考虑土体各向异性的沉降计算

在前人研究的基础上,利用积分法推导出了均布矩形荷载作用下考虑土体各向异性的附加应力计算公式;选用双曲型模型描述土体的变形特性,进而发展了一种考虑土体各向异性的沉降计算方法;选用实例进行了计算分析。结果表明,土体的各向异性对沉降计算结果有较为显著的影响。      

矩形基础受垂直荷载作用下地基土中任意点的竖向附加应力系数计算公式

矩形基础受垂直均布荷载作用下,地基土中任一点的附加应力虽然可以通过角点法和应力叠加原理求得,但是除了矩形角点下各点计算较容易外,其余的点计算均较繁琐;矩形基础受垂直三角形分布荷载作用下,矩形基底面积垂直投影范围内地基土中各点的附加应力虽然可以通过角点法和应力叠加原理求得,但是除基底荷载分布为零的边的角点下各点计算较容易外,其余的点计算都很繁琐,而矩形基底面积外的点则无法计算。本文通过推导得出两个公式,借助电脑,能很容易地计算矩形基础受垂直荷载作用下地基土中任意点的附加应力系数,并通过计算对比,验证了公式是正确的。     

Y型桩桩端阻力产生附加应力的分析计算

Y型沉管灌注桩截面形式复杂,截面几何特性存在4个独立控制变量、8个积分区间。Y型桩桩端均布荷载在地基内部任意点产生附加应力系数的解析表达式求解困难,目前尚无得出简单的解析表达式。借助数学分析软件Mathematica的NIntegrate数值积分功能,以及Geddes推导应力解的思想,得出了Y型桩桩端均布荷载作用在地基内部任意点竖向附加应力系数的数值计算方法,经校核有很高精度。分析了Y型截面4个独立变量外包圆半径R、模板弧度?、开弧间距s、夹角度数? 对附加应力系数的影响及采用Geddes应力解计算产生的误差。分析了随荷载作用面积变化、计算深度变化Y型、三角形、矩形、方形、圆形、圆环、H形、T形截面桩端均布荷载作用在地基内部时截面中心点下附加应力系数的差异及变化规律。将考虑Y型桩截面形状的附加应力计算方法应用于Y型桩单桩的沉降计算,计算结果与静载荷试验数据吻合较好。     

非均布荷载作用下各向异性地基应力分布

在集中力作用下应力表达式的基础上推导一组非均布荷载作用下考虑地基各向异性的应力分布公式,并讨论非均布荷载,地基各向异性对地基应力分布的影响。     

垂直荷载作用下地基附加应力系数公式推导

地基附加应力系数是地基沉降计算的一个重要参数。目前,该参数主要通过查表内插获得,虽然用起来较为方便,但结果总会因人有所差异。在本文中,笔者利用积分法导出了矩形、圆形、条形等一些常见基础在均布及三角形荷载下地基附加应力系数的计算公式,编制了相应的Excel程序计算表,使得地基附加应力系数的获取更加方便,可更方便工程技术人员在今后实际工作中的运用。     

基于三维破坏面的地基极限承载力计算方法

为确定作用在给定基础形状地基土上的极限承载力,对基底下的土体进行网格划分,先假定一矩形均布荷载作用在此地基土上,运用布氏解的积分公式,结合角点法,编制MATLAB语言程序,求出每个网格结点上的附加应力,进而求得每个网格结点上的主应力,根据破坏准则,由程序找出破坏点的坐标,利用MATLAB的图形处理功能,把破坏点的坐标在坐标图中显示出来。继续加大矩形均布荷载,直至这些破坏点在坐标图中刚好能够形成一个连续的破坏面,此时的矩形均布荷载即为该地基的极限承载力。此方法不仅可以有效地避免地基承载力经验公式中一些不合理的假设带来的误差,更符合实际情况,而且可以直观地了解到地基土的三维破坏面。     

挡土墙受局部连续荷载作用的附加土压力

求解附加应力的布西涅斯克解答和弗拉曼解答与朗肯土压力理论结合,可用来计算挡土墙受矩形铅直均布荷载和条形铅直均布荷载作用,在墙背处引起的附加主动土压力和附加被动土压力的变化情况,这种计算方法可以较准确的考虑荷载作用型式,作用位置,作用范围和极限平衡状态的影响,可以反映外荷通过填土传递过程的变化,得出的附加土压力较小。     

偏心荷载作用下软弱下卧层承载力验算方法研究

以均布荷载作用下软弱下卧层竖向附加应力的简化计算方法为基础,导出了偏心荷载作用下软弱下卧层竖向附加应力的简化计算公式,并提出偏心荷载作用下软弱下卧层承载力验算的基本原则。     

条形荷载作用于挡土墙的侧压力计算

挡土墙受连续铅直均布荷载作用时的侧压力以往只是按朗肯作图法近似计算,其中存在不阔问题。本文从计算附加应力的布西涅斯克解答出发,假定条形作用荷载是矩形作用荷载的特殊情况,分别讨论条形铅直均布荷载生趣于挡土墙和平行于挡土墙作用时,在墙背处引起的侧压力计算公式。     

半无限弹性体内作用竖向矩形和条形均布荷载时的应力计算公式

传统土力学处理岩土工程问题时,经常采用弹性力学方法分析土中应力分布。土中应力通常依据较为简单的Boussinesq解计算,该解答假定荷载作用于土体表面;但是,建筑物基础一般都埋置在地表以下一定深度,此时,应依据Mindlin解计算应力分布。在半无限弹性体内作用竖向矩形和条形均布荷载时的应力分布对计算基础沉降以及分析基坑尺寸对稳定性和变形的影响均有重要意义,在其他岩土工程问题中也有诸多应用。尽管文献[1-2]给出了相关计算公式,但存在几处错误。基于Mindlin解,通过积分重新推导了在半无限体内部作用竖向矩形均布荷载时应力分布的解析表达式,进一步得到了条形均布荷载作用时应力分布的解析表达式,这2组公式均与文献[1-2]给出的结果存在不同。最后,采用数值积分方法验证了新给出的2组公式的正确性。     

垂直荷载下地基平均附加应力系数公式推导

按照《建筑地基基础设计规范》（以下简称《规范》）进行地基沉降计算,要使用地基平均附加应力系数。目前,该参数一般都是通过查表内插获得,虽然方便,但结果会因人而异。笔者利用积分法导出常见基础下地基平均附加应力系数计算公式,并编制了Excel计算表。通过对比,矩形基础角点及圆形基础中点均布荷载下的数据（以下简称“公式数据”）与《规范》及相关书籍中的数据（以下简称“表列数据”）完全一致,而矩形基础三角形荷载下的公式数据与表列数据有些误差,本文对这些误差也进行了分析。虽然未见到条形基础的表列数据,但实际工程中条形基础仍大量存在,因此,本文也给出了其推导公式。以上公式可极大地方便工程技术人员在实际工作中的运用。     

埋深基础地基极限承载力的数值求解方法

为确定作用在已知埋深、给定基础形状地基土上的极限承载力,对基底下的土体进行网格划分,先假定一均布荷载作用在此地基土上,运用明德林解的积分公式,结合角点法,编制MATLAB语言程序,求出每个网格节点上附加应力,进而求得每个网格节点上主应力,根据破坏准则,结合程序找出破坏点的坐标,利用MATLAB的图形处理功能,把破坏点的坐标在坐标图中显示出来。继续加大矩形荷载,直至这些破坏点在坐标图中刚好能够形成一个连续的破坏面,此时的矩形荷载即为此地基的极限承载力。此方法不仅可以有效地避免了地基承载力经验公式中一些不合理的假设带来的误差,更符合实际情况,而且可以直观地了解到地基土的三维破坏面。     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

Displacement and stress distributions under a uniform inclined rectangular load on a cross‐anisotropic geomaterial

In practical engineering, an applied rectangular area load is not often horizontally or vertically distributed but is frequently inclined at a certain angle with respect to the horizontal and vertical axes. Thus, the solutions of displacements and stresses due to such a load are essential to the design of foundations. This article yields the analytical solutions of displacements and stresses subjected to a uniform rectangular load that inclines with respect to the horizontal and vertical axes, resting on the surface of a cross‐anisotropic geomaterial. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The procedures to derive the solutions can be integrated the modified point load solutions, which are represented by several displacement and stresses elementary functions. Then, upon integrations, the displacement and stress integral functions resulting from a uniform inclined rectangular load for (1) the displacements at any depth, (2) the surface displacements, (3) the average displacements in a given layer, (4) the stresses at any depth, and (5) the average stresses in a given layer are yielded. The proposed solutions are clear and concise, and they can be employed to construct a series of calculation charts. In addition, the present solutions clarify the load inclinations, the dimensions of a loaded rectangle, and the analyzed depths, and the type and degree of geomaterial anisotropy profoundly affect the displacements and stresses in a cross‐anisotropic medium. Parametric results show that the load inclination factor should be considered when an inclined rectangular load uniformly distributed on the cross‐anisotropic material. Copyright © 2008 John Wiley & Sons, Ltd.     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

油罐基础不均匀沉降主要影响因素的敏感性分析

在上部均布荷载作用下柔性基础基底压力是均匀分布的,基底以下土体在同一深度附加应力呈现中间大、周围小的分布规律,导致基础沉降中间大、周围小。刚性基础的沉降是均匀的,必然导致基底压力的分布为周围大、中间小。软基上的油罐筏板基础是具有一定刚度的基础,但并非刚性基础,因而基底压力分布应该介于柔性基础和刚性基础之间,沉降为中间大、周围小的不均匀分布。基于ABAQUS有限元分析,结合工程实际情况,采用UH模型作为土体本构模型进行了模拟分析,对筏板厚度、地基刚度等影响基础不均匀沉降的主要因素进行敏感性分析,探求变刚度地基在油罐基础不均匀沉降中的影响规律。     

车辆荷载作用下钙质砂路基的动态响应试验研究

钙质土颗粒因形状不规则而产生咬合嵌固效应,导致土压力传递特性不同于一般黏性土。为研究不同工况下钙质土地基及挡土墙土压力的分布与响应特征,在某珊瑚礁场地对在建的护岸和道路路基在填土和车辆动荷载作用下的土压力进行了动态监测,重点对填土自重、车辆移动荷载及压路机振动碾压荷载下钙质土中土压力的传递与分布特征进行研究。结果表明：填土过程中钙质土中的侧压力系数为0.2～0.3,平均值为0.25;实际观测到的路基竖向土压力远高于按照理论公式计算的土压力;经过碾压的路基在深度为3.28 m处,重型车辆的附加荷载很小。22 t振动压路机在振动碾压时,地基在深度为2.73 m处附加应力增量极小,因此难以提高该深度处土体的密实度;而浅层土体的土压力增量较大,可有效得到压实。