Vertical stress distributions around batter piles driven in cross‐anisotropic media

This work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.     

Stresses due to vertical subsurface loading for an inhomogeneous cross‐anisotropic half‐space

In this article, we present the solutions for the stresses induced by four different loads associated with an axially loaded pile in a continuously inhomogeneous cross‐anisotropic half‐space. The planes of cross‐anisotropy are parallel to the horizontal surface of the half‐space, and the Young's and shear moduli are assumed to vary exponentially with depth. The four loading types are: an embedded point load for an end‐bearing pile, uniform skin friction, linear variation of skin friction, and non‐linear parabolic variation of skin friction for a friction pile. The solutions for the stresses due to the pile load are expressed in terms of the Hankel integral and are obtained from the point load solutions of the same inhomogeneous cross‐anisotropic half‐space which were derived recently by the authors (Int. J. Rock Mech. Min. Sci. 2003; 40 (5):667–685). A numerical procedure is proposed to carry out the integral. For the special case of homogeneous isotropic and cross‐anisotropic half‐space, the stresses predicted by the numerical procedure agree well with the solutions of Geddes and Wang (Geotechnique 1966; 16 (3):231–255; Soils Found. 2003; 43 (5):41–52). An illustrative example is also given to investigate the effect of soil inhomogeneity, the type and degree of soil anisotropy, and the four different loading types on the vertical normal stress. The presented solutions are more realistic in simulating the actual stratum of loading problem in many areas of engineering practice. Copyright © 2004 John Wiley & Sons, Ltd.     

Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd.     

竖向荷载作用下斜桩荷载传递性状试验研究

通过模型试验研究了竖向荷载作用下砂土中斜桩的荷载传递性状,分析了桩身倾角及长径比对斜桩桩身轴力、弯矩、剪力、桩侧摩阻力及端阻比的影响。试验结果表明：在桩顶竖向荷载作用下,斜桩桩身轴力均小于相应直桩桩身轴力,桩身倾角越大,轴力沿深度衰减得越快,桩长径比越大,轴力沿深度衰减得也越快;斜桩桩身最大弯矩随桩身倾角及长径比的增加而增加,最大弯矩出现的深度与桩身倾角无关,只与长径比相关;不论桩身倾角及长径比的大小,斜桩桩身最大剪力均出现在桩顶截面处,桩身最大剪力随着桩身倾角的增加而增大;桩身倾角越大,斜桩最大摩阻力越大,长径比越大,斜桩最大摩阻力越小,斜桩最大摩阻力出现在桩顶下1/4～1/5桩长处;斜桩端阻比随着桩顶竖向荷载的增加而增大,随着桩身倾角及长径比的增加而减小。     

Lateral stress caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This study derives analytical solutions for estimating the lateral stress caused by horizontal and vertical surcharge strip loads resting on a cross‐anisotropic backfill. The following loading types are employed in this work: point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load and downward nonlinear‐varying strip load. The cross‐anisotropic planes are assumed to be parallel to the horizontal surface of the backfill. The solutions proposed herein have never been mentioned in previous literature, but can be derived by integrating the point load solution in a Cartesian co‐ordinate system for a cross‐anisotropic medium. The calculations by the presented solutions are quick and accurate since they are concise and systematized. Additionally, the proposed calculations demonstrate that the type and degree of material anisotropy and the horizontal/vertical loading types decisively influence the lateral stress. This investigation presents examples of the proposed horizontal and vertical strip loads acting on the surface of the isotropic and cross‐anisotropic backfills to elucidate their effects on the stress. The analytical results reveal that the stress distributions accounting for soil anisotropy and loading types are quite different from those computed from the available isotropic solutions. Restated, the derived solutions, as well as realistically simulating the actual surcharge loading circumstances, provide a good reference for the design of retaining structures for the backfill materials are cross‐anisotropic. Copyright © 2005 John Wiley & Sons, Ltd.     

加载次序引起的负摩阻力桩摩阻力分布的变化

简要分析了加载次序对于负摩阻力桩基桩土相互作用影响的机理。采用有限元方法计算比较了这种差异。计算结果表明,加载次序的变化会引起桩身摩阻力分布、中性点位置和下拉力的变化。桩身摩阻力的分布差异主要是桩身上部负摩阻力的大小,负摩阻力先出现时的负摩阻力值较小,这种状况在各级桩顶荷载下不会改变。负摩阻力先出现时,中性点的位置比较低,两者的差距随着桩顶荷载的增大而变得加大。负摩阻力先出现时下拽力小于桩顶荷载先施加的情况。这对于负摩阻力桩基检测的研究和应用是有益的。     

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.     

桩顶荷载对负摩阻力性状影响的现场试验

负摩阻力是桩周土体沉降产生的桩附加沉降和下拽力的综合效应。为了研究不同的桩顶荷载对负摩阻力基桩性状的影响,在同一个试验场地上,对不同桩顶荷载作用下完全相同的3根桩的负摩阻力性状进行了现场测试。测试结果表明,桩顶荷载对于桩的负摩阻力性状有明显影响。随着桩顶荷载的增加,负摩阻力引起的桩附加沉降越大,桩周土体沉降引起的负摩阻力就越小;负摩阻力引起的下拽力也随着桩顶荷载的增加而减小;中性点位置随着桩顶荷载的增加而上升。这对桩基负摩阻力特性的研究是有益的。     

自重湿陷性黄土场地桩的负摩阻力

通过对郑州-西安客运专线的关中某地钻孔灌注桩在预湿和后湿状态下的静载试验和同步进行的桩身应力测试,探讨了自重湿陷性黄土中桩侧负摩阻力的发生和发展过程,中性点位置的变化过程及桩侧阻力的发挥规律等,对自重湿陷性黄土中桩侧负摩阻力的理论研究及其工程应用具有重要的参考价值。     

堆载下单桩负摩阻力工作性状非线性数值分析

利用三维非线性数值方法对一算例在堆载作用下桩侧负摩阻力进行了计算分析。计算结果揭示了摩擦型、端承型桩负摩阻力工作性状的异同;分析了堆载速度、桩顶荷载对负摩阻力的影响:堆载越快,负摩阻力越小;在无桩顶荷载作用下,由负摩阻力引起的下拉荷载最大,可视为常规方法设计的上限值;桩顶荷载与堆载施工顺序对负摩阻力的影响也很大,先施加桩顶荷载,后进行堆载所产生的负摩阻力最大,反之最小。     

基于极限平衡法的现浇X形桩群桩负摩阻力计算分析

软弱土及湿陷性黄土等地区桩基负摩阻力计算是桩基础设计与施工必须考虑的问题之一,目前针对群桩负摩阻力计算方面的研究相对较少。采用有效应力法计算单桩负摩阻力,基于极限平衡原理计算负摩阻力群桩效应系数,从而得到群桩负摩阻力计算公式。结合现场试验结果,对现浇X形桩群桩负摩阻力及桩身下拽力进行计算分析,并讨论了群桩基础中各基桩位置对桩身下拽力的影响,以及群桩效应系数随相关影响因素的变化规律。研究结果表明,文中计算结果与现场实测结果具有良好的一致性;地面堆载等级越高,群桩所受的桩身下拽力越大,且群桩效应系数随着桩间距的增大而增大,随着负摩阻力系数和中性点深度比的增大而减小。     

A hypoplastic macroelement formulation for single batter piles in sand

Batter piles are widely used in geotechnical engineering when substantial lateral resistance is needed or to avoid the interference with existing underground constructions. Nevertheless, there is a lack of fast numerical tools for nonlinear soil‐structure interactions problems for this type of foundation. A novel hypoplastic macroelement is proposed, able to reproduce the nonlinear response of a single batter pile in sand under monotonic and cyclic static loadings. The behavior of batter piles (15°, 30°, and 45°) is first numerically investigated using 3D finite element modeling and compared with the behavior of vertical piles. It is shown that their response mainly depends on the pile inclination and the loading direction. Then, starting from the macroelement for single vertical piles in sand by Li et al (Acta Geotechnica, 11(2):373‐390, 2016), an extension is proposed to take into account the pile inclination introducing simple analytical equations in the expression describing the failure surface. 3D finite element numerical models are adopted to validate the macroelement that is proven able to reproduce the nonlinear behavior in terms of global quantities (forces‐displacements) and to significantly reduce the necessary computational time.     

高速铁路超长桥桩承载特性试验研究

超长桩广泛已应用于土木工程各个领域,但黄土地区超长桩的承载性状和变形特性尚不十分清楚,需要进一步研究。通过对郑西铁路客运专线某特大桥的4根超长桩现场测试项目的资料分析,得出了超长桩桩身轴力及侧阻力的变化规律,对超长桩的承载特性有了更为清晰的了解。试验结果表明,在桩顶竖向荷载作用下,桩身轴力随荷载的增加发生了局部调整,砂性土层的桩侧摩阻力具有增强效应,黏性土层的桩侧摩阻力具有退化效应;单桩竖向刚度随桩顶荷载的增加而减小,单桩竖向刚度降低40 %～70 %。     

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.     

Elastic solutions of displacements for a transversely isotropic full space with inclined planes of symmetry subjected to a point load

This work presents analytical solutions for displacements caused by three‐dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed toyield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (?), (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (P_x, P_y, P_z). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22 (6):425–447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three‐dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering. Copyright © 2007 John Wiley & Sons, Ltd.     

考虑土体屈服的纵横荷载单桩变形内力分析

为提高桩身变形较大时纵横荷载单桩的设计计算水平,假定地基反力系数沿深度线性增加,考虑土体屈服及纵向荷载的P-?效应并计入桩身自重和桩侧摩阻力的影响,得到了地面以下桩身变形和内力的幂级数解。结合已有的地面以上桩身响应的幂级数解,采用Fortran语言编制了计算程序。计算结果表明：桩顶位移、地面处桩身位移及桩身最大弯矩均随纵横向荷载和自由段桩长的增加而增大,并随土体屈服位移的增加而减小;纵向荷载足够大时桩基失稳;桩顶约束条件对桩的响应影响很大。计算值与模型试验的实测值吻合较好,所得解和程序是可靠的。     

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.     

桩基负摩阻力时间效应试验研究

由于黏土固结缓慢,桩基负摩阻力存在明显的时间效应,然而目前相关研究仍显不足。设计实施了能实现桩顶加载及较大超载值的单桩及双桩负摩阻力模型试验,桩周土采用砂土和软黏土夹层,测定了模型桩身应力、桩顶位移以及土体分层沉降随固结时间的变化。试验结果显示,沉降、负摩阻力具有明显的时间效应。土表超载作用下土体沉降带动桩沉降,桩与土体的沉降均表现出早期快、后期慢的趋势。试验加载初期,黏土夹层处的负摩阻力略小于砂层,但随土体固结而增长,其基本变化规律与沉降相同。因桩端砂土层沉降稳定迅速,中性点随桩身沉降增长略呈上移趋势。此外,相同荷载作用下桩间距较小的双桩,由于下拉力较小,其沉降较小。试验条件下,3D桩间距的负摩阻力群桩效应系数在0.71～0.77之间,6D桩间距时不存在负摩阻力群桩效应。     

基于改进荷载传递法计算降水引起的基桩沉降

现有研究采用荷载传递法时均未计算桩体自重,若直接应用于国内软土地区超长桩基的沉降计算,其精度难以满足高速铁路线下工程严格的沉降控制要求。基于佐藤?悟双折线模型提出侧阻荷载传递函数的假定模式,引入桩体自重并对荷载传递法的基本微分方程进行修正和求解,结合降水引起的桩周土体沉降计算和基于端阻弹性模型的桩端土体沉降计算,获得地下水位变化诱发的基桩沉降计算方法;采用理论推导的基桩沉降解析解,并借助嵌入荷载传递函数的有限元方法,分别对单纯桩顶荷载作用和桩顶荷载与降水共同作用两种工况下的桩侧摩阻力、桩体轴力和基桩沉降进行算例对比分析;有限元计算因考虑了由桩体沉降产生的桩周土体附加竖向位移而与理论计算略有偏差,但两种方法计算结果的变化规律基本一致,验证了降水引起的基桩沉降理论计算公式的合理性及正确性。     

灌注桩侧摩阻力发挥模式的研究

桩侧摩阻力的发挥主要与桩周土的力学性质、侧向有效压力、桩土的相对位移量、桩土的接触性质、时间效应等有关。采用双曲线侧摩阻力发挥模型,通过分析上海某地区灌注桩的现场试验实测资料,提出了双曲线模型的计算参数取值范围。此外,对桩侧摩阻力的时间效应也作了初步探讨。结果表明：采用双曲线函数对灌注桩侧摩阻力与相对位移间的变化关系进行拟合是合理的;由于各级荷载下桩体沉降同样具有时间性,桩侧摩阻力同时具有明显的时间效应