Consolidation analysis of non-homogeneous soil by the weak form quadrature element method

A weak form quadrature element formulation for consolidation analysis of non-homogeneous saturated soil is established based on Biot’s theory. Numerical examples are given, and the results are compared with the analytical solutions available or those from the commercial finite element software ABAQUS, demonstrating accuracy and rapid convergence of quadrature element solutions. The disparity between various treatments of non-homogenous soil is discussed, and the effectiveness and advantages of the quadrature element formulation in consolidation analysis of non-homogeneous soil are demonstrated.     

Performance of square footing with structural skirt resting on sand

The paper presents the performance of a square footing with a structural skirt resting on sand and subjected to a vertical load through an experimental study. A series of tests were conducted in a model test tank to evaluate the performance in terms of improvement in bearing capacity and reduction in settlement of a square footing with and without a structural skirt. The results of the study reveal that this type of reinforcement increases the bearing capacity, reduces the settlement and modifies the load settlement behaviour of the footing. The various factors influencing the bearing capacity improvements and settlement reduction using a structural skirt are identified. Skirt factors are proposed which can be introduced into the general ultimate bearing capacity equation for a square footing resting on sand. The predictions made through the modified equation are in reasonable agreement with the experimental results. The bearing capacity of square footing is increased in the range of 11.2 to 70%. The improvement in bearing capacity decreases with the increase in base roughness of the footing. Further, an equation for a settlement reduction factor is proposed which can be used to calculate the settlement of the square footing with structural skirt resting on sand. The settlement reduction factor (SRF, defined as the ratio of settlement of footing with structural skirt to the settlement of footing without structural skirt at a given load) was in the range 0.11 to 1.0 depending on applied load and skirt depth ratio with the use of a structural skirt. The results further reveal that for a given depth of the skirt, the settlement reduction factor decreases with the increase in applied load. The improvement in the bearing capacity and reduction in settlement of a square footing with a structural skirt resting on sand are dependent on the geometrical and structural properties of the skirt, footing, sand characteristics and interface conditions of the sand–skirt–footing system.     

Bearing capacity of rectangular footing on reinforced soil

In the present paper, a method of analysis for calculating the pressure intensity corresponding to a given settlement for a rectangular footing resting on reinforced soil foundation has been presented. The process has been simplified by presenting non-dimensional charts for the various terms used in the analysis, which can be directly used by practicing engineers. An empirical method has been suggested to find out the ultimate bearing capacity of footing on reinforced soil. The results have been validated with large-scale model tests also. The procedure has been made clear by giving an illustrative example. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of a rigid footing lying on three-layered soil using the finite difference method

A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff.     

土钉加固黏性土坡加载的离心模型试验研究

进行了不同坡度土钉加固边坡坡顶加载的离心模型试验,观测了土坡的破坏过程并测量土坡的位移场,研究了土钉加固黏性土坡的承载力、变形和破坏规律以及坡角对其破坏规律的影响。试验结果表明,坡顶荷载的增加引起土坡变形的增加,变形的集中产生和发展导致滑裂面的形成并使土坡发生破坏。土钉变形规律受加载阶段和加载底板的综合影响,坡顶荷载越大,接近坡顶的土钉弯曲挠度越大,钉土间的相互作用越强。土坡的坡角越大,承载力越低,土体呈现出更显著的向坡面位移的趋势。     

非均质地基中群桩竖向荷载沉降关系分析

运用剪切位移法计算了桩轴向荷载传递因子。对于桩端采用线性的荷载传递函数,推导了基于弹塑性模型的单桩竖向荷载沉降的解析解。分析过程中考虑了土体强度沿深度线性变化的特性和桩土间的滑移现象,因此更符合大部分土体的实际性状。在此基础上,建立了考虑桩土滑移的桩-桩相互作用系数的计算公式,并将上述方法应用于群桩的分析,获得了群桩的荷载沉降特性。该分析方法克服了目前应用较多的弹性理论方法夸大桩土相互作用的缺点,单桩和群桩的荷载沉降曲线的分析结果和实测数据吻合,证明了该方法的合理性。     

Vertical vibration of an elastic strip footing on saturated soil

Based on Biot's dynamic coupled equations, the vertical vibration of an elastic strip footing on the surface of saturated soil is studied. Utilizing the Fourier transform, the governing dynamic differential equations for saturated poroelastic medium are solved. Considering the mixed boundary value conditions at the bottom of the foundation, a pair of dual integral equations about the vertical vibration of an elastic strip footing is derived, which can be converted to a set of linear equations by means of infinite series of orthogonal functions. The relation between the dynamic compliance coefficients and the dimensionless frequency tends to be gentle with decreasing footing rigidity, while the dimensionless frequency has only small effect on the dynamic compliance coefficients. When the dynamic permeability is large, its effect on the dynamic compliance coefficients should be taken into consideration. Furthermore, the dynamic compliance coefficients are found to be not sensitive to Poisson's ratio of the soil for footing on saturated soil. Copyright © 2007 John Wiley & Sons, Ltd.     

饱和地基上条形弹性基础的摇摆振动

基于Biot动力方程,研究了饱和均质弹性半空间上弹性条形基础的摇摆振动问题。通过Fourier积分变换求解了饱和土的动力控制方程,然后结合基础底部为混合边界的条件得到了弹性条形基础的摇摆振动对偶积分方程,利用正交多项式将对偶积分方程转化为求解一组线性代数方程组,同时利用复合Simpson法则,得到了动力柔度系数的表达式,通过算例得出了不同参数时地基动力柔度系数随无量纲频率的关系曲线。     

Rocking vibration of a rigid strip footing on saturated soil

The dynamic response of a rigid strip footing lying on saturated soil is greatly affected by the pore pressure induced by a rocking moment. To consider the complex behavior of the soil under the rocking load, an analytical solution for a rigid strip foundation on saturated soil under a rocking moment is developed under the framework of Biot’s coupling theory. The boundary-value problem for the governing coupling equations for saturated soil is solved using a Fourier transform to yield a pair of dual integral equations. These dual integral equations are transformed into a set of linear equations using an infinite series of orthogonal Jacobi polynomials to yield the compliance functions. In addition, a parametric study has been carried out to examine the influence of: (1) the dimensionless frequency, (2) the dynamic permeability and (3) the Poisson’s ratio on saturated soil under a rocking rigid strip footing.     

移动荷载作用下Winkler地基板的等参元分析

采用基于Mindlin板理论的8节点等参单元和Newmark逐步积分法,对Winkler地基上的弹性薄板和厚板在移动荷载作用下的动力响应进行了分析,并与已有的薄板有限条法分析结果进行了对比。考察了荷载移动速度、地基基床系数、系统阻尼比对地基板动力响应的影响。分析结果表明,系统存在固有的共振速度,地基基床系数是确定共振速度的最重要因素,薄板与厚板的挠度响应模态有很大差异。结果证明了该方法的有效性和准确性,对实际工程有重要的应用价值。     

有关砂土地基承载力数值解析问题的讨论

以砂土地基的极限承载力为对象,讨论了古典理论解与室内模型实验值之间的差异,并结合试验中所观察到的现象对其原因进行了简要的分析,最后,利用有限元解析对各种极限承载力的计算方法进行了客观地评价.砂土材料强度具有明显的各向异性以及软化特性,并与周围压力大小以及密度相关.另外,砂土地基的破坏呈渐进性,砂土的粒径大小影响它的承载力以及变形破坏.结果表明,只有考虑砂土以上的各种特性的数值解析方法才能合理地得到砂土地基的极限承载力.     

Analysis of soil consolidation by vertical drains with double porosity model

The soil around a drain well is traditionally divided into smeared zone and undisturbed zone with constant hydraulic conductivity. In reality, hydraulic conductivity of the soil changes continuously and it may not be always appropriate to approximate its distribution with two zones. In this study, the horizontal hydraulic conductivity of the soil is described by an arbitrary function of radial distance. The horizontal flow under equal strain condition is analysed for a soil–drain system with a circular or regular polygonal boundary. It is found that the horizontal flow can be generally characterized with a linear equation in which the flow rate of water through soil–drain interface is proportional to the difference between the average excess pore pressure in the soil and the excess pore pressure in the drain well. The water exchange between the drain and the soil is analogous to that between fractures and matrix in a double porosity system, a popular conceptual model of fracture rocks. On the basis of this characterization, a simplified approach to analyse soil–drain systems is developed with one‐dimensional double porosity model (DPM). Analytical solutions for both fully and partially penetrating drains are derived. The solution for partially penetrating drains is compared with both numerical and approximate analytical results in literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Elasto-viscoplastic finite element study of the effect of degradation on bearing capacity of footing on clay ground

The bearing capacity of footing has been studied by both conventional and numerical methods by many researchers. However, degradation of the microstructure of material, that is, a change in the microstructure of the soil, has not been adequately taken into account. Degradation of microstructure causes strain softening of materials and it leads to strain localization such as shear bands and slip bands. From an engineering point of view the strain localization is crucial because it is a precursor of failure. In the present study, finite element analyses of the bearing capacity of a shallow foundation on homogeneous and inhomogeneous saturated clay strata have been conducted using an elasto-viscoplastic soil constitutive model of microstructure change. A series of analyses of footing on clay deposit with different microstructure parameters have been carried out. Numerical results show that strain localization can be predicted during the loading of rigid footing on highly structured soil and strain localization affects the footing–soil interaction. The effects of footing roughness on the failure mechanism are also discussed in the study.     

ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil

In reality, footings are most likely to be founded on multi-layered soils. The existing methods for predicting the bearing capacity of 4-layer up to 10-layer cohesive soil are inaccurate. This paper aims to develop a more accurate bearing capacity prediction method based on multiple regression methods and multi-layer perceptrons (MLPs), one type of artificial neural networks (ANNs). Predictions of bearing capacity from the developed multiple regression models and MLP in tractable equations form are obtained and compared with the value predicted using traditional methods. The results indicate ANNs are able to predict accurately the bearing capacity of strip footing and outperform the existing methods.     

上拔扩底基础与地基土体承载特性差异性分析

工程中多采用基础上拔静载试验中基础顶部荷载-位移曲线获取基础的承载力,忽略了基础周围土体的变形破坏过程,而实际工程中均是基础周围地基土体发生破坏。为研究扩底基础与其周围土体在抗拔承载特性方面的差异,以黄土地基中的9个扩底基础为研究对象,通过现场全尺寸基础的上拔静载试验,分别获得基础顶部与地表的上拔荷载-位移曲线,并进一步对基顶与地表处的荷载-位移曲线变化特征、抗拔承载力取值进行对比分析。结果表明,两处的荷载-位移曲线变化特征相似,相同上拔荷载作用下地表处的位移量均小于基础处位移量,差异以初始弹性阶段变形最为突出;两者在弹性极限荷载QL1取值方面,相差较大,但随着地基基础由弹性向塑性发展,差异逐渐减小,两者塑性极限荷载QL2取值基本相同。结合上拔扩底基础的破坏模式,分析出上述差异主要由于基础与周围土体之间变形不协调所致,加载初期基础顶部的上拔位移包括基础拔出量和上部土体压缩量,当上部土体压密后压缩变形消失,地基基础成为一个整体,上拔基础与周围土体的变形趋于协调。     

Reliability analysis for bearing capacity of surface strip footing using fuzzy finite element method

ABSTRACT

This paper presents the reliability analysis on the basis of the foundation failure against bearing capacity using the concept of fuzzy set theory. A surface strip footing is considered for the analysis and the bearing capacity is estimated using the conventional Finite Element Method (FEM). The spatial variability of the variables is taken into consideration to capture the physical randomness of the soil parameters for an isotropic field. A variation of the probability of failure (P_f) against a varying limiting applied pressure (q) is presented for different Coefficient of Variation (COV) of the variables and different scale of fluctuation (θ). The results reveal that the friction angle of soil (?) is the most influencing parameter among the other variables. Further, the influence of the scale of fluctuation (θ) on the probability of failure (P_f) is also examined. It is observed that for a particular COV of ?, higher value of θ predicts higher P_f whereas, P_f increases as COV of ? increases for a particular θ value. Later, a comparison study is accomplished to verify the viability of the present method and it can be noticed that the present method compares well with the other reliability method (First Order Reliability Method) to a reasonably good extent.     

横观各向同性地基上刚性矩形基础分析

对横观各向同性地基上刚性矩形板进行了求解。首先,利用表面受矩形均布荷载作用下的层状横观各向同性地基的位移解答,获得地基的柔度矩阵;然后,通过刚性矩形基础与层状横观各向同性地基的协调条件,建立刚性矩形基础与横观各向同性地基共同作用的方程,进而求得基础的地基反力。通过编制相应的程序,确定了合理的网格划分值;最后,进行算例分析,分析了地基横观各向同性性质、矩形刚性基础的长宽比以及地基分层性对地基反力的影响。分析表明：以上3种因素对地基反力有重要影响。     

Effect of spatial variability of cross‐correlated soil properties on bearing capacity of strip footing

Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.     

基于有限元法的高速列车引起土的动力响应分析

基于有限元法分析了高速列车引起的土的动力响应.对列车荷载进行了简化,并且考虑地基土性质不同的影响,对各个区域采用了不同的材料参数.     

Response of multilayer geosynthetic-reinforced bed resting on soft soil with stone columns

In the present study, a mechanical model has been developed to study the behavior of multilayer geosynthetic-reinforced granular fill over stone column-reinforced soft soil. The granular fill and geosynthetic reinforcement layers have been idealized by Pasternak shear layer and rough elastic membranes, respectively. The Kelvin–Voight model has been used to represent the time-dependent behavior of saturated soft soil. The stone columns are idealized by stiffer springs and assumed to be linearly elastic. The nonlinear behavior of the soft soil and granular fill is considered. The effect of consolidation of soft soil due to inclusion of the stone columns on settlement response has also been included in the model. Plane strain conditions are considered for the loading and reinforced foundation soil system. An iterative finite difference scheme is applied for obtaining the solution and results are presented in nondimensional form. It has been observed that if the soft soil is improved with stone columns, the multilayer reinforcement system is less effective as compared to single layer reinforcement to reduce the total settlement as there is considerable reduction in the total settlement due to stone column itself. Multilayer reinforcement system is effective for reducing the total settlement when stone columns are not used. However, multilayer reinforcement system is effective to transfer the stress from soil to stone column. The differential settlement is also slightly reduced due to application of multiple geosynthetic layers as compared to the single layer reinforcement system.