A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Axial kinematic response of end‐bearing piles to P waves

Kinematic pile–soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady‐state kinematic response of a cylindrical end‐bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed‐form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth‐independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free‐field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

Exact solutions for one‐dimensional consolidation of single‐layer unsaturated soil

Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi₁ and ψ₂, where ψ₁ and ψ₂, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

弹性地基上水工结构各向异性Mindlin底板计算分析的无单元法（EFGM）

无单元法（element free galerkin method）是一种基于滑动最小二乘法构造插值函数的无网格数值方法。以该方法中插值函数及其导函数为基础,从变分原理出发,建立了弹性地基上正交各向异性Mindlin板的无单元法求解控制方程,其中弹性地基采用Winkler地基模型。对该理论方法进行了相应的程序实现,最后通过算例分析表明了提出方法用于水工结构中弹性地基板问题分析的可行性和有效性。     

基于Mindlin理论Winkler地基参数的Kalman滤波识别

提出了Winkler地基参数的Kalman滤波识别方法。引入Mindlin理论后,推导了Winkler地基上板的控制微分方程。利用Fourier变换,推求了Winkler地基上简支板的Fourier闭式解。推导了Winkler地基参数的Kalman滤波方程,研究了Winkler地基参数的Kalman滤波识别的具体计算步骤。研究表明,运用Kalman滤波理论进行Winkler地基参数的识别,能有效地估计Winkler地基参数;Winkler地基参数的滤波收敛速度和精度受地基参数初始值选取和位移实测资料的影响,且Kalman滤波理论也可用于其他地基模型地基参数的识别。     

Analytical model for the prediction of building deflections induced by ground movements

The objective of this study is to develop an analytical model that can predict the building‐relevant deflections induced by tunnelling or mining subsidence. The model takes into account soil–structure interactions due to differences in stiffness between the ground and the building. The ground is modelled by the Winkler model with an initial ground curvature equivalent to the free‐field ground movements. The building is modelled by a horizontal beam with uniform loading. The static and cinematic equilibrium of both the ground and the building are then calculated to assess the final building and ground shape, and the building deflection is derived. The resulting analytical model is used to investigate the influence of the ground and the building's mechanical properties, the building load and the initial value of the free‐field ground curvature (hogging or sagging). The model appears to be more comprehensive than those reported elsewhere that address the problem with numerical models. In particular, the analytical model makes it possible to distinguish two different final situations—with continuous or discontinuous contact between the ground and the building. The model is compared with numerical results and used to analyse a case study. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical solution for consolidation and desiccation of soft soils

The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd.     

双排门式抗滑桩的空间计算模型

滑坡推力大时单排抗滑桩不能产生良好的抗滑效果,而抵抗力大、桩顶位移小的双排门架式抗滑桩能有效地限制支挡结构的变形。目前的计算方法忽略了双排抗滑桩间联系梁和圈梁所起的变形协调及桩梁岩土间的相互作用,具有一定的局限性。针对这一问题,将双排门架式抗滑桩视为桩梁岩土共同作用的单层多跨框架结构,综合考虑桩间土拱效应、框梁及联系梁对双排门架式抗滑桩的空间协同作用,提出了桩梁土空间协同作用下的双排门架式抗滑桩受力模型;基于静力平衡及变形协调原理,建立了双排门架式抗滑桩受力模型的变形方程;采用有限元理论编制了双排门架式抗滑桩的有限元程序,计算内力和变形特性;最后在三峡库区防治工程中对研究成果进行了验证,计算结果及对比分析表明该模型符合于抗滑桩的特性。     

Vertical impedance of an end‐bearing pile in viscoelastic soil

This paper presents a new method to derive the analytical solution for the vertical impedance of an end‐bearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one‐dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil–pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. Copyright © 2014 John Wiley & Sons, Ltd.     

An analytical continuum model for axially loaded end-bearing piles in inhomogeneous soil

An approximate static solution is derived for the elastic settlement and load-transfer mechanism in axially loaded end-bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed-form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth-dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth-independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.     

The axisymmetric consolidation of a semi‐infinite transversely isotropic saturated soil

This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd.     

Load transfer approach for laterally loaded piles

A two‐parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two‐parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile‐head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile–soil relative stiffness. Copyright © 2001 John Wiley & Sons, Ltd.     

An elasto‐plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling

This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd.     

A quasistatic analysis of a plate on consolidating layered soils by analytical layer‐element/finite element method coupling

In this paper, a coupling method between finite element and analytical layer‐elements is utilized to analyze the time‐dependent behavior of a plate of any shape and finite rigidity resting on layered saturated soils. Based on the integral transform techniques together with the aid of an order reduction method, an analytical layer‐element solution is derived from the governing equations for three‐dimensional Biot consolidation with respect to a Cartesian coordinate system and then extended to be the fundamental solution for the layered saturated soil under a point load. The Mindlin plate is modeled by eight‐noded isoparametric elements. The governing equations of the interaction between soil and plate in the Laplace‐Fourier transformed domain are deduced by referring to the coupling theory of FEM/BEM, and the final solution is obtained by applying numerical inversion. Numerical examples concerned with the time‐dependent response of a plate are performed to demonstrate the influence of soil and plate properties on the interaction process. Copyright © 2014 John Wiley & Sons, Ltd.     

Elastic‐plastic solutions for expanding cavities embedded in two different cohesive‐frictional materials

An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large‐strain quasi‐static expansion of both spherical and cylindrical cavities in elastic‐plastic soils is considered. A non‐associated Mohr–Coulomb yield criterion is used for both soils. Closed‐form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground‐freezing around shafts, tunnelling, and mining. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Modelling chemo‐hydro‐mechanical behaviour of unsaturated clays: a feasibility study

Effective capabilities of combined chemo‐elasto‐plastic and unsaturated soil models to simulate chemo‐hydro‐mechanical (CHM) behaviour of clays are examined in numerical simulations through selected boundary value problems. The objective is to investigate the feasibility of approaching such complex material behaviour numerically by combining two existing models. The chemo‐mechanical effects are described using the concept of chemical softening consisting of reduction of the pre‐consolidation pressure proposed originally by Hueckel (Can. Geotech. J. 1992; 29 :1071–1086; Int. J. Numer. Anal. Methods Geomech. 1997; 21 :43–72). An additional chemical softening mechanism is considered, consisting in a decrease of cohesion with an increase in contaminant concentration. The influence of partial saturation on the constitutive behaviour is modelled following Barcelona basic model (BBM) formulation (Géotech. 1990; 40 (3):405–430; Can. Geotech. J. 1992; 29 :1013–1032). The equilibrium equations combined with the CHM constitutive relations, and the governing equations for flow of fluids and contaminant transport, are solved numerically using finite element. The emphasis is laid on understanding the role that the individual chemical effects such as chemo‐elastic swelling, or chemo‐plastic consolidation, or finally, chemical loss of cohesion have in the overall response of the soil mass. The numerical problems analysed concern the chemical effects in response to wetting of a clay specimen with an organic liquid in rigid wall consolidometer, during biaxial loading up to failure, and in response to fresh water influx during tunnel excavation in swelling clay. Copyright © 2005 John Wiley & Sons, Ltd.     

An improved shear strength model of unsaturated soils over a wide suction rangeEI北大核心

不同类型的非饱和土在自然界中广泛存在。由于不同类型土的颗粒级配和矿物组成成分的不同,其强度特性存在较大的差异。为了建立一种适用于不同类型非饱和土的强度预测统一模型,本研究系统地分析了土体类型对非饱和土强度演化趋势的影响,在综合考虑两种常用模型优越性的基础上,提出了一种改进的非饱和土抗剪强度模型,同时,利用现有常用的强度模型,对不同类型土在广吸力范围内的强度特性进行了预测,并对拟合结果进行了对比分析。研究结果表明:(1)在广吸力范围内,不同类型土的强度演化规律可分为两类,山峰型和增长稳定型;(2)改进模型可以较为准确地预测不同类型土在广吸力范围内的强度特性;(3)明确了改进模型中各参数的物理意义,并初步给出了改进模型在应用于不同类型土时各参数取值的建议范围。     

Stochastic finite element modelling of water flow in variably saturated heterogeneous soils

Water flow is greatly influenced by the characteristics of the domain through which the process occurs. It is generally accepted that earth materials have extreme variations from point to point in space. Consequently, this heterogeneity results in high variation in hydraulic properties of soil. In order to develop an accurate predictive model for transport processes in soil, the effects of this variability should be considered. In this study a two‐dimensional stochastic finite element flow model was developed for simulation of water flow through unsaturated soils. In this model, the stochastic partial differential governing equation of water flow, obtained from implementation of the perturbation‐spectral stochastic method on classical Richard's equation, was solved using a finite element method in the space domain and a finite difference scheme in the time domain. The effective hydrological parameters embedded in the mathematical model depend on time derivatives of capillary tension head; this makes possible to consider the hysteresis due to large‐scale variability of soil hydrological properties. The model is also capable of simulating infiltration and evaporation events and rapid change in the land surface boundary condition from one type event to another, based on a scheme used in the model for implementation of land surface boundary condition. The model was validated with the data obtained from a layered lysimeter test. The model was also used to simulate water flow under a long irrigation furrow. The results obtained with this model show better agreement with experimental measurements in comparison with a deterministic model. The possible reason for this agreement is that in the developed model, the influence of the variability of the properties of soil and effects of parameter hysteresis on water flow and water content redistribution are considered. Copyright © 2010 John Wiley & Sons, Ltd.