The behaviour of an elastic non-homogeneous half-space. Part II–circular and strip footings

Solutions developed in the first part of this paper (i.e. describing the response of a non-homogeneous half-space subjected to surface point and line loads) are used in this part to obtain solutions for a variety of surface loadings. Consideration is given to a distributed load acting over a circular area or strip and a rigid disk or strip subjected to applied normal load and moment. It is established that the profiles of surface settlement due to uniformly distributed loads acting over a strip or circular area are strongly dependent on the degree of non-homogeneity. This dependency is reduced when the footing is rigid. When α = 1 the moduli variation is identical to the Gibson soil and the equivalence with the Winkler soil model is established.     

On the dynamic stiffness of circular ring footings on an elastic stratum

Circular ring footings on an elastic stratum are considered. The static and dynamic stiffnesses are calculated using an efficient numerical technique. The results indicate that the static torsional and rocking stiffnesses of a ring footing do not deviate significantly from the corresponding stiffness of the circular footing for values of the inner-radius-to-outer-radius ratio up to about 0.75. The static horizontal and vertical stiffnesses change considerably only for values of this ratio greater than about 0.60. The change in the stiffness and damping coefficients is small for values of the ratio between 0 and 0.5.     

黄土中圆形抗拔锚板基础承载力分析

在三维状态下运用极限平衡理论,对黄土中圆形抗拔锚板基础在受到垂直于板面荷载作用下的承载力进行理论分析,该理论研究考虑了锚板在上拔过程中板周土体的破裂方程、破裂面上的正应力和剪应力、埋深率等影响因素。理论公式计算结果表明：抗拔锚板承载力系数随着锚板埋深的增加而增大,并且当深度达到一定值时,承载力系数将达到其极限值;当埋深率h/D=1~2之间时,上覆土重对承载力系数影响较小;当h/D=4时,土体和锚板之间的吸力对承载力系数的影响大于锚板上覆土重;当h/D>4时,上覆土重对锚板抗拔承载力起着决定作用。理论计算公式与已有学者的试验结果进行对比表明提出的模型理论计算结果和其他学者的试验结果有良好的一致性,验证了该理论的正确性,为工程中抗拔锚板的设计提供了有价值的参考。     

The axial loading of a rigid circular anchor plate embedded in an elastic half-space

The present paper examines the axisymmetric problem related to the loading of a rigid circular anchor plate which is embedded in bonded contact with an isotropic elastic half-space. A Hankel transform development of the governing equations is used to reduce the associated mixed boundary value problem to a set of coupled Fredholm integral equations of the second kind. These equatons are solved in a numerical fashion to generate results of engineering interest. In particular, the results indicate the influence of the depth of embedment on the axial stiffness of the rigid anchor plate.     

Charts for probabilistic design of strip footings in cohesionless soils

Design charts that enable quick determination of the probability distribution parameters related to the ultimate bearing capacity of shallow foundations resting on (c = 0) soils are developed. These charts are intended to assist foundation designers and analysts in studying the reliability of structures as related to the capacity of the foundation system. The approach presented herein provides a more reliable alternative to foundation design and analysis than the current conventional design procedure which employs the assumption of an appropriate factor-of-safety. © Rapid Science Ltd. 1998     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Stability of end-bearing piles in a non-homogeneous elastic foundation

The stability of end-bearing piles that are supported laterally along their entire length by an elastic Winkler foundation is investigated for the case when the coefficient of horizontal subgrade reaction varies linearly with depth. A pattern of clustering of buckling modes is shown to occur and the approximate modelling of the elastic foundation by averaging the stiffness of the subgrade is discussed. © 1997 by John Wiley & Sons, Ltd.     

Finite element modelling of pressuremeter tests and footings on frozen soils

A finite element code is developed to model the structure-frozen soil/ice interaction using a time incrementing, fully implicit, iterative algorithm, and a constitutive model based on the concept that total strain tensor consists of an elastic and a creep component. The code is used to investigate the applicability and limitations of the power law as the creep model for frozen soil by simulating two pressuremeter tests. Two extended phenomenological models based on the generalized power law are used in axisymmetric finite element analyses to simulate two, long-term, stage-loaded pressuremeter tests, and comparison of results with test data indicates that one model demonstrates a better ability to approximate the actual response to subsequent load steps, under certain restrictions. Stress analyses demonstrate the ability of the constitutive model to show transient as well as subsequent quasi-stationary stress stages in creep analysis. Additional simulations of short-term pressuremeter tests on ice are performed to further illustrate some limitations of the power-law model. Examples for prediction of creep settlements on frozen geomaterials are demonstrated by considering the interaction of fully flexible circular footings and concrete cylindrical footings (of different embedment depths) with frozen sands.     

Nonlinear elastic analysis of shallow footings subjected to eccentric inclined loads

In this study, the behaviour of shallow foundations subjected to eccentric inclined loads is presented using nonlinear elastic finite element analysis. The material non-linearity of the soil has been taken into consideration by employing the hyperbolic stress-strain model. The formulation of an isoparametric interface/joint element which is used between footing base and soil media has been presented. Tests have been conducted to determine the characteristics of soil-footing interface. Forty cases of strip footing resting on sand and subjected to eccentric-inclined load which were studied by Agrawal (1986) through model tests, have been analysed. The predicted pressure-settlement, pressure-horizontal displacement and pressure-tilt characteristics have been compared with experimental results of Agrawal (1986) and a reasonable agreement between the two has been observed.     

Dynamic analysis of piles and pile groups embedded in non-homogeneous soils

A hybrid boundary element formulation for the steady state analysis of piles and pile groups embedded in a soil stratum in which the modulus increases linearly with depth is presented. The piles are represented by compressible columns or flexible beams and the soil as a hysteretic, layered medium. The explicit Green's function corresponding to dynamic loads in the interior of a layered stratum, developed earlier by Kausel is used in the study. The governing differential equations for the pile domain are solved for a distributed periodic loading intensity and those for the soil domain by a system of boundary elements at the pile-soil interface. These are then assembled into a system of algebraic equations by satisfying interface equilibrium and compatibility. The results of the analysis have been compared against those from alternative formulations, e.g. finite elements, and confirm the accuracy of the proposed formulation. Representative results for single piles and pile groups are presented.     

Uplift response of symmetrical anchor plates in reinforced cohesionless soil

The uplift response of symmetrical anchor plates with and without geogrid reinforcement layers has been evaluated in model tests and numerical simulations using PLAXIS. Many parameters of the reinforcement layers were used to reinforce the sandy soil over circular, square, and rectangular symmetrical anchor plates of various sizes. In the current research, different parameters, such as relative density of sand and embedment ratios, in conjunction with geogrid reinforcement layer parameters including size, number of layers, and the proximity of the layer to the circular anchor plate, were investigated in a scale model. The failure mechanism and the associated rupture surface were observed and evaluated. Test results showed that using geogrid reinforcement layers significantly improves the uplift capacity of symmetrical anchor plates. It was found that inclusion of one geogrid layer resting directly on top of the symmetrical anchor plate was more effective in enhancing the symmetrical anchor capacity than the layer itself. It was also found that the inclusion of one geogrid layer on the symmetrical anchor plate improved the uplift capacity more than the same symmetrical anchor plate embedded without a reinforcement layer. The single geogrid layer was also more effective in enhancing the uplift capacity compared to the multiple geogrid layer reinforcement approach. In general, the results show that the uplift capacity of symmetrical anchor plates in loose and dense sand can be significantly increased by the inclusion of geogrid layers. It was also observed that the inclusion of geogrid layers reduces the requirement for a higher L/D ratio to achieve the required uplift capacity. The results of the laboratory and numerical analysis are found to be in agreement in terms of the breakout factor and failure mechanism pattern.     

临近基坑既有建筑物地基的抗剪强度指标取值问题

基坑开挖不仅改变了半无限空间体边界条件,卸载时还会引起周围地层移动,导致既有建筑物地基承载力的附加损失。在临近基坑既有建筑物地基承载力计算中,其抗剪强度参数的选取有别于斜坡上地基计算参数的常规取值方法。通过探讨临近基坑既有建筑物地基抗剪强度指标的取值问题,建议以地基土的完全软化强度与残余抗剪强度的平均值作为临近基坑既有建筑物地基抗剪强度指标,并据此估算了临近基坑既有建筑物地基承载力。所得结果与斜坡上地基承载力的试验值和理论解对比分析后显示出其具有一定的合理性。所建议的抗剪强度指标取值方法,还有待于试验的进一步验证。     

基于局部变形理论的非均质地层中预应力锚固受力分析

将非均质地层中的预应力锚索沿锚固段离散为一系列子锚固段,导出基于局部变形理论的各子锚固段理论解,并由子锚固段之间的相互作用关系分别建立非均质地层中拉力集中型和压力集中型预应力锚索锚固分析方法,编写了相应的分析程序。对位于非均质地层中的拉力型和压力型预应力锚索在多级测试荷载作用下的响应进行分析。结果表明,所提出的分析方法和程序是可行的,特别地,对于拉力集中型预应力锚索,考虑第一界面作用效应的分析结果更符合实际。     

极限荷载作用下临近基坑c-ψ土地基的破坏模式

与地面水平时地基土体的对称破坏模式不同,临近基坑(边坡)地基土体的破坏模式呈现明显的非对称性.利用FLAC-3D数值模拟技术,研究了在竖向极限荷载作用下临近基坑c-ψ土地基不同工况时的破坏模式,得出了与J.Graham所假设的边坡附近无黏性土地基破坏模式相一致的结论.最后将数值模拟结果与大尺寸模型试验数据以及J.Graham的基于应力特征线法的非对称滑动破坏模式的地基承载力理论解进行了分析对比.结果表明,采用叠加计算方法得到的承载力系数Nγq偏于安全.     

抗浮锚杆应力-应变状态的线弹性理论分析

假定抗浮锚杆各部分贡献的位移与锚杆轴力均呈线弹性关系,运用力学原理分析锚杆轴力与锚侧摩阻力、锚-土变形之间的相互关系,推导出锚杆的摩阻力、轴力及各部分变形与锚杆各参数的相互关系。实例验证结果表明：基于线弹性模型基础上建立的摩阻力、轴力和位移公式能够较好地描述垂向抗浮锚杆在弹性变形阶段的内力和变形形态;获得了抗浮锚杆摩阻力和剪切位移沿锚固长度的分布规律;证实了锚土界面处变形为土层抗浮锚杆变形的主要部分。     

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.     

The behaviour of an elastic non-homogeneous half-space. Part I-line and point loads

In the first part of this paper solutions are developed for the response of a non-homogeneous half-space subjected to either a surface point load or a surface line load. The non-homogeneity considered is a variation in Young's modulus (E) with depth (z) which takes the form E=m_EZ^α where m_E is a constant and α is referred to as the non-homogeneity parameter. The variation of these solutions as the non-homogeneity parameter α varies between the limits of zero (homogeneous soil) to unity (Gibson soil) gives some fresh insight into both these limiting cases.     

极限荷载作用下临近基坑c-土地基的破坏模式

与地面水平时地基土体的对称破坏模式不同,临近基坑（边坡）地基土体的破坏模式呈现明显的非对称性.利用FLAC-3D数值模拟技术,研究了在竖向极限荷载作用下临近基坑c-ψ土地基不同工况时的破坏模式,得出了与J.Graham所假设的边坡附近无黏性土地基破坏模式相一致的结论.最后将数值模拟结果与大尺寸模型试验数据以及J.Graham的基于应力特征线法的非对称滑动破坏模式的地基承载力理论解进行了分析对比.结果表明,采用叠加计算方法得到的承载力系数Nγq偏于安全.     

非均质地基承载力及破坏模式的FLAC数值分析

利用基于Lagrangian显式差分的FLAC算法，通过数值计算，对黏结力随深度线性增长的非均质地基上条形基础和圆形基础的极限承载力及地基破坏模式进行了对比计算与系统分析。研究表明：（1）随着地基黏结力沿深度非均匀变化系数的增大，地基的破坏范围逐渐集中在地基表层和基础两侧：（2）即使地基的非均质程度较小，当将非均质地基近似地按均质地基考虑时，由此所估算的承载力可能过于保守；（3）地基承载力系数随黏结力沿深度非均匀变化系数的增大而非线性地增大。与数值解相比，skempton与Peck等近似公式均可能高估了非均质地基承载力。