bluuebunny/crossref_metadata_2025 huggingface dataset:
Vertical stress distribution due to an arbitrarily shaped foundation using triangulation and an analytical expression for a triangular loaded region
Authors: Murti V. , Wang Y. C.
Published: August 2005

Using the basic Boussinesq's equation, the expression for the vertical stress distribution (σz) underneath any point on the ground surface due to a general triangular loaded region in a preferred orientation with a linearly varied loading has been successfully derived. When the triangle is not in a preferred orientation, a simple axis transformation is required and the expression will be equally applicable. Based on this expression, σz due to an arbitrarily shaped loaded foundation can simply be determined by first triangulating the loaded area and summing up the contributions from each generated triangular region. The procedures for triangulating and calculating the stress distribution can be simply automated through computer programs.
Verification for numerical modelling of jointed rock mass using thin layer elements
Authors: Fishman K. L. , Derby C. W. , Palmer M. C.
Published: August 2005

Thin layer finite elements are employed to model the response of rock joints in finite element analyses of rock mechanics problems. The case of a circular opening embedded in a rock mass is investigated. Results are obtained for both solid and jointed rock masses, and the effects of the presence of joints on the stress and strain field are investigated. Results from the finite element analysis are verified with respect to measurements from physical modelling. It is shown that the comparison between measured and computed results is satisfactory and that the presence of joints has a pronounced effect on the stress and strain field as compared to that realized in the absence of any rock joints. This study provides valuable data which contribute to the verification of thin layer finite elements for modelling the response of rock joints.
Material instability for drained and undrained behaviour. Part 1: Shear band generation
Authors: Molenkamp F.
Published: August 2005

To increase the insight into the phenomenon of liquefaction a theoretical study has been performed of material instability for undrained behaviour. Material instability concerns the instability of an equilibrium state of an infinite homogeneous solid for both uniform deformation and shear‐band generation. In this paper shear‐band generation is considered. In a companion paper the case of uniform deformation is elaborated and combined with the current results. In this paper it is shown that, for a contractant material, shear‐band generation is accelerated by decreasing the drainage.
Continuum modelling of jointed porous rock
Authors: Cho Taechin F. , Plesha Michael E. , Haimson Bezalel C.
Published: August 2005

Constitutive equations for the mechanical and hydraulic behaviour of saturated porous rock with joint sets of specified orientations are developed by superposing continuum representations for the mechanical and hydraulic properties of the intact rock and each of the joint sets. The resulting continuum theory allows for fluid diffusion through and between interconnected rock pores and joint sets of specified orientation, and also accounts for the anisotropy of the mechanical properties due to joint stiffnesses. The accuracy and reliability of this model are verified by finite element simulation of example problems. The first example considers joint orientation‐dependent rock deformation in a hypothetical porous medium with one joint set of different dip angles. More realistic examples related to rock slope stability and reservoir‐induced seismicity are also considered in which the constitutive law's utility for modelling time‐dependent fluid pressures is illustrated.
Convolution operator techniques and asymptotic expansions for long‐term behaviour of laterally loaded piles in permafrost
Authors: Foriero A. , Ladanyi B.
Published: August 2005

Long‐term predictions of pile displacements, bending moments and soil reactions for laterally loaded piles in a hereditary elastic medium are presented. Asymptotic estimates on fractional exponential operators yield predictions for large time.
Dynamic response of a thick plate on viscoelastic foundation to moving loads
Authors: Zaman Musharraf , Taheri Michael R. , Alvappillai A.
Published: August 2005

A finite element algorithm is presented to evaluate the dynamic response of pavements including aircraft‐guideway‐foundation interaction. The pavement‐foundation system is modeled by a series of thick plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. The moving aircraft loads are represented by masses each supported by a spring and dashpot suspension system and having a specified horizontal velocity and acceleration. The accuracy of the algorithm is verified by comparing the finite element solution with available analytical results. A parametric study is conducted to determine the effects of various parameters on the dynamic response of pavements to moving loads.
An analytical technique for evaluation of coupled heat and mass flow coefficients in unsaturated soil
Authors: Yong R. N. , Xu D. M. , Mohamed A. M. O. , Cheung S. C. H.
Published: August 2005

This study was done to evaluate a phenomenological approach for determining the coupled heat and water diffusion parameters. This technique requires the use of both theory and experimental data. The transport equation was solved analytically using nondimensional analysis.

The calculated diffusion parameters of a compacted sand–bentonite‐based material are presented. The agreement between the back calculated values and the experimental volumetric water content profiles was good. Practical application of the technique is also discussed.
Bounding solutions for the pressuremeter modulus using variational principles in elasticity
Authors: Dormieux L.
Published: August 2005

It is classically assumed that the pressuremeter modulus (determined from the initial slope of the pressuremeter expansion curve) can be used as an estimate for the soil's shear modulus, provided disturbance effects can be neglected. This approximation is only rigorous in the plane‐strain case and requires that the height of the cell be large in comparison with its diameter. The present paper allows to quantify the error that results from this approximation as a function of the height over diameter ratio. The analysis is based on an application of the variational principles of elasticity. It is shown that the static and the kinematic approaches lead, respectively, to a lower‐ and an upper‐bound estimate of the pressuremeter modulus expressed in terms of the soil's elastic coefficients.

The calculations are completely carried out in the case of an infinite cavity subjected to a pressure on a finite length. It is shown that the plane‐strain approximation overestimates the shear modulus. Based on the kinematic approach, a method is developed to derive the shear modulus from the pressuremeter modulus which accounts for the finite slenderness of the cell. This method can be extended to more complex geometries and material properties, including soil heterogeneity and anisotropy.
Spurious bifurcation modes for cohesive solids under uniform stress
Authors: Moore Ian D.
Published: August 2005

Singularities leading to the calculation of spurious velocity fields have been observed in the tangent stiffness equations assembled during the finite‐element analysis of square blocks of purely cohesive perfectly plastic material. These occur because of weaknesses in conventional implementations of the plastic flow rule. Both twisting and swaying modes occur which interfere with the calculation of uniform velocity fields for blocks responding to uniform applied stress. Various techniques can be used to eliminate the problem. The phenomenon does not eventuate when non‐uniform stress fields are acting, so does not affect the solution of practical plasticity problems.
Liquefaction of unstable slopes
Authors: Koenders M. A. , Sellmeijer J. B.
Published: August 2005

Two liquefaction effects are described here which account for the fluidization phenomena observed in the collapse of water‐saturated sloped‐embankments. A surface erosion effect is a process in which the top layer of a submerged embankment liquefies. The subsequent reconstitution is a gradual process for which the time dependence is calculated.

Internal liquefaction takes place suddenly and a criterion is derived to describe its onset. It is shown that the process is associated with the change from loading to unloading of an external shearing loaded on top of the slope and that there is no stable elastic unloading process.
A boundary integral method for steady flow in unsaturated porous media
Authors: Martinez M. J. , McTigue D. F.
Published: August 2005

The governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary‐pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well‐suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non‐linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel.
A note on non‐linear elasticity of isotropic overconsolidated clays
Authors: Hueckel T. , Tutumluer E. , Pellegrini R.
Published: August 2005

An empirically established rule of Wroth1 for the dependence of the shear modulus on the mean effective pressure and the overconsolidation ratio in clays is investigated within the framework of non‐linear elasticity. The resulting isotropic‐deviatoric coupling is derived and compared to experiments.
Incident P and SV wave scattering effects under different canyon topographic and geological conditions
Authors: Zhao Chongbin , Valliappan S.
Published: August 2005

A numerical model for wave scattering problems due to P and SV wave incidences is outlined in this paper. After verifying the present model, a general parametric study on the displacement patterns along the canyons of different shapes due to P and SV wave incidences is also performed. In order to investigate the effects of geologic conditions on ground motions, a weathered V‐shaped canyon, which has different elastic moduli in the weathered layer, is also considered herein. The numerical results from this investigation demonstrated that (1) the present model is very suitable to simulate the problem of P and SV wave scattering along a natural canyon; (2) the shape of a canyon may have important effects on the displacement patterns along the canyon, so that a rectangular canyon is not appropriate to be a dam site due to its high amplification effects on incident waves; (3) the weathered layer on the surface of a canyon will significantly amplify the free field motion, especially for the case of softer weathered layer. Therefore, the excavation or grouting on a dam or a bridge abutment is not only necessary for static stability under static loads, but also beneficial to earthquake resistance because less amplification can be expected for sound rock abutments.
The numerical simulation of seasonal soil drying in an unsaturated clay soil
Authors: Thomas Hywel Rhys , Rees Stephen William
Published: August 2005

The results of a numerical simulation of the observed field‐drying behaviour of an unsaturated clay are described. In particular, the simulation of soil drying during the summer of 1983 is addressed.

Richards' pressure‐based unsaturated flow formulation is adopted. Transient numerical solutions are achieved by making use of the finite element method coupled with a finite difference timestepping scheme.

The application of the algorithm to the simulation of the problem in hand is described. The initial moisture content distribution represents saturated conditions as indicated by field‐measured data. Boundary conditions are determined from an interpretation of meteorological data. A simple method of representing plant root extraction of soil moisture is proposed.

Comparisons of numerical results with field‐measured data collected by British Gas are presented. Good correlation is obtained. The numerical simulation is shown to be capable of representing the observed field‐drying behaviour. The complexity of modelling soil drying, as opposed to infiltration, is clearly illustrated by the work presented.
Derivation of material variability from settlement measurements
Authors: Zeitoun D. G. , Uzan J.
Published: August 2005

In pavement evaluation using non‐destructive testing (NDT), a large amount of deflection bowls are analysed in terms of the elastic moduli of the layers. The results are used to evaluate the material variability, which could serve in an overlay design procedure based on the concept of reliability. The model currently used for interpreting deflection bowls is based on the random variable theory which neglects the spatial distribution of the elastic modulus of the material. Since the subgrade and pavement materials have a spatial distribution, the analysis of NDT could lead to an underestimate of the material variability. The random field theory, which is more adequate than the random variable theory, is presented and used to correct the NDT analysis.

The pavement is modelled as a multilayer random elastic medium with, for each layer, a constant Poisson's ratio and a random shear modulus characterized by three statistical moments: average value, standard deviation and autocorrelation function. The stochastic integral formulation presented in the previous publications is generalized here for a multilayer system. The multilayer system is analysed with the random field theory and the covariance matrix of the deflection bowl is obtained and used to generate deflection bowls corresponding to the properties of the random field. These bowls are then interpreted with the current procedure and elastic modulus variabilities are computed. It is found that the current procedure for interpreting deflection bowls underestimates the variability of the subgrade, by a factor of 0.4–1.0. It is interesting to note that the average moduli of the Boussinesq layer and of the two layers are not affected by the type of theory used. The variability of the upper layer in the two‐layer system is also unaffected for a small variation range.
Transient infinite elements for seepage problems in infinite media
Authors: Zhao Chongbin , Valliappan S.
Published: August 2005

In this paper, a time‐dependent infinite element which can be used to simulate transient seepage problems in infinite media is presented. The hydraulic head distribution function of the element has been derived in detail and the property matrices of the element have been well formulated. Since both space and time variables are used in the course of constructing the hydraulic head distribution function of the element, the present infinite element can be referred to as a transient one. Using the present infinite element to model the far field of a system, the mechanism of transient seepage problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Since explicit expressions can be written for the property matrices of the infinite element, they may be evaluated quite easily and this can be carried out by writing a simple subroutine in a computer program. In order to examine the accuracy and efficiency of the present infinite element, both a one‐dimensional (ID) transient seepage problem in a semi‐infinite medium and a 2D transient seepage problem in a full plane have been solved using the finite and infinite element technique. It has been demonstrated that the present infinite element is very useful for the numerical simulation of transient seepage problems in infinite media.
The axial loading of a rigid circular anchor plate embedded in an elastic half‐space
Authors: Selvadurai A. P. S.
Published: August 2005

The present paper examines the axisymmetric problem related to the loading of a rigid circular anchor plate which is embedded in bonded contact with an isotropic elastic half‐space. A Hankel transform development of the governing equations is used to reduce the associated mixed boundary value problem to a set of coupled Fredholm integral equations of the second kind. These equatons are solved in a numerical fashion to generate results of engineering interest. In particular, the results indicate the influence of the depth of embedment on the axial stiffness of the rigid anchor plate.
Boundary element analysis of contaminant transport in fractured porous media
Authors: Leo C. J. , Booker J. R.
Published: August 2005

A two‐dimensional boundary integral method to analyse the flow of contaminant in fractured media having a two‐ or three‐dimensional orthogonal fracture network is presented. The method assumes that the fractures provide the paths of least resistance for transport of contaminants while the matrix, because of its low permeability, acts as ‘storage blocks’ into which the contaminant diffuses. Laplace transform is used to eliminate the time variable in the governing equation in order to facilitate the formulation of a boundary integral equation in the Laplace transform space. Conventional boundary element techniques are applied to solve for the contaminant concentrations at specified locations in the spatial domain. The concentration in the time domain is then obtained by using an efficient inversion technique developed by Talbot. The method is able to analyse the behaviour of waste repositories which have diminishing concentration due to the mass transport of the contaminant into the surrounding fractured media.
Negative skin friction on single piles in a layered half‐space
Authors: Lim C. H , Chow Y. K. , Karunaratne G. P.
Published: August 2005

Settlement of the surrounding soil due to surcharge placement may give rise to negative skin friction developed in piles. In this paper, a simple discrete element approach using subgrade reaction method is proposed to analyse negative skin friction on single piles. The pile is embedded in a two‐layer soil where the upper soil layer undergoes consolidation while the lower soil layer acts as a stiffer bearing stratum. Two different and uncoupled deformation modes, one at the pile shaft and the other at the pile toe have been assumed in the determination of the soil stiffness. The effects of a compressible bearing stratum and embedment length of the pile in the bearing stratum are considered in the analysis. This simple approach is verified by comparison with rigorous methods of modelling the soil as an elastic continuum. Three reported case histories are analysed and the computed results are shown to be in reasonable agreement with the field measurements.
Tensile stresses around boreholes due to transient fluid flow
Authors: Chan Derek Y. C. , Hughes Barry D. , Paterson Lincoln
Published: August 2005

We present solutions for the effective stress induced by gas flow through a porous solid into a borehole resulting from sudden pressure reduction. Tensile effective stress that exceeds the strength of the solid will lead to borehole failure. This has applications to the intentional creation of cavities, relevant to the efficient recovery of coalbed methane, and the avoidance of borehole stability problems in conventional gas production.
A semi‐analytical solution procedure for predicting damage evolution at interfaces
Authors: Chen Zhen
Published: August 2005

A semi‐analytical solution procedure is developed to predict damage evolution at the interface between two dissimilar geologic materials. The procedure consists of an analytical field solution within each finite element, and a numerical scheme for simulating structural responses. For static problems, an incrementaliterative solution strategy is constructed through the use of an initial elasticity stiffness matrix, and an evolving‐localization constraint in terms of a suitable measure of damage at the most severely damaged element. For simplicity, one‐dimensional problems are considered to illustrate the features of the proposed procedure, and future research is discussed based on the preliminary results obtained.
An approximate numerical analysis of pile–raft interaction
Authors: Poulos H. G.
Published: August 2005

This paper presents an approximate method of numerical analysis of piled–raft foundations in which the raft is modelled as a thin plate and the piles as interacting springs of appropriate stiffness. Allowance is made for the development of limiting pressures below the raft and of the ultimate axial load capacity of the piles.

Comparisons between this analysis and existing solutions verify that, despite the approximations involved, the analysis can provide solutions of adequate accuracy for the settlement and pile load distribution within a piled raft.

Comparisons are also made with the results of a series of centrifuge tests and with measurements of the performance of a full‐scale piled raft. In both cases, the analysis predicts very well the settlement and proportion of load carried by the piles.
A continuum theory of granular media partially saturated with a viscous fluid
Authors: Pietruszczak S.
Published: August 2005

This paper is concerned with the behaviour of granular media containing voids penetrated by a mixture of viscous liquid and gas (air). It is assumed that, for such materials, the skeleton may be considered as rate‐independent and the sensitivity to the applied loading rate may be attributed to the viscosity of the liquid filling the void space. Within the context of geomechanics, such assumptions appear to be relevant to all coarse‐grained cohesionless materials, including saturated sands. A mathematical formulation for the description of undrained response is presented. The macroscopic properties are estimated based on volume averaging, which is applied to both stress and strain measures within the heterogeneous constituent medium. Numerical examples are provided illustrating the influence of the viscosity of the liquid on the liquefaction potential of a loose granular assembly.
Elastic stress waves in rockbolts subject to impact loading
Authors: Yi Xiaoping , Kaiser Peter K.
Published: August 2005

Due to rock bursting or blasting, violent rock ejections can occur. In underground excavations, rockbolts are often used to retain rock blocks that otherwise would be ejected. Employing the stress wave approach, general formulae are derived to compute the elastic stress waves in rockbolts subject to rock block impact loading. Weight‐drop tests on steel rods, simulating impact loading of rockbolts, were performed, and a reasonable agreement is found between theoretical predictions and experimental results. The elastic stress wave in an impact loaded steel rod consists of a rider wave and a lower‐frequency carrier wave. With the same drop height, the carrier wave becomes more sinusoidal as the mass ratio of steel rod to drop weight is decreased.
Comparison of calculational approaches for structural deformation in jointed rock
Authors: Senseny Paul E. , Simons Donald A.
Published: August 2005

Results from five different computer models for structural deformation in jointed rock are compared for a problem involving stress‐wave loading of a lined circular tunnel in a jointed medium. The computer models include two discrete element codes, The Direct Interacting Block Systems (DIBS) and The Universal Distinct Element Code (UDEC), and three finite element codes, The Finite Element Code for Largely Explicit Calculation (FLEX), The Explicit Calculations of Interacting Bodies Under Rapid Loading Code (EXCALIBUR), and PRONTO. The finite element codes used either slidelines or joint elements to simulate the motion on joints.

All codes had some difficulties with a sequence of preliminary problems solved to ‘shake down’ the computer codes. However, most of the shortcomings of each code were readily overcome. Results showed that three codes could obtain similar answers for tunnel closure, stress around the tunnel and slip on the joints.
Cracking in clays: Solutions to problems in earth structures
Authors: Harison Jack A. , Hardin Bobby O.
Published: August 2005

Methods are presented for analysing earth structures subjected to tensile stresses that may produce cracking. The linear elastic fracture mechanics approach is emphasized. Methods of solution are proposed for cracking of a clay layer above the water table due to desiccation; cracking of layered earth structures subjected to external loads; cracking of clay caps for landfills due to differential settlement; and radial cracking in pressurized boreholes. Causes and mechanisms of cracking are discussed for each problem and models pertinent to each problem are proposed. Solutions have been developed by synthesizing analytical and numerical methods. Published experimental data have been incorporated in modelling matric suction and cracked beams on elastic foundations. Finite element analyses were employed to obtain solutions for cracking due to differential settlement and radial cracking in boreholes. The solutions presented herein can be used to assess the soundness of existing structures or to assess the risk of cracking for the design of new structures.
Numerical modelling of transient contaminant migration problems in infinite porous fractured media using finite/infinite element technique. Part I: Theory
Authors: Zhao Chongbin , Valliappan S.
Published: August 2005

The leakage effect in porous fissured media has been considered in a general sense by introducing a new expression of the leakage term in this paper. The double porosity concept is employed and the related expressions are formulated using the upwind finite element approach. Considering the infinite extension of the problem domain, a mapped transient infinite element has been presented to simulate the far field of the infinite medium. Since the mass transfer function of the present mapped transient infinite element is dependent on both space and time variables, the mechanism of transient contaminant migration problems in infinite porous fractured media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest. By comparing the current numerical results with the analytical ones, the accuracy, correctness and effectiveness of the present method have been established. Three different time discretization schemes were examined and it was found that either the central difference or the backward difference approximation is suitable for the upwind finite element simulation of transient contaminant migration problems.
Contaminant leakage from deeply buried cylindrical repositories
Authors: Booker J. R. , Leo C. J.
Published: August 2005

The presence of any leak in a waste repository is going to cause some concern since it may lead to the contamination of the surrounding soil and groundwater. This is an important problem which occurs and recurs, sometimes despite the precautions taken to minimize the possibility of development of any leak. The effects of contaminant leakage in general are not well understood. Thus it is the aim in this paper to develop some semi‐analytical solutions of leakage problems occurring in deeply buried cylindrical repositories. In the solution approach, a series of integral transforms is used to simplify the governing equations and solutions are found in the transform space before numerical inversions are applied to obtain the contaminant concentrations in real space and time. To illustrate the application of the technique, results of some leakage cases are presented.
Simulation of arch dam – foundation interaction with a new friction interface element
Authors: Swoboda G. , Lei X. Y.
Published: August 2005

A new model for three‐dimensional non‐linear contact problems with irreversible friction is presented here for the interaction between the rock foundation and an arch dam structure. Based on the finite element method and load incremental theory, a constraint contact element with displacements and contact stresses as node parameters is developed. In this approach, four contact conditions are considered, i.e. fixed, slip, free and mixed. This model can simulate frictional slippage, decoupling and re‐bonding of two bodies initially mating at a common interface or with any initial gaps. Furthermore boundary conditions for this element are discussed and treatment measures proposed. This method is shown to be effective and to have the advantage of being easily implemented into standard finite element programs. Solutions are obtained for a centrally loaded, simply supported composite beam and for an end‐loaded elastica with initial gaps in regional contact with a rigid surface. The results obtained for these examples are compared to the plane stress solutions by contact friction analysis. As an application example, Quanshui arch dam located in Ruyuan County of Guangdong Province in southern China is simulated with the new element.
Finite element modelling for simulating the surface subsidence above a compacting hydrocarbon reservoir
Authors: Lewis R. W. , Sukirman Y.
Published: August 2005

The surface subsidence above a compacting saturated oil reservoir is the main topic of this paper. From a literature review, it is obvious that extensive efforts have been conducted for investigating this phenomenon in various situations. Herein, a numerical model, based on the finite element method, was used for simulating three‐dimensional three‐phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation system which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous media. An elastoplastic soil model, based on a Mohr Coulomb yield surface, was utilized. The finite element method was applied to obtain simultaneous solutions to the governing equations where the displacements and the fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. A linear analysis was used to study the stability conditions of the present model. Finally, a series of simulations were conducted to indicate the validity and the utility of the developed model.
Zero thickness interface elements—numerical stability and application
Authors: Day R. A. , Potts D. M.
Published: August 2005

Many methods have been proposed to model joints in rocks or the interface between soil and a structure. Many analysts have reported numerical problems when using zero thickness interface elements while others have presented satisfactory results without comment of such difficulties. The numerical behaviour of zero thickness interface elements is further investigated in this paper. Some simple examples illustrate the application of interface elements to practical situations and highlight the numerical difficulties that may be encountered. Both ill‐conditioning of the stiffness matrix and high stress gradients were found to cause numerical instability. Ill‐conditioning can be reduced by careful selection of the size of the 2D elements adjacent to the interface. The problem of steep stress gradients is entirely one of inadequate mesh design. Contrary to other reports, this paper shows that the Newton–Cotes integration scheme has no benefit over Gaussian integration.

Analyses of a retaining wall using interface elements confirm the analytical values of active and passive earth pressure coefficients which are commonly used in analysis and design of retaining walls.
Inverse analysis of an embankment on soft clay by extended Bayesian method
Authors: Honjo Yusuke , Wen‐Tsung Liu , Guha Soumitra
Published: August 2005

A new type of indirect inverse analysis procedure is proposed to overcome the difficulties the geotechnical inverse analyses are encountering (such as unstability and non‐uniqueness of the solutions as well as multicollinearity). These difficulties are eased by combining the objective information (i.e. the observation data) and the subjective information (i.e. the prior information) in an appropriate manner by so‐called extended Bayesian method. The method is based on a new view on Bayesian model proposed by Akaike. The problem of model identification in the inverse analysis is also tackled by applying well‐known AIC but of the Bayesian version. A case study on an embankment on soft clay is presented to illustrate the effectiveness of the new method. A rather thorough review on the geotechnical inverse analysis is also presented to indicate the necessity of the proposed procedure. An appendix is attached to summarize the statistical background of the new method.
Unified 3D critical state bounding‐surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part II: Calibration and simulations
Authors: Crouch Roger S. , Wolf John P.
Published: August 2005

A systematic calibration procedure for the constitutive model gUTS using conventional triaxial data for all but one of the material constants is described. Typical ranges for the constants for clay and sand are specified together with default values. When all default values are adopted, just eight material constants need to be determined (gUTS‐lite). A comprehensive series of 49 simulations on clays, silt and sands in loose and dense states under a wide range of monotonic and cyclic stress paths, initial states and drainage conditions provide very satisfactory agreement with experimental results.
A simple hypoplastic constitutive model for sand
Authors: Wu Wei , Bauer Erich
Published: August 2005

The paper presents a hypoplastic constitutive model for the three‐dimensional non‐linear stress–strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non‐linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions.
Transient response of reservoir–dam–soil systems to earthquakes
Authors: Guan F. , Moore I. D. , Lin G.
Published: August 2005

A direct time‐domain numerical procedure is proposed to analyse the transient dynamic response of two‐dimensional reservoir–dam–soil systems. The reservoir extends to infinity and the dam is supported by an unbounded soil. The structure with either linear or non‐linear material properties is modelled by the Finite Element Method (FEM). The soil is assumed to be an elastic, isotropic and homogeneous half‐space represented by a boundary condition in the form of generalized impedance determined by the transient Lamb's solution due to a uniformly distributed traction imposed on the free surface, Guan and Novak.1 Moreover, a technique is developed to include the influence of the reservoir on the dam in terms of nodal accelerations along their interface at different time steps. The advantages of the proposed procedure are obvious. For example, it avoids any additional discretization of the boundaries except the soil–dam interface, and the influence matrix of the fluid is obtained explicitly using shape functions defined at the upstream face of the dam without the finite analysis of the reservoir so that it works very efficiently. Numerical results for a system consisting of reservoir, elastic dam and foundation subjected to the San Fernando, 1971 earthquake ground motion are presented.
Boundary element analysis of stresses in an axisymmetric soil mass undergoing consolidation
Authors: Chopra Manoj B. , Dargush Gary F.
Published: August 2005

A time domain boundary element method (BEM) for evaluating stresses in an axisymmetric soil mass undergoing consolidation has been developed. Previous BEM work on axisymmetric poroelasticity for boundary displacements and pore pressures is extended to permit the computation of stresses at both boundary and interior points. The stress formulation preserves the surface‐only discretization.

The boundary displacement integral equation is progressively differentiated to obtain the related stress and strain integral equations. Explicit expressions for the steady‐state axisymmetric fundamental solutions are derived in this process. The transient components of the integrands are obtained directly from the transformation of the three‐dimensional kernels into a cylindrical system. Numerical implementation of these integral equations is carried out within a general purpose BEM computer code and several illustrative examples are presented to validate the method.
An elasto‐plastic constitutive model for soft rock with strain softening
Authors: Adachi T. , Oka F.
Published: August 2005

Dense sands, overconsolidated clays and soft rocks exhibit strain‐hardening and strain‐softening behaviour in a certain range of confining pressure. The aim of the present paper is to construct a constitutive model of soft rock that can describe not only the strain‐hardening behaviour, but also the strain‐softening behaviour. An elasto‐plastic constitutive model for soft rock is derived by introducing a stress history tensor

The preliminary idea was first reported in the reference, the conference paper16. This paper is a complete version of the theory with interpretations and experimental validations

. The model is evaluated through a comparison of the calculated results and the experimental results of tests on sedimentary soft rock (porous tuff). In addition, the applicability of the model to numerical analyses is discussed in relation to the uniqueness of the solution in initial and boundary value problems.
A comparison of field measured and numerically simulated seasonal ground movement in unsaturated clay
Authors: Thomas H. R. , Zhou Z.
Published: August 2005

This paper presents the results of a numerical simulation of field measured seasonal ground movement. The constitutive model employed was proposed as a practical method of modelling the complex stress/strain behaviour of unsaturated soil. Its use within a consolidation‐type analysis is explored here, as a means of assessing its suitability for practical application. Comparisons are given of numerical results and field measured behaviour over a 9 month period of time. Overall good correlation is achieved, covering a series of drying and wetting cycles. Confidence can thus be ascribed to the performance of the constitutive model.
Three‐dimensional joint elements applied to concrete‐faced dams
Authors: Justo J. L. , Segovia F. , Jaramillo A.
Published: August 2005

In the study of concrete‐face dams it is essential to provide joint elements; otherwise the calculated stresses at the facing will be non‐allowable. Three‐dimensional joint elements must be simple so as not to increase in excess the CPU time. Seven non‐incremental joint elements have been formulated or developed, and their relative advantages discussed. It is shown that quasi‐linear or linear joint elements at the perimeter of the solid elements can have calculation advantages, specially for interfaces with ‘no tension’ resistance.

A system of thin solid finite elements (FE) joints at the face may reproduce qualitatively the displacements and stresses, but not quantitatively. With a system of quasi‐linear elements placed at the boundaries of the solid FE we have been able to predict correctly the displacements, strains and joint openings at Cethana concrete‐faced rockfill dam.
Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media
Authors: Hong‐Wu Zhang
Published: August 2005

Finite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic‐plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non‐associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.
Approximate factorizations with modified S/P consistently ordered M‐factors
Authors: Beauwens R.
Published: August 2005

Preconditioned iterative methods are widely used to solve linear systems such as those arising from the finite element formulation of boundary value problems and approximate factorizations are widely used as preconditioners. The ordering of the unknowns is therefore an important issue because it has a strong influence on the convergence behaviour of the iteration method while it is also a decisive aspect for their parallel implementation. Consistent orderings are attractive for parallel implementations and it has been shown that some subclasses of these orderings also enhance the convergence behaviour of the associated iteration methods. This has in particular been shown for the so‐called S/P consistent orderings. A wider definition of this class of orderings has recently been proposed and we investigate here how approximate factorizations should be implemented when using such more general orderings (still called S/P consistent) in order to keep their expected high convergence properties. A simple practical conclusion is suggested, supported by both theoretical and numerical arguments.
Properties of generalized conjugate gradient methods
Authors: Weiss Rüdiger
Published: August 2005

The solution of linear systems has considerable importance for the computation of problems resulting from engineering, physics, chemistry, computer science, mathematics, medicine and economics. The calculation of costly and time‐consuming problems, e.g. crash tests, simulation of the human lung and skin, calculation of electrical and magnetical fields, thermal analysis and fluid dynamics, to name only a few, has become possible with the recent developments of advanced computer architectures and iterative solvers. Generalized conjugate gradient (CG) methods are the most important iterative solvers because they converge very quickly under certain conditions. Therefore they are widely used and in a rapid further development.

The purpose of this paper is to present new results for the convergence of generalized CG methods. A convergence result for non‐symmetric and non‐positive definite matrices is given that includes the classical theory for symmetric, positive definite matrices as a special case.

The norm of the residuals resulting from CG methods may oscillate heavily. Different remedies for smoothing this sequence have been proposed, for example by van der Vorst. Schönauer introduced in the 1980s a smoothing algorithm to get a norm nonincreasing function of the iteration index. For this algorithm a complete theoretical analysis is given. A surprising result is obtained showing that the smoothing algorithm is in a sense optimal. Convergence estimates are derived therefrom. A geometric interpretation of the smoothing algorithm is given showing the propagation of the errors.

It should be stressed that a smooth convergence of the residuals is not equivalent to a smooth convergence of the errors which is the proper aim. A class of error minimizing methods can be easily derived from the theory.
Variable‐step multilevel preconditioning methods, I: Self‐adjoint and positive definite elliptic problems
Authors: Axelsson O. , Vassilevski P. S.
Published: August 2005

When solving large size systems of equations by preconditioned iterative solution methods, one normally uses a fixed preconditioner which may be defined by some eigenvalue information, such as in a Chebyshev iteration method. In many problems, however, it may be more effective to use variable preconditioners, in particular when the eigenvalue information is not available.

In the present paper, a recursive way of constructing variable‐step of, in general, nonlinear multilevel preconditioners for selfadjoint and coercive second‐order elliptic problems, discretized by the finite element method is proposed. The preconditioner is constructed recursively from the coarsest to finer and finer levels. Each preconditioning step requires only block‐diagonal solvers at all levels except at every k0, k0 ≥ 1 level where we perform a sufficient number ν, ν ≥ 1 of GCG‐type variable‐step iterations that involve the use again of a variable‐step preconditioning for that level.

It turns out that for any sufficiently large value of k0 and, asymptotically, for ν sufficiently large, but not too large, the method has both an optimal rate of convergence and an optimal order of computational complexity, both for two and three space dimensional problem domains.

The method requires no parameter estimates and the convergence results do not depend on the regularity of the elliptic problem.
A general theory of finite elements. II. Applications
Authors: Oden J. Tinsley
Published: August 2005

In Part I of the this paper, topological properties of finite element models of functions defined on spaces of finite dimension were examined. In this part, a number of applications of the general theory are presented. These include the generation of finite element models in the time domain and certain problems in wave propagation, kinetic theory of gases, non‐linear partial differential equations, non‐linear continuum mechanics, and fluid dynamics.
Derivation of stiffness matrices for problems in plane elasticity by Galerkin's method
Authors: Szabo Barna A. , Lee George C.
Published: August 2005

Solution of plane elastic problems by piecewise linear approximation is outlined. This method is based upon Galerkin error distribution technique, which leads to simultaneous algebraic equations identical to those associated with the Finite Element Method. In addition, this method permits definition of the discretization error, which can be computed once the displacement components are known. Properties of the interpolation functions are discussed, and a sequence of internally compatible plane elastic elements is defined.
Finite element solution to an elastica problem of beams
Authors: Tada Yasuo , Lee George C.
Published: August 2005

In this study, finite element solution procedures are developed for an elastica problem of inextensible beams. The element stiffness matrices are obtained by using Galerkin's method. Results of a numerical example compare reasonably well with those obtained by using the elliptical integral.

Extensions of this research are currently being made to include membrane effects of beams and to develop plate element stiffness matrices for elastica problems of plate structures.