The behaviour of an impermeable flexible raft on a deep layer of consolidating soil

Analytic solutions to the problem of the time-settlement behaviour of raft foundations have been limited in the past to flexible or rigid loadings, and have treated the foundation as being completely permeable. In this paper, solutions are presented for smooth circular rafts of any flexibility causing consolidation of a deep homogeneous clay layer, where the raft may be considered permeable or impermeable. Results for the time-dependent behaviour of contact stresses, pore pressures, raft displacements and moment in the raft are presented.     

One-dimensional consolidation under haversine repeated loading with rest period

Presented in this paper is a study of the one-dimensional consolidation process under haversine repeated loading with and without rest period. The analysis was carried out using a hybrid coupled, analytical and numerical implicit finite difference technique. The rate of imposition of excess pore-water pressure was determined analytically, and the remaining part of the governing differential equation was solved numerically. The clay deposit considered was a homogeneous clay layer with permeable top and/or impermeable bottom hydraulic boundary conditions with constant coefficients of permeability and of consolidation. The study reveals that although the loading function is positive for all times, the excess pore-water pressure at the base of the clay deposit with permeable top and impermeable bottom oscillates with time reaching a ‘steady state’ after few cycles of loading depending on whether there is a rest period or not. An increase in the rest period causes a decrease in the number of cycles required to achieve the steady state. The paper shows also that the rest period in the haversine repeated loading decelerates the consolidation process. Similarly, the paper reveals that the effective stress at the bottom of the clay layer with permeable top and impermeable bottom increases with time but showing mild fluctuations that do not change the sign. The maximum positive effective stress achieved depends on the rest period of the haversine repeated loading. A haversine repeated loading without a rest period gives the highest value for the positive effective stress.     

Analytical solution for 1D consolidation under haversine cyclic loading

Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one‐dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T₀. The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T₀. An increase in T₀ also causes an increase in maximum effective stress. Copyright © 2013 John Wiley & Sons, Ltd.     

粗糙透水床面明渠水流的垂线流速分布

为了进一步揭示粗糙透水床面明渠水流运动特性,针对垂线流速分布研究存在的问题,根据边界层理论,推导了含有摩阻流速、理论床面流速和原点位移等3个参数的修正对数公式;通过水槽试验,运用激光多普勒测速仪,分别对用直径1 cm玻璃珠构成的粗糙不透水和透水床面明渠水流的垂线流速分布进行了测量。结果表明:推导的修正对数公式与实测符合很好;相同水流条件下,透水床面的摩阻流速要大于不透水床面,各自的阻力系数保持基本不变;理论床面流速是主流平均流速的0.35~0.45倍,且床面相对流速随着雷诺数的增大而略有减小。     

The response of a deep rigid anchor due to undrained elastic deformations of the surrounding soil medium

The equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load-deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load-deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity.     

Analytical solution to one-dimensional consolidation in unsaturated soils under loading varying exponentially with time

This note presents an analytical solution to one-dimensional consolidation in unsaturated soils with a finite thickness under confinement in the lateral direction and vertical loading varying exponentially with time. The boundary conditions are that the top surface is permeable to water and air and the bottom is impermeable to water and air. The transfer relationship between the state vectors at the top surface and any depth is gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial and boundary conditions. By performing the inverse Laplace transforms, the analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement are obtained in the time domain.     

海底泉对在海底有限延伸的越流含水层系统中地下水潮汐效应的增强作用

海底泉在滨海地下水排泄过程中起着重要的作用。本文给出了含有一个海底泉的在海底延伸的越流承压含水层系统中地下水水头在海潮作用下波动的近似解析解。该含水层顶底板隔水且向海底延伸有限距离。假设含水层的海底露头被一层隔水层覆盖,海底泉由一个渗透性很好的完全穿透海底含水层硕板的圆柱体渗漏天窗（海底泉孔）来表示。近似解析解中包含了6个参数：承压含水层的海潮传播参数,海底泉孔中心到海岸线的距离,表示泉的圆柱体的等效半径,海底泉孔中心到含水层海底露头处的距离,承压含水层的海潮载荷效率和弱透水层的越流。分析表明,如果海底泉孔中心到海岸线的距离远大于泉孔的等效半径,且海底泉孔中心到含水层海底露头处的距离远大于泉孔的等效半径时,解析解的近似误差可以忽略。然后本文讨论了解析解的两个基本性质,分析了海底泉对海底地下水水头波动的影响。     

Analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings

This paper presents the analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings. By introducing the empirical relation between permeability and compressibility, along with the conformal transformation, the governing equations of nonlinear consolidation are established, and the corresponding analytical solutions are derived. Then, the Terzaghi consolidation solutions are derived from the degenerate governing equation of nonlinear consolidation. Through the predictions of different consolidation theories in both completely permeable and impermeable lining conditions, the influences of a tunnel acting as a drain and impacting the dissipation of pore pressure, degree of consolidation, long-term ground settlements and ground settlement rates are investigated. During the early stages of consolidation, the case studies reveal that the predictions made by this study strongly agree with the field data when a completely permeable lining is applied. This study confirms that a tunnel acting as a drain can accelerate the consolidation of soil and enlarge soil deformation due to consolidation. During long term consolidation, a notable nonlinearity of the soil consolidation is exhibited by a small and gradually decreasing settlement rate, showing agreement with the tendency of field data from the impermeable conditions.     

二维饱和土体动态孔隙率及相关动力响应特性研究

饱和多孔介质的动力响应研究在众多工程领域具有重要意义。充分考虑孔隙率的变化规律与影响因素,有利于合理揭示饱和多孔介质的相关力学行为。为此,将动态孔隙率模型与用于表征饱和多孔介质动力特性的u-U-p型方程结合,构建相应的非线性力学模型,利用Comsol Multiphysis PDE求取相应的数值解,以此研究不同透水条件下,受谐波载荷激励的二维饱和土体的孔隙率、变形量及孔隙水压力的变化规律。结果表明：孔隙率的变化与土骨架的体应变及孔隙水压力直接相关,土体压缩过程中,孔隙率相应减小,土骨架与孔隙流体的相互作用增强,土体运动时所受阻力增大,其无量纲竖向位移小于孔隙率被视为常数时的情况,在此条件下,由于土体的变形量减小,其孔隙水压力也相对减小。故充分考虑动态孔隙率,有利于更加精确地研究等饱土体和多孔介质的相关力学行为。此外,土体上表面透水条件下,孔隙流体可以从土体表面自由排出,土骨架承受的载荷更大,与不透水条件相比,土体孔隙率、竖向位移、孔隙水压力等变化更为显著。     

试论连云港海相软土路堤沉降规律

根据连云港至徐州高速公路连云港段60多个断面的现场实测沉降资料,分析了在路堤荷载作用下连云港海相软土的沉降和固结规律。实测数据表明,在路堤荷载作用下连云港海相软土地基的沉降曲线符合双曲线形式,故可采用双曲线法预测最终沉降。由此可以分析在不同施工期的地基沉降和固结特性,得到不同地基处理条件下路堤填筑期和预压期地基平均固结度与施工时间的关系。分析亦表明,粉喷桩加固能加速地基的固结速率。最后,针对沉降和固结理论计算中计算参数的难以合理确定的局限性,对现场实测沉降数据采用数理统计方法,提出了适用于连云港地区海相软土路堤沉降和固结估算经验公式。     

Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils

This paper presents a semi-analytical solution to one-dimensional consolidation of viscoelastic unsaturated soils with a finite thickness under oedometric conditions and subjected to a sudden loading. The solution is obtained by using Lee’s correspondence principle based on the semi-analytical solution to one-dimensional consolidation of elastic unsaturated soils. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. A typical example is given to show the evolution of excess pore-air and pore-water pressures as well as the total degree of consolidation of the soil layer with time for different ratios of air–water permeability coefficient, elastic modulus and viscoelastic coefficient. The one-dimensional consolidation behavior of viscoelastic unsaturated soil is discussed according to the semi-analytical solution. These results contribute to a better understanding of the consolidation behavior of viscoelastic unsaturated soils.     

A semi-analytical solution for swelling around a borehole

Previous field and laboratory studies have shown that the creation of a borehole in a saturated cohesive soil mass induces significant pore water suctions in the vicinity of the hole. The dissipation of these pore water suctions (swelling) leads to local increases in the moisture content and hence a softening of the soil around the hole. This softening may have important consequences for the stability of the hole and also for the ultimate load capacity of any foundation elements (bored piles or drilled shafts) constructed in these holes. This paper presents a semi-analytical solution for the radial dissipation of pore water pressure around a freshly created, vertical hole. It is assumed the soil deforms elastically during the swelling process. The solutions are presented in the form of isochrones of excess pore water pressure and may be used to obtain estimates of the time required for the soil around the hole to swell and therefore to soften. Both permeable and impermeable borehole interfaces have been considered, together with either no support for the hole or partial support provided by hydrostatic pressure within the hole.     

超大综采工作面开采地表层含水性自修复研究

研究超大综采工作面开采对地表层（0~15 m）含水性影响规律是确定生态修复策略的基础。针对西部风积沙区大规模高强度煤炭开采的特点,采用时移高分辨率探地雷达探测方法进行了开采全周期（采前-采中-采过-趋稳后）观测,获得了基于现代ARMA谱分析的风积沙区地表层含水率反演方法。研究表明:研究区内地表层含水性与地下潜水含水层没有直接的水力联系;风积沙区超大综采工作面开采对地表层起到"疏松"作用,对含有粘土隔水层区域的含水性影响不显著,而对不含隔水层区域的含水性影响相对较强;地表层含水性自修复周期小于一个自然年,而大气降水是提升和修复地表层含水性的重要外因。      

饱和多孔介质表面透水性对表面波传播特性影响薄层分析法

饱和半无限体表面透水性会影响表面波（瑞利波和斯通利波）存在及其传播特性。在表面透水情况下,只有瑞利波存在,而在不透水情况,不仅有瑞利波而且还有斯通利波。表面波在工程勘探及声波测试中扮演很重要角色,因此,有必要研究表面透水性对表面波传播特性的影响。采用薄层法,将表面波频率方程根的搜索问题转换成求特征值问题。根据表面波沿深度衰减特性,从一组计算的特征值及特征向量中筛选出与表面波对应特征值、特征向量,由特征值得到表面波频率特性（频散和衰减特性）,由特征向量得到孔隙压力、骨架位移随深度变化,进而分析在表面不透水情况下瑞利波和斯通利波影响深度及程度。     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

Consolidation due to shear loads distributed over a rectangular area

The paper presents an analytical study of the consolidation of a semi-infinite clay layer subjected to a shear load distributed over a rectangular area. Biot's theory is made use of, along with the three displacement functions suggested by Verruijt. A complex Fourier and Laplace transformation technique enables the solution to be obtained in terms of non-dimensional parameters. Settlements and pore pressures under the loaded area are evaluated for two types of surface drainage conditions. Extension of the solutions to point loads is also suggested. The Mandel–Cryer effect is seen in the behaviour of the pore pressure.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

The time–deflection behaviour of a rigid under-reamed anchor in a deep clay layer

The behaviour of an under-reamed anchor in a consolidating soil is examined by approximating the anchor as an impermeable circular plate embedded in a deep soil layer. Hankel and Laplace transforms are applied to the equations governing the consolidation process, and this greatly simplifies the equations, allowing a solution to be obtained for the transformed variables. Numerical inversion of both the Hankel and Laplace transforms is used to obtain the solution at any time. A particular feature of the solution method is that the unknown contact stress between the anchor and the soil and the unknown flows in the plane of the anchor are approximated as a series of simple functions with unknown coefficients. By determining the coefficients of the terms in the series, the complete solution may be found. Computations have been carried out using the method proposed, and results are presented for the time–settlement behaviour of an impermeable anchor. These results are compared with some published and some recomputed finite element data, and this highlights some of the difficulties encountered in using such numerical techniques.     

A semi-analytical solution to consolidation of unsaturated soils with the free drainage well

Based on Fredlund’s one-dimensional consolidation equation for unsaturated soil, Darcy’s law and Fick’s law, a semi-analytical solution was presented to the free drainage well with a finite thickness under application of uniform vertical loading and the boundary of the top and bottom surfaces impermeable to water and air. According to the polar governing equations of water and air phases and the boundary and initial conditions, the excess pore-air and pore-water pressures and the soil layer settlement in the Laplace transformed domain are obtained by performing the Laplace transform and utilizing the Bessel functions. Crump’s method is used to perform the inversion of Laplace transform in order to obtain numerical solutions in the real time domain. Finally, a typical example is given to illustrate the changes in the excess pore-air and pore-water pressures and soil layer settlement with time factor at different ratios of air–water permeability coefficient and/or different distances from the well.     

Development of Intermediate Microfabric in Kaolin Clay and Its Consolidation Behaviour

The effect of microfabric on the mechanical behaviour of clays has been explored previously based on the response of dispersed and flocculated microfabrics only. However, the natural clays often have the geometric arrangement of particles between these two extreme cases which can be termed as intermediate microfabric. This paper explores the formation of intermediate microfabric of kaolin clay and its impact on soil’s consolidation behaviour by performing self-weight consolidation, slurry consolidation and 1-D consolidation tests. The effect of calgon content (dispersing agent) on geometric arrangement of the particles has been evaluated through cluster size distribution by performing double hydrometer tests. Then these clay slurries have been used to perform the AFM (Atomic Force Microscopy) test to obtain the variation in average angle of particle orientation with respect to the calgon content present in the slurry. AFM technique provides 3D image of the clay sample and 2D image with Z-information with the potential of measuring intermediate microfabric of clayey soil quantitatively including dispersed and flocculated microfabrics. Other traditional techniques such as SEM, TEM & XRD are limited to only qualitative analysis of soil’s microfabric, thus, having no capability to measure intermediate microfabric of clay. A methodology of preparing bulk specimens of clay with intermediate microfabric has been developed using slurry consolidation technique; and then these specimens have been consolidated under 1-D loading to evaluate the effect of intermediate microfabric on compressibility and permeability of clay. In this study, all the experiments reports that the dispersed type geometric arrangement increases with the increase in calgon content in soil up to 2 % and then the reverse behaviour is observed at 3 %; which may depend on the required amount of sodium cations to neutralize the negatively charged faces of the clay platelets present in the slurry.