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This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.

First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.

The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.

Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

In the framework of the finite element method, the problem of elasto‐plastic consolidation gives rise to a system of non‐linear, coupled residual equations which satisfy the conditions of balance of momentum and balance of mass. In determining the roots of these equations it is necessary that the coupled equations be linearized. To this end, the concept of ‘consistent linearization’ proposed by Simo and Taylor for a single‐phase system is applied to the two‐phase soil‐water system. The roots of the coupled residual equations are solved iteratively by employing Newton's method. It is shown that in non‐linear consolidation analyses, the use of a tangent coefficient matrix derived consistently from the integrated constitutive equation defining the characteristics of the solid skeletal phase results in an iterative solution scheme which preserves the asymptotic rate of quadratic convergence of Newton's method. Numerical examples involving combined radial and vertical flows through an elasto‐plastic soil medium are presented to demonstrate the computational superiority of the above technique over the method based on standard ‘elasto‐plastic continuum formulations’ adopted in most finite element codes.

Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

Elasto‐plastic models based on critical state formulations have been successful in describing many of the most important features of the mechanical behaviour of soils. This review paper deals with the applications of this class of models to the numerical analysis of geotechnical problems. After a brief overview of the development of the models, the basic critical state formulation is presented together with the main modifications which have actually been used in computational applications. The problems associated with the numerical implementation of this type of models are then discussed. Finally, a summary of reported computational applications and some specific examples of analyses of geotechnical problems using critical state models are presented.

A derivation for the finite element equations of consolidation by the principle of virtual work and virtual complementary work is presented. This provides a simple alternative to derivation by variational principles or the Laplace transform. In the final part of the paper the equations are rearranged into a form suitable for time stepping for non‐linear applications.

The implementation of the finite element solution of Biot's consolidation theory on a low‐cost microcomputer is described. A two‐dimensional linear elastic model is solved using bilinear rectangular elements and a fully implicit timestepping algorithm. The machine used is the Acorn Computers model B, BBC microcomputer, a popular low‐cost engineering applications machine. The program is written in Basic but to increase speed of computation certain sections of the solution procedure involving matrix manipulation are written in Assembly language. The results obtained are encouraging from the point of view of accuracy, problem size and computational time. It is concluded that there is scope for the use of the present generation of low‐cost microcomputer, as typified by this machine, in the numerical solution of the more straightforward, but still realistic, consolidation problems.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

A three‐dimensional dynamic analysis program for saturated porous‐rocks and soils (MPDAP‐3D) is developed in this study. The theoretical formulations incorporated in the proposed computer program are the extension of Biot’s two‐phase theory to non‐linear region. The generalized Hoek and Brown model is used to represent the skeleton constitutive relation. A three‐dimensional elasto‐plastic matrix for the generalized Hoek and Brown model is derived by extending two‐dimensional formulation. Numerical study for typical verification problems is carried out to show the validation of the computational algorithms of the computer program.

Several constitutive models are available in the literature to describe the mechanical behaviour of cement stabilized soils. However, difficulties in implementing such models within commercial finite element programs have hindered their application to solve related boundary value problems. Therefore, the aim of this study is to implement a constitutive model, which has the capability to simulate cement stabilized soil behaviour, into the finite element program ABAQUS through the user material subroutine UMAT.

After a detailed review of existing constitutive models for cement stabilized soils, a model based on the elasto‐plastic theory and the extended critical state concept with an associated flow rule is selected for the finite element implementation. A semi‐implicit integration method (cutting plane algorithm) with a continuum elasto‐plastic modulus and path dependent stress prediction strategy has been used in the implementation. The performance of the new finite element formulation of the constitutive model is verified by simulating triaxial test data using the finite element program with the new implementation and predictions from constitutive equations as well as experimental data.

The paper provides the implementation procedure of the constitutive model into ABAQUS but this method is useful for the implementation of any other constitutive model into ABAQUS or any other finite element program. Simulated results for the volumetric deformation of cement stabilized soils show that the cement stabilized soils do not obey the associated flow rule at high confining pressures. The parametric study shows that the influence of cementation increases the brittle nature and the bearing capacity of treated clay. In addition the results show that proposed finite element implementation has the ability to illustrate key features of the cement stabilized clay.

This paper presents an implementation of an elasto‐plastic constitutive model, based on the extended critical state concept, for cement stabilized soils into a finite element programme, which has been identified as an important and challenging topic in computational geomechanics. This implementation is useful in solving boundary value problems in geomechanics involving cement stabilized soils, incorporating key characteristics of these soils.

The purpose of this paper is to evaluate the co-seismic and post-seismic behaviors of an existed soil-foundation system in an actual alternately layered sand/silt ground including pore water pressure, acceleration response, and displacement et al. during and after earthquake.

The evaluation is performed by finite element method and the simulation is performed using an effective stress-based 2D/3D soil-water coupling program DBLEAVES. The calculation is carried out through static-dynamic-static three steps. The soil behavior is described by a new rotational kinematic hardening elasto-plastic cyclic mobility constitutive model, while the footing and foundation are modeled as elastic rigid elements.

The shallow (short-pile type) foundation has a better capacity of resisting ground liquefaction but large differential settlement occurred. Moreover, most part of the differential settlement occurred during earthquake motion. Attention should be paid not only to the liquefaction behavior of the ground during the earthquake motion, but also the long-term settlement after earthquake should be given serious consideration.

The co-seismic and post-seismic behavior of a complex ground which contains sand and silt layers, especially long-term settlement over a period of several weeks or even years after the earthquake, has been clarified sufficiently. In some critical condition, even if the seismic resistance is satisfied with the design code for building, detailed calculation may reveal the risk of under estimation of differential settlement that may give rise to serious problems.