配方式仍存在较大争议,桩土相互作用关系复杂,传统方法在求解其内力时往往面临较大困难。有限单元法和强度折减法的结合为解决这类问题提供了一条可行的途径,该方法求解这一类问题时不需要假定抗滑桩系统的结构类型以及岩土体作用在抗滑桩上的荷载分布形式,因此获得的计算结果往往更符合实际情况。本文以某隧道进口岸坡的“П”形抗滑桩为例,在详细分析岸坡稳定性状况以及可能失稳模式的基础上,采用有限元强度折减法对桩身内力、桩土作用关系以及治理效果进行计算和分析,结果表明利用有限元强度折减法求解这类具有复杂超静定结构抗滑桩系统的内力是一条有效的途径,计算结果对该治理工程的设计具有一定的应用参考意义。     

饱和黏土中考虑土塞效应的柱孔扩张分析

为研究静压开口管桩的挤土效应,在考虑土塞效应的前提下,采用柱孔扩张理论对管桩压入饱和软黏土时的扩孔过程进行了分析。基于可以合理描述黏性土强度特性的拓展Lade-Duncan屈服准则,对柱孔扩张过程中的桩周土体进行了弹塑性理论推导,得到了桩周土体应力场、位移场、塑性区半径、极限扩孔压力和塑性区外侧边界径向位移的解析解。在此基础上,通过室内模型实验获得了软土中开口管桩的土塞高度,且运用等效替代法验证了理论解答的合理性;并通过引入土塞长度比对参数进行了分析。结果表明:在沉桩过程中随着土塞长度比的增大,塑性区半径、极限扩孔压力和塑性区外侧边界径向位移均逐渐减小;土体的剪切模量和黏聚力对沉桩挤土效应有显著的影响,挤土效应始终随着土塞效应的增强而减弱。该研究成果对开口管桩工程的实际应用具有一定理论指导意义。     

沉桩扩孔速度对非饱和土中柱形扩孔挤土效应的影响

以柱形孔扩张模型模拟沉桩过程,推导出考虑速度因素时桩周土体的位移、应力解析解.以弹塑性交界面处单元体的运动情况作为参考标准,将区域内任何一点的应力、位移描述成塑性区半径和扩张后土体单元距孔心的距离函数.采用小变形理论求解出r处的径向扩张速度与弹塑性交界面的径向扩张速度之比应满足的关系式.最后结合沉桩扩孔速度的已知条件推导出沉桩后桩周土体塑性区、破坏区的范围.整个土体范围内应力、位移表达式形式仍与不考虑沉桩扩孔速度因素时一样.对比分析表明:相同桩径条件下,随着沉桩扩孔速度的增加,沉桩影响范围也越来越大;随着桩径的增加,沉桩影响范围受沉桩扩孔速度的影响程度则降低.此外,相应于一定的桩径存在一个临界速度,当沉桩扩孔速度大于临界速度时,需要考虑速度因素;小于临界速度时不考虑则是偏于安全的.本文的研究成果主要适合于软土.     

灌注桩桩土相互作用试验及有限元模拟研究

以灌注桩桩土相互作用的原位试验为基础, 结合西安土层结构、性质; 采用有限单元法对黄土地区的砼灌注桩桩—土相互作用进行仿真模拟, 研究了桩土相互作用、荷载的传递规律、桩土相对位移与桩侧摩阻力的关系。通过桩载试验资料对比, 得出三维有限单元法的模拟结果与实测值相近, 该研究进一步揭示了桩土相互作用的实质, 为最优桩长的选取和单桩承载力的确定奠定了基础。     

从深基坑护壁桩桩身弯矩分析桩侧土压力

根据某高层建筑深基坑护壁桩从实测钢筋应力求得的桩身变矩,用数值分析的方法,对桩侧土压力的分布和大小进行了反分析,所得结果与经典土压力理论有显差别,中用土拱的概念对桩侧土压力的分布进行了解释,并给出了桩侧土压力建议图式。     

考虑土-结构相互作用效应的三维桩基结构动力有限元分析

结合简化阻抗法建立了三维相互作用结构的动力有限元分析模型,导出了考虑群桩刚体、惯性效应作用时的结构相互作用时程积分方程式,以近乎纯结构有限元的建模途径合理地反映出桩-土-上部结构在水平地震作用下的动力相互作用特性。模型中引入具有桩(筏)-土阻抗特性的弹阻单元来描述不同群桩布置、土层状况因素对体系反应的参与作用,而在动力方程中竖向SV剪切波经桩土刚体相互作用产生的水平、摇摆分量对体系的影响亦得以体现。20层桩承刚框架结构的动力分析表明:较柔的桩、土基础使得体系的SSI效应增强,但其参与程度与群桩效应相关,而结构构件内力较不考虑相互作用时有较大折减;应用该法可精确、快速地进行复杂上、下部结构时程反应分析。     

侧移土体被动桩成拱效应及主动侧土压力计算

采用三维数值模型模拟土体水平位移条件下被动桩的成拱效应。分析结果表明,被动桩的成拱效应和桩间距关系最为密切,桩间距较小时,侧移土体在桩周附近呈现出明显的土拱效应,应力等值线密集,相互连通成一整体,并向两端突出,桩间距增大时土拱效应减弱;随着作用于土体侧向荷载的增大,土拱效应增强,桩周应力区增大。在数值分析的基础上,以T.Itos土压力为依据,考虑土体的实际分层,探讨了考虑土拱效应的土压力计算方法,给出了被动桩计算模式,最后将简化方法与数值分析的桩侧土压力进行了对比。     

单桩沉降可靠度的配点谱随机有限元分析

基于配点的谱随机有限元方法(CSFEM)可以实现随机分析与确定性有限元分析的解耦,并通过采样,重复多次确定性有限元分析,从而得到随机有限元的解.本文以处于粘土中的柔性单桩为例,用CSFEM 方法对线性土弹簧及非线性土弹簧时的单桩沉降进行随机有限元分析,计算了沉降可靠度指标,并与蒙特卡罗模拟的结果对比.算例结果显示,CS...     

Variable penalty method for finite element analysis of incompressible flow

A new scheme is applied for increasing the accuracy of the penalty finite element method for incompressible flow by systematically varying from element to element the sign and magnitude of the penalty parameter λ, which enters through ?.v + p/λ = 0, an approximation to the incompressibility constraint. Not only is the error in this approximation reduced beyond that achievable with a constant λ, but also digital truncation error is lowered when it is aggravated by large variations in element size, a critical problem when the discretization must resolve thin boundary layers. The magnitude of the penalty parameter can be chosen smaller than when λ is constant, which also reduces digital truncation error; hence a shorter word-length computer is more likely to succeed. Error estimates of the method are reviewed. Boundary conditions which circumvent the hazards of aphysical pressure modes are catalogued for the finite element basis set chosen here. In order to compare performance, the variable penalty method is pitted against the conventional penalty method with constant λ in several Stokes flow case studies.     

A transient finite element analysis of natural convection around a horizontal hot cylinder

This paper presents an advanced method for a 2-dimensional analysis of transient natural convection by finite element method. The present method, based on stream function—vorticity formulation, could get rid of numerical errors and constraint of perpendicular mesh subdivision, since we excluded a finite difference approximation of vorticity on no-slip boundaries. A considerable effect of upwind weighting function was examined. The method was successfully applied to a problem of natural convection around a horizontal hot cylinder.     

A compatible mixed design and analysis finite element method for the design of turbomachinery blades

In this paper the development of a compatible mixed design and analysis method is presented for the quasi-three-dimensional finite element blade-to-blade program FINSUP. The method consists of two parts. The first is concerned with a method of modelling changes to a blade shape using a surface transpiration model. The second is concerned with determining the relationship between the displaced blade surface and the surface velocity distribution. It is shown that with the Newton-Raphson procedure adopted in the method a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. A number of examples are given to illustrate how the mixed design and analysis mode can be used in practical blade design.     

Development and application of an adaptive finite element method to reaction-diffusion equations

An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.     

A frequency–time domain finite element model for tidal circulation based on the least-squares harmonic analysis method

An iterative type harmonic finite element model is developed for solving the full non-linear form of the shallow water equations. The scheme iteratively updates time histories of the non-linear terms which are then harmonically decomposed and used as forcing terms for the linear sets of equations which result from the harmonic separation of the shallow water equations. A least-squares harmonic analysis procedure is used to decompose the non-linear forcing terms. This procedure allows for the very efficient separation of extremely closely spaced harmonics, since it is highly selective with respect to the frequencies it considers. In addition tailoring the procedure and using very specific time steps and sampling periods significantly reduces the number of time samplings points required. In conjunction with the iterative nature of our scheme, the least-squares procedure makes the scheme entirely general, allows for the direct assessment of all tidal constituents, including compound tides, and permits the clear cut and complete investigation of their mutual interaction through the non-linearities. In addition this procedure readily computes very-low-frequency or residual type circulations. The FE formulation used shows a very low degree of spurious oscillations while remaining quite simple to implement. This control on nodal oscillations is especially important due to the energy transfer mechanisms involved in this type of iterative scheme. In an example application the effects of the various non-linear overtide and compound tide type interactions are examined. It is demonstrated that not only are compound tides significant relative to the overtides, but they also influence the overtides.     

基于有限断裂法和比例边界有限元法的裂纹扩展模拟

基于有限断裂法和比例边界有限元法提出了一种裂缝开裂过程模拟的数值模型。采用基于有限断裂法的混合断裂准则作为起裂及扩展的判断标准,当最大环向应力和能量释放率同时达到其临界值时,裂缝扩展。结合多边形比例边界有限元法,可以半解析地求解裂尖区域附近的应力场和位移场,在裂尖附近无需富集即可获得高精度的解。计算能量释放率时,只需将裂尖多边形内的裂尖位置局部调整,无需改变整体网格的分布,网格重剖分的工作量降至最少。裂缝扩展步长通过混合断裂准则确定,避免了人为假设的随意性,并可以实现裂缝变步长扩展的模拟,更符合实际情况。通过对四点剪切梁的复合型裂缝扩展过程的模拟,对本文模型进行了验证,并应用于重力坝模型的裂缝扩展模拟,计算结果表明,本文提出的模型简单易行且精度较高。     

Comparison between the traction and pressure-imposed boundary conditions in finite element flow analysis

A formulation is developed to impose pressure-prescribed boundary conditions in the penalty finite element method. Some numerical experiments for the Poiseuille flow problem are performed to compare it with the conventional traction-prescribed boundary condition. Also the incorrectness of the traction-free outlet boundary condition for contained-flows is studied with explanatory numerical examples. Discussion is focused on the inlet and outlet boundary conditions to simulate fully developed flows. Finally, the three-dimensional flow in a bifurcated pipe is analysed with the proposed formulation.     

A finite element approximation of steady flow through a rotating non-aligned straight tube

A finite element solution is developed for a penalty function formulation of the equations which govern the steady motion of a Newtonian fluid through a pipe that rotates about an axis not parallel to its own. The motion in this system is driven by the Coriolis acceleration, which has components in the axial direction as well as in the transverse plane of the pipe. The relative magnitudes of these components significantly affect the qualitative and quantitative nature of the primary and secondary flow field. The present results compare favourably with those of previously reported experimental and theoretical studies over a wide range of flow regimes.     

基于扩展有限元法的混凝土细观断裂破坏过程模拟

扩展有限元法（XFEM）是分析不连续力学问题（特别是断裂问题）的一种有效的数值方法。在常规的有限元位移模式中,基于单位分解的思想加入一个跳跃函数和渐进缝尖位移场来对不连续体附近的节点自由度进行局部加强,从而反映了位移的不连续性。介绍了扩展有限元的基本原理,给出了扩展有限元进行混凝土开裂及裂纹扩展的分析方法,最后采用扩展有限元法模拟了湿筛混凝土单轴拉伸作用下及WinklerL-型混凝土板的细观断裂破坏过程。分析了混凝土裂纹萌生、扩展的过程及破坏形态,数值结果与实验结果吻合良好。研究表明：扩展有限元法通过特定的位移模式,使裂纹两侧不连续位移场的表达独立于网格划分,能有效地模拟混凝土材料细观断裂破坏过程。     

A finite element for incompressible plane flows of fluids with memory

Flows of fluids with single-integral memory functionals are considered. Evaluation of the stress at a material point involves the deformation history of that point, and a dominant computational cost in finite element approximation is the construction of streamlines. It is shown that the simple crossed-triangle macro-element is in many ways an ideal finite element for the difficult non-linear, non-self-adjoint problem. The question as to whether this element produces convergent velocity and pressure solutions is addressed in the light of its failure to satisfy the discrete LBB condition. The effect of the element's ill-disposed (‘spurious’) pressure modes is discussed, and a pressure smoothing scheme is given which gives good results in Newtonian and non-Newtonian flows at various Reynolds and Deborah numbers. As an example of the element's success in modelling such flows, the problem of pressure differences in flows over transverse slots is studied numerically. The results are compared with experimental observations of such flows. The effect of fluid memory on the relation between first normal-stress differences and pressure differences is investigated.