Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

A rigorous semi‐analytical solution for undrained cylindrical cavity expansion in critical state soils

This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate‐based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two‐invariant constitutive model from the critical state (Cam‐clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton–Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam‐clay model). The solution derived can be useful for estimating the instantaneous response of saturated low‐permeability soils around piles and self‐boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes. Copyright © 2016 John Wiley & Sons, Ltd.     

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semi-analytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.     

Analytical layer‐element method for non‐axisymmetric consolidation of multilayered soils

A numerically efficient and stable method is developed to analyze Biot's consolidation of multilayered soils subjected to non‐axisymmetric loading in arbitrary depth. By the application of a Laplace–Hankel transform and a Fourier expansion, the governing equations are solved analytically. Then, the analytical layer‐element (i.e. a symmetric stiffness matrix) describing the relationship between generalized displacements and stresses of a layer is exactly derived in the transformed domain. Considering the continuity conditions between adjacent layers, the global stiffness matrix of multilayered soils is obtained by assembling the inter‐related layer‐elements. Once the solution in the Laplace–Hankel transformed domain that satisfies the boundary conditions has been obtained, the actual solution can be derived by the inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the influence of the layered soil properties and time history on the consolidation behavior. Copyright © 2011 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.     

Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

基于广义SMP准则及应力路径法的柱孔扩张分析

柱孔扩张理论广泛用于旁压试验机制分析、沉桩挤土效应等岩土工程问题中。基于经典的Vesic孔扩张理论,采用能够考虑中主应力效应的广义SMP屈服准则,并结合有限应变理论对均质土体中柱孔扩张问题进行分析,根据应力路径假设提出确定塑性区平均体应变的解析步骤。通过大量变参数计算给出具有不同刚度指标 、泊松比 和内摩擦角 的土中柱孔扩张极限状态下的塑性区平均体应变、孔扩张半径比和孔扩张系数。分析结果表明, 、 、 越大,塑性区平均体应变越小,塑性区半径比越大,孔扩张系数越大;随着 增加, 的变化对孔扩张系数的影响更显著。同时,将结果与基于Mohr-Coulomb准则的孔扩张解答进行比较,探讨不同土性参数时中主应力效应对孔扩张系数的影响。文中分析方法及给出的考虑中主应力效应的柱孔扩张系数表可为原位试验分析及桩侧摩阻力估算提供参考。     

Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (k_s), desaturation coefficient (α), and saturated volumetric water content (θ_s) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.     

A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

This paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd.     

基于广义SMP破坏准则的柱形孔扩张问题理论分析

采用应力跌落的简化应力-应变模型考虑土的应变软化特性,同时采用简化的体积应变?v与大主应变?1及大主应变?1与小主应变?3之间的相互关系反映土的剪胀特性,根据空间准滑动面(SMP)理论和平面应变轴对称问题的柱形孔扩张基本方程,推导并给出一般黏性土中柱形孔扩张问题的应力场、应变场、位移场、塑性区半径和孔扩张压力。通过算例分析,探讨了土的剪胀因素、软化特性对孔扩张问题的影响程度。为了反映中主应力的影响,将本文解与基于Mohr-Coulomb破坏准则的解答进行了比较。计算结果表明,土的剪胀性和软化特性及中主应力对孔扩张问题的影响是显著的,基于Mohr－Coulomb破坏准则的孔扩张解答往往偏于保守。     

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.     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytical solutions of a finite two‐dimensional fluid‐saturated poroelastic medium with compressible constituents

An analytical solution is proposed for transient flow and deformation coupling of a fluid‐saturated poroelastic medium within a finite two‐dimensional (2‐D) rectangular domain. In this study, the porous medium is assumed to be isotropic, homogeneous, and compressible. In addition, the point sink can be located at an arbitrary position in the porous medium. The fluid–solid interaction in porous media is governed by the general Biot's consolidation theory. The method of integral transforms is applied in the analytical formulation of closed‐form solutions. The proposed analytical solution is then verified against both exact and numerical results. The analytical solution is first simplified and validated by comparison with an existing exact solution for the uncoupled problem. Then, a case study for pumping from a confined aquifer is performed. The consistency between the numerical solution and the analytical solution confirms the accuracy and reliability of the analytical solution presented in this paper. The proposed analytical solution can help us to obtain in‐depth insights into time‐dependent mechanical behavior due to fluid withdrawal within finite 2‐D porous media. Moreover, it can also be of great significance to calibrate numerical solutions in plane strain poroelasticity and to formulate relevant industry norms and standards. Copyright © 2014 John Wiley & Sons, Ltd.     

A non‐coaxial critical state soil model and its application to simple shear simulations

The yield vertex non‐coaxial theory is implemented into a critical state soil model, CASM (Int. J. Numer. Anal. Meth. Geomech. 1998; 22 :621–653) to investigate the non‐coaxial influences on the stress–strain simulations of real soil behaviour in the presence of principal stress rotations. The CASM is a unified clay and sand model, developed based on the soil critical state concept and the state parameter concept. Without loss of simplicity, it is capable of simulating the behaviour of sands and clays within a wide range of densities. The non‐coaxial CASM is employed to simulate the simple shear responses of Erksak sand and Weald clay under different densities and initial stress states. Dependence of the soil behaviour on the Lode angle and different plastic flow rules in the deviatoric plane are also considered in the study of non‐coaxial influences. All the predictions indicate that the use of the non‐coaxial model makes the orientations of the principal stress and the principal strain rate different during the early stage of shearing, and they approach the same ultimate values with an increase in loading. These ultimate orientations are dependent on the density of soils, and independent of their initial stress states. The use of the non‐coaxial model also softens the shear stress evolutions, compared with the coaxial model. It is also found that the ultimate shear strengths by using the coaxial and non‐coaxial models are dependent on the plastic flow rules in the deviatoric plane. Copyright © 2006 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.     

Coupled computations for an elastic‐perfectly plastic soil using adaptive mesh refinement

An adaptive mesh refinement algorithm has been developed for non‐linear computations in geomechanics, based on a smoothed stress–strain finite element formulation. This uses estimates of error in the incremental shear strain invariant to guide the regeneration of unstructured meshes at regular intervals during loading. Following each mesh‐update, no re‐analysis of previous increments with the new mesh is necessary. Algorithm performance has been investigated by analysing a passive earth pressure problem using a linear elastic‐perfectly plastic Mohr–Coulomb soil model. Perfectly drained behaviour has been considered, as have partially drained situations using hydromechanical coupling, while undrained behaviour has been approximated using time steps close to zero. In all cases, mesh adaptivity has been successful in capturing regions of high strain gradient. The results have been compared with analytical solutions. Accurate computations of limit load and shear band orientation have been obtained for a wide range of material dilation angles. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

A novel analytical approach for predicting the noncylindrical pile penetration‐induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods

Since development of cavity expansion theory and strain path method, almost all the conventional analyses of pile penetration problem have been based on circular cross section penetrometer. However, noncylindrical pile (with noncircular cross section) is also required in geotechnical engineering such as rectangular cross‐sectional pile, X‐sectional cast‐in‐place concrete pile, H‐shaped steel pile, prefabricated vertical drains, and flat dilatometer. This paper presents a novel and general analytical approach for capturing the soil deformation mechanism around the pile with arbitrary cross section. The penetration problem is simulated by a new 2‐dimensional (radial and circumferential) cavity expansion model. Based on the theoretical framework of strain path method, the kinematics (velocity field) of the noncylindrical cavity expansion is reduced to solve the Laplace equation with arbitrary velocity boundary conditions by using the conformal mapping technique. Then, solutions for the strain and displacement, which could consider the large deformation effect, are obtained by the integration of the strain rate and velocity along the streamline. The analytical solution is validated by comparing the degenerate solution of this study with conventional circular (cylindrical) cavity expansion theory. Subsequently, typical numerical examples for the deformation mechanism of elliptical and rectangular cavity expansion are presented to prove the advantage of the proposed new solution particularly in capturing the noncylindrical symmetric displacement field. A brief application of the proposed new analytical solution to the interpretation of the smear effect of prefabricated vertical drain installation confirms its useful in geotechnical engineering.