bluuebunny/crossref_metadata_2025 huggingface dataset:
The use of polarization effects in electromagnetic inverse scattering problems
Authors: Colton David , Kirsch Andreas
Published: August 2005

We consider the scattering of plane, time‐harmonic electromagnetic waves by a perfect conductor D. We first show that the set ℱλ consisting of the span of a fixed linear combination of the electric and magnetic far‐field patterns is dense in the space of square‐integrable tangential vector fields defined on the unit sphere for all values of the wave number k ≠ 0 provided that Im k ≥0. We next consider the affine hull 𝒜λ of ℱλ and characterize the set ℱ in terms of electric Herglotz fields. This result is then used to derive an optimization scheme for solving the inverse scattering problem of determining D from a knowledge of ℱλ and it is shown that this (unconstrained) optimization scheme has zero as its greatest lower bound.
On a neutral Lotka–Volterra system
Authors: Gopalsamy K.
Published: August 2005

Sufficient conditions are obtained for the linear stability of the positive equilibrium of the neutral system
magnified image
in terms of the parameters of the system. The case n=2 is considered in detail and the general case is discussed briefly.
The double‐layer potential operator over polyhedral domains II: Spline Galerkin methods
Authors: Elschner Johannes
Published: August 2005

We examine the numerical approximation of the integral equation (λ − K)u =f, where K is the double layer (harmonic) potential operator on a closed polyhedral surface in ℝ3 and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method in L2. Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a smooth surface.
A symmetry theorem for condensers
Authors: Alessandrini Giovanni
Published: August 2005

We prove the radial symmetry of the solution of degenerate quasilinear capacity problems, when constant overdetermined Neumann data are assigned.
A stream‐function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
Authors: Girault V. , Giroire J. , Sequeira A.
Published: August 2005

In this paper we derive a mixed variational formulation for the exterior Stokes problem in terms of the vorticity and stream function, or the vector potential in three dimensions. The main steps are the construction of the stream function (or vector potential) and the proof of the Babuška–Brezzi ‘inf‐sup’ condition. The two‐ and three‐dimensional cases are treated separately because the structure of the stream function differs substantially according to the number of dimensions considered. The conclusion of this work is that if the problem is set in the weighted Sobolev spaces of Hanouzet and Giroire, the analysis of the exterior Stokes problem is quite the same as if the domain were bounded.
Existence of stationary, collisionless plasmas in bounded domains
Authors: Rein Gerhard
Published: August 2005

We consider a collisionless plasma, which consists of electrons and positively charged ions and is confined to a bounded domain in ℝ3. The distribution functions of the particles are assumed to satisfy specular reflections on the boundary of the domain and the boundary is assumed to be perfectly conducting. We establish the existence of stationary plasmas in the non‐relativistic, electrostatic case described by the Vlasov–Poisson system as well as in the relativistic, electrodynamic case described by the relativistic Vlasov–Maxwell system.
On the asymptotic growth of the solutions of the vlasov–poisson system
Authors: Horst E.
Published: August 2005

We show the global existence of classical solutions of the Vlasov‐Poisson system and improve the known growth estimates.
Radially symmetric global classical solutions of non‐linear wave equations
Authors: Pecher Hartmut
Published: August 2005

The Cauchy problem for semilinear wave equations utt − Δu + h(|x|)up = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non‐negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.
The effects of chemically induced polarisation in the out‐of‐cage products of methyl and other alkyl radicals during the decomposition of di‐t‐butylperoxalate
Authors: Kessenikh A. V. , Ignatenko A. V. , Rykov S. V.
Published: August 2005

The out‐of‐cage CIDNP effects, and kinetics of the out‐of‐cage reactions between the methyl radicals and the other radicals produced from the donor admixtures have been studied during the thermal decomposition of di‐t‐butylperoxalate (DTBPO). The DTBPO decomposition proves to be a good source of methyl radicals.

The CIDNP effects on the methyl protons and on the nuclei of the other alkyl radicals are determined both by the out‐of‐cage radical collisions and the kinetics of out‐of‐cage recombination.
Microscopic magnetic resonance elastography (μMRE)
Authors: Othman Shadi F. , Xu Huihui , Royston Thomas J. , Magin Richard L.
Published: August 2005

Magnetic resonance elastography (MRE) was extended to the microscopic scale to image low‐frequency acoustic shear waves (typically less than 1 kHz) in soft gels and soft biological tissues with high spatial resolution (34 μm × 34 μm × 500 μm). Microscopic MRE (μMRE) was applied to agarose gel phantoms, frog oocytes, and tissue‐engineered adipogenic and osteogenic constructs. Analysis of the low‐amplitude shear wave pattern in the samples allowed the material stiffness and viscous loss properties (complex shear stiffness) to be identified with high spatial resolution. μMRE experiments were conducted at 11.74 T in a 56‐mm vertical bore magnet with a 10 mm diameter × 75 mm length cylindrical space available for the elastography imaging system. The acoustic signals were generated at 550–585 Hz using a piezoelectric transducer and high capacitive loading amplifier. Shear wave motion was applied in synchrony with the MR pulse sequence. The field of view (FOV) ranged from 4 to 14 mm for a typical slice thickness of 0.5 mm. Increasing the agarose gel concentration resulted in an increase in shear elasticity and shear viscosity. Shear wave motion propagated through the frog oocyte nucleus, enabling the measurement of its shear stiffness, and in vitro shear wave images displayed contrast between adipogenic and osteogenic tissue‐engineered constructs. Further development of μMRE should enable its use in characterizing stiffer materials (e.g., polymers, composites, articular cartilage) and assessing with high resolution the mechanical properties of developing tissues. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Quantifying dynamic contrast‐enhanced MRI of the knee in children with juvenile rheumatoid arthritis using an arterial input function (AIF) extracted from popliteal artery enhancement, and the effect of the choice of the AIF on the kinetic parameters
Authors: Workie Dagnachew W. , Dardzinski Bernard J.
Published: August 2005

Quantification of dynamic contrast‐enhanced (DCE) MRI based on pharmacokinetic modeling requires specification of the arterial input function (AIF). A full representation of the plasma concentration data, including the initial rise and decay parts, considering the delay and dispersion of the bolus contrast is important. This work deals with modeling of DCE‐MRI data from the knees of children with a history of juvenile rheumatoid arthritis (JRA) by using an AIF extracted from the signal enhancement data from the nearby popliteal artery. Three models for the AIFs were considered: a triexponential (AIF1), a gamma‐variate plus a biexponential (AIF2), and a biexponential (AIF3). The pharmacokinetic parameters obtained from the model were Ktrans′, kep, and V. The results from AIF1 and AIF2 showed no statistically significant difference. However, some statistically significant differences were seen with AIF3, particularly for parameters Ktrans′ and V in the synovium (SNVM). These results suggest the importance of obtaining an appropriate AIF representation in pharmacokinetic modeling of JRA. Specifically, the initial rising part of the AIF should be incorporated for optimal pharmacokinetic modeling results. The pharmacokinetic parameters (mean ± SD) derived from AIF1, using the average plasma concentration data, were as follows: SNVM Ktrans′(min−1) = 0.52 ± 0.34, kep(min−1) = 0.71 ± 0.39, and V = 0.33 ± 0.16, and for the distal femoral physis (DFP) Ktrans′(min−1) = 1.83 ± 1.78, kep(min−1) = 2.65 ± 1.80, and V = 0.46 ± 0.31. The pharmacokinetic parameters in the SNVM may be useful for investigating activity and therapeutic efficacy in studies of JRA. Longitudinal studies are necessary to find or demonstrate the parameter that is more sensitive to disease activity. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Improved data reconstruction method for GRAPPA
Authors: Wang Ze , Wang Jiongjiong , Detre John A.
Published: August 2005

This paper presents an improved data reconstruction method for generalized autocalibrating partially parallel acquisitions (GRAPPA) using multicolumn multiline interpolation (MCMLI). Both nearest acquired line (ky) neighboring points and column (kx) neighboring points from all components of an array coil were used to reconstruct each missing datum through interpolation. A new fitting scheme was designed to estimate the interpolation weights. Both simulations and in vivo experiments demonstrated that the proposed method yields higher‐quality data reconstruction than the original GRAPPA method, especially with high acceleration factors. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Practical approaches to the evaluation of signal‐to‐noise ratio performance with parallel imaging: Application with cardiac imaging and a 32‐channel cardiac coil
Authors: Reeder Scott B. , Wintersperger Bernd J. , Dietrich Olaf , Lanz Titus , Greiser Andreas , Reiser Maximilian F. , Glazer Gary M. , Schoenberg Stefan O.
Published: August 2005

In this work, two practical methods for the measurement of signal‐to‐noise‐ratio (SNR) performance in parallel imaging are described. Phantoms and human studies were performed with a 32‐channel cardiac coil in the context of ultrafast cardiac CINE imaging at 1.5 T using steady‐state free precession (SSFP) and TSENSE. SNR and g‐factor phantom measurements using a “multiple acquisition” method were compared to measurements from a “difference method”. Excellent agreement was seen between the two methods, and the g‐factor shows qualitative agreement with theoretical predictions from the literature. Examples of high temporal (42.6 ms) and spatial (2.1 × 2.1 × 8 mm3) resolution cardiac CINE SSFP images acquired from human volunteers using TSENSE are shown for acceleration factors up to 7. Image quality agrees qualitatively with phantom SNR measurements, suggesting an optimum acceleration of 4. With this acceleration, a cardiac function study consisting of 6 image planes (3 short‐axis views, 3 long‐axis views) was obtained in an 18‐heartbeat breath‐hold. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Transmitting boundaries: A comparison
Authors: Roesset José M. , Ettouney Mohammed M.
Published: August 2005

The use of discrete models for the dynamic analysis of a contiuum requires the existence of a finite domain with well defined boundaries. When these boundaries do not exist naturally but have to be artificially imposed it may be necessary to apply appropriate conditions on forces or displacements at the boundary nodes to reproduce the physical behaviour of the actual problem. In the solution of soil structure interaction problems these conditions are simulated through the use of transmitting boundaries. In this paper several of these boundaries are evaluated comparing the results they produce in the amplification of seismic motions, the determination of foundation stiffnesses and the structural response. The distance of the boundaries to the zone of interest, the level of excitation (influencing the amount of internal soil damping), the geometry of the problem (finite soil layer versus a half‐space) and the relative frequency of the structure with respect to the soil and the specified motion are all parameters which must be taken into account for this evaluation.
Seepage flow problems by variational inequalities: Theory and approximation
Authors: Kikuchi Noboru
Published: August 2005

The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h1.25‐δ), 0 < δ < 0.25, respectively, if the permeability is constant.
Finite element simulation of freezing processes in soils
Authors: Del Giudice S. , Comini G. , Lewis R. W.
Published: August 2005

The finite element method, formulated for non‐linear heat conduction, allows the solution of practically any ground freezing problem. Stabilization of wet soils by artificial freezing and freezing under roads induced by cold winter conditions are considered in this paper.

Special features of the program used include parabolic isoparametric elements, a new time stepping scheme and an improved procedure for the estimation of thermal properties.
Strain‐softening of brittle geologic materials
Authors: Sture Stein , Ko Hon‐Yim
Published: August 2005

Stability equations for a strain‐softening system are derived from expressions describing the energy variation in a variable stiffness stiff testing machine and a brittle rock specimen. A normal strain‐softening expression and a shear strain‐softening expression are derived to predict the stability of laboratory tests on brittle rocks, which through machine stiffness adjustment, exhibited critical stability in the strain‐softening range. From these comparisons it was found that the shear strain‐softening model gave consistently good results. The analytical and laboratory modelling indicates that strain‐softening in brittle geologic media is closely connected with joints, faults, and interfaces where shear distortions take place.
Dynamic response of elastic plates on the surface of the half‐space
Authors: Savidis S. A. , Richter T.
Published: August 2005

A ‘mixed method’ for the dynamic calculation of foundations on soil is presented. The half‐space is computed analytically, the foundation with finite elements. The method is very well suited for the solution of three‐dimensional problems including interaction. Numerical results for a simple case involving a dynamically loaded elastic plate are presented and the influence of plate stiffness is studied.
Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity
Authors: Carter J. P. , Randolph M. F. , Wroth C. P.
Published: August 2005

The disturbance of a clay mass, due to either the installation of a driven pile or the expansion of a pressuremeter membrane, is often modelled as a cylindrical cavity expansion. In addition, it is usual (and convenient) to assume that the expansion occurs under conditions of plane strain. For this problem a method of analysis is presented which considers the soil to be a saturated two‐phase material with a pore fluid which flows according to Darcy's Law. Non‐linearity in material behaviour is permitted as long as the effective stress–strain law can be written in an incremental or rate form. The use of a consolidation analysis allows the changes in effective stress and pore pressure to be determined at any stage during both the cavity expansion and the subsequent period of reconsolidation. Expansions may occur at any prescribed rate, including the very fast (undrained) and the very slow (fully drained) case. The technique is illustrated by considering the expansion of a cavity in two different types of elastoplastic soil. It is shown how these solutions may be used to model the disturbance of the soil due to pile driving.
The reliability of earth slopes
Authors: Tobutt D. C. , Richards E. A.
Published: August 2005

Methods recommended for calculating the probability of failure of earth slopes, as distinct from factor of safety, are discussed. In particular the ‘Level II’ and ‘Level II’ approaches as defined by the Joint Committee of Structural Safety (J.C.S.S.) are referred to; these are set forth in C.I.R.I.A. Report No. 631 and attention is drawn to the contributions therein by M. J. Baker and M. Horne, and to how these considerations affect this particular problem. The mechanical model used throughout is Bishop's simplified method2.
Optimal lower bound of passive earth pressure using finite elements and non‐linear programming
Authors: Basudhar P. K. , Valsangkar A. J. , Madhav M. R.
Published: August 2005

The present study pertains to the finding of the lower bound solution, formulating it as a non‐linear programming problem using the generalized method developed by Lysmer with certain variations to incorporate the non‐linear no‐yield condition constraints directly in the analysis. The method considers the family of plane stress fields having the property that all stresses vary linearly within each triangular element of some mesh which covers the soil mass under study. For this type of stress field it is possible to express all equilibrium conditions as a set of linear constraints and the no‐yield as a set of non‐linear constraints. The boundary condition constraints may be of linear equality or inequality type. By expressing some of the design variables in terms of the remaining variables the linear equality constraints are implicity satisfied. Such a technique minimizes the complexity of the problem by eliminating the equality constraints and reduces the dimensionality of the problem, saving much, computational effort. The optimal lower bound is isolated by formulating it as a non‐linear programming (NLP) problem subjected to both linear and non‐linear inequality constraints. The sequential unconstrained minimization technique using the extended penalty function method as suggested by Kavlie has been used to isolate the optimal lower bound. The method has successfully been applied to the passive earth pressure and bearing capacity problem.

Numerical results are obtained and compared with Lysmer's solution to show the effectiveness of the present approach.
The eccentric loading of a rigid circular foundation embedded in an isotropic elastic medium
Authors: Selvadurai A. P. S.
Published: August 2005

This paper examines the problem of the eccentric loading of a rigid circular disc‐shaped foundation embedded in bonded contact with an istropic elastic medium of infinite extent. The solution of this problem is achieved by using a Hankel integral transform technique which reduces the problem to two sets of dual integral equations. These systems of dual integral equations represent the equations which govern the axisymmetric and asymmetric states of deformation induced by the loaded foundation. Explicit results are derived both for the displacement and rotation of the circular foundation and for the contact stress at the interface.
Pile capacity in a softening soil
Authors: Murff James D.
Published: August 2005

A method for determining the load–deformation response of a pile in a softening soil is presented. The results demonstrate the degree to which the flexibility of the pile can affect its ultimate capacity.
Flow nets from finite element data
Authors: Christian John T.
Published: August 2005

Finite element solutions for steady‐state flow of fluids through porous media do not include an explicit develpoment of the flow net, and many engineers find this lack frustrating. To solve for the stream function, the analyst can use essentially the same finite element routines as he used for the potential, but the matrix corresponding to the hydraulic conductivity isnotthe inverse of the conductivity. Contouring the potential and the stream function is done element by element; certain anomalous situations are described in an appendix.
Finite element modelling of ground surface displacements due to underground blasting
Authors: Blair D. P.
Published: August 2005

Elastic wave radiation from an equivalent cylindrical cavity due to an underground explosion is considered in detail. Both static and steady state dynamic finite element models are used to investigate the surface displacements due to the interaction of such wave radiation with both the free surface topography and stope formation. For a blast 430 m below the surface the models predict a negligible displacement effect due to the irregular topography but a significant effect due to the stope. A comparison between the models and a site experiment verified the cylindrical wave nature of the problem. Due to experimental uncertainties however it was difficult to clearly detect the surface displacement effect due to the large underground open stope.
Consolidation with threshold gradients
Authors: Pascal Florica , Pascal Henry , Murray D. W.
Published: August 2005

Evidence for threshold gradients is reviewed. The consolidation problem, with threshold gradient, is properly formulated and solved numerically. An approximate analytical solution is also developed. The influence of a threshold gradient on the time rate of settlement is examined, and it is shown that by modifying the definition of the degree of consolidation a good approximation to the threshold gradient problem can be obtained directly from the Terzaghi solution. It is also shown that threshold gradients will have no influence on odometer testing and their effect is, therefore, to reduce the primary compression below that predicted from standard tests.
Multiplicity of numerical solutions for slope stability problems
Authors: Chugh Ashok K.
Published: August 2005

Existence of more than one numerical solution to the slope stability equations derived on the basis of force and moment equilibrium requirements of statistics is indicated. These solutions satisfy the boundary conditions at both ends of a potential slide mass. In the particular case considered, the details of the calculated response for the slices for each solution set assist the designer in selecting the more reasonable solution to the problem.
Analysis of rigid rafts supported by granular piles
Authors: Balaam N. P. , Booker J. R.
Published: August 2005

Solutions for the magnitude and rate of settlement of rigid foundations supported by soil reinforced with granular piles are presented. An analytic solution using the theory of elasticity is developed for the settlement of the foundation and expressions for evaluating the moment and shear distributions across the foundation are given. A solution for the increase of the rate of settlement due to the presence of the granular piles has been found by a numerical solution of Biot's equations of consolidation.
Pore water pressure in natural slopes
Authors: Chugh Ashok K.
Published: August 2005

Estimating subsurface pore water pressures in natural slopes along the periphery of rivers and reservoirs for future conditions, created by the operational requiremets to meet increases in energy demand from the observed data of the past and present, operations, is possible with the use of a mathematical model. An effective algorithm for calculating pore water pressure at any location in a slope stability section is to use a complete polynomial and to assure geometric invariance of the calculated results.
Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model
Authors: Chang C. S. , Duncan J. M.
Published: August 2005

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non‐linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.
Finite element methods for geothermal reservoir simulation
Authors: Zyvoloski George
Published: August 2005

Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.
Effects of fluid resistance in the mine waste dam‐break problem
Authors: Jeyapalan Jey K.
Published: August 2005

A characteristic common to most mine tailings dam failures is that the mine tailings tend to liquefy and flow over substantial distances, with the potential for extensive damage to property and life. In order to be able to assess the potential for damage in case of such a failure, it is necessary to be able to predict the characteristics of the flow and the possible extent of flood movement. A procedure that has some potential for such flow analyses is described in this paper. When fluid resistanceis neglected, the solution of the simple dam‐break problem is readily found using the shallow water theory. However, near the head of the mine waste dam‐break flood wave the laminar resistance resistance effects are appreciable. In this paper the retardation of the wave‐front behind the position predicted by the inviscid shallow water theory is found.
Non‐associative constitutive laws for low porosity rocks
Authors: Senseny Paul E. , Fossum Arlo F. , Pfeifle Tom W.
Published: August 2005

Two simple constitutive laws appropriate for elastic–plastic deformation up to peak load of low porosity rocks are presented. Both laws account for mean stress dependence of yield hardening between yield and peak strength and non‐associative plastic straining. The two constitutive laws are based on the Mohr–Coulomb and the Mises–Schleicher yield criteria. The yield criteria are matched at axisymmetric compression and the relationships among the constitutive parameters are given. The parameters are then evaluated for two evaporite rocks anhydrite and polyhalite based on axisymmetric compression data. Comparison of predicted stress–strain laws with those measured in the laboratory show that these laws can be used for engineering analysis.
Computational procedures for non‐linear three‐dimensional analysis with some advanced constitutive laws
Authors: Siriwardane H. J. , Desai C. S.
Published: August 2005

Computational procedures for implementing some constitutive models are described and introduced in three‐, and two‐dimensional finite element procedures; here variable moduli, Drucker–Prager, critical state and cap models are considered. Consistent numerical schemes are presented with applications to a number of example problems. These procedures can provide successful results with advanced constitutive laws for three‐dimensional analysis of a wide range of non‐linear problems.
A displacement discontinuity approach to modelling the creep behaviour of rock and its discontinuities
Authors: Crawford A. M. , Curran J. H.
Published: August 2005

Using the correspondence principle of viscoelasticity the Displacement Discontinuity Method has been extended to model the rate‐dependent behaviour of a jointed rock mass. The intact rock is assumed to behave as a linear viscoelastic material while, in general, a non‐linear rate‐dependent behaviour of the rock joints can be accounted for. A number of numerical examples are presented which illustrate the accuracy and potential of the method for analysing complex engineering problems.
Rapid shearing in a rate‐type soil surrounding a cylindrical cavity
Authors: Mullenger G. , Scott R. F. , Davis R. O.
Published: August 2005

The stress and deformation resulting from rapidly applied axial traction on the face of a cylindrical cavity in a saturated soil are analysed. A simple rate‐type constitutive model is used for the effective stress response.
The flexure of an infinite strip of finite width embedded in an isotropic elastic medium of infinite extent
Authors: Selvadurai A. P. S.
Published: August 2005

This paper examines the problem of the flexure of a strip of finite width which is embedded in bonded contact with an isotropic elastic medium of infinite extent. The analysis of the problem is applicable to flexible beams of narrow width which experience flexure only in the longitudinal direction. Numerical results are developed for the maximum flexural moment induced in the embedded beam due to the action of a concentrated force.
An investigation of numerical errors in the analysis of consolidation by finite elements
Authors: Reed M. B.
Published: August 2005

A smoothing technique is developed to remove the oscillatory errors in initial nodal pore pressures, associated with the use of quadratic isoparametric elements to model soil consolidation. Numerical results using this technique are compared with the performance of other types of element in problems of one‐and two‐dimensional consolidation.
The effect of the plastic potential in boundary value problems involving plane strain deformation
Authors: Potts D. M. , Gens A.
Published: August 2005

A large proportion of the constitutive models currently employed in Geomechanics are based on the theory of plasticity. Owing to the limitations of the data obtained from conventional testing equipment, arbitrary assumptions are often made about the behaviour of the material in generalized stress space.

In this paper it is shown that the Lode angle of the stress state at failure in plane strain deformation is dependent on the shape adopted for the plastic potential. The influence of the shape of the plastic potential in the deviatoric plane on the predicted behaviour of two boundary value problems both prior to and at failure is then considered. In both cases a form of the Modified Cam Clay model is employed to describe the soil behaviour, and numerical predictions are obtained using a finite element computer code. For drained situations it is shown that the Lode angle of the stress state at failure has a dominating influence on the predicted behaviour. However, for undrained cases the effects are not so important as long as the correct undrained strength at failure is enforced.
Torsional surface waves in inhomogeneous elastic media
Authors: Vardoulakis I.
Published: August 2005

The dispersion of torsional surface waves in two types of inhomogeneous elastic media is discussed (1) in a half‐space with shear modulus varying linearly with depth and with constant density (Gibson'S half‐space) and (2) in a half‐space with shear modulus varying with the square‐root of the depth co‐ordinate and with constant density. Inhomogeneous media with constant shear wave velocity are also reviewed and the obtained solutions are discussed in relation to appropriate boundary conditions.
Finite element seepage flow nets
Authors: Aalto J.
Published: August 2005

A variational principle and the corresponding finite element equations for determination of the stream function for soil seepage problems is given using the standard finite element potential solution as data. The procedure is very simple and independent of the element type employed. Generalization of the method to multiply connected domains is included.
A finite difference method for measuring soil thermal diffusivity in situ
Authors: Coleman J. D.
Published: August 2005

A method is devised for measuring soil thermal diffusivity in situ. It is based on direct experimental simulation of the finite difference approximation to the one‐dimensional heat conduction equation.

The method does not require the soil to be homogeneous except between the three thermometers that are used, at depths z + d, z and z − d. Nor need the energy input curve be sinusoidal. However, it must be fairly smooth for the finite difference approximation to be accurate.

Experimental results for London Clay are presented, obtained using thermometers at depths of 1, 6 and 11 cm to give a mean thermal diffusivity of 0.0074 cm2/s at a depth of 6 cm. This value is consistent with other estimates of diffusivity for clay soils.

The method is capable of automation, and should be suitable for use on engineering sites, at low cost.

The method is capable of generalization to other linear diffusion equations containing one independent parameter. The same limitation also applies to its application to constitutive or geometrical non‐linear one dimensional diffusion equations, and each equation requires individual study to assess feasibility of use of the method.

The method in effect uses the usual finite difference approximation, not to prepare a numerical solution, but to design an experiment carried out essentially within the finite difference ‘molecule’. The measured parameter of the diffusion equation is the usable product of the method.
An approximate F.E. analysis of seepage with a free surface
Authors: Cividini Annamaria , Gioda Giancarlo
Published: August 2005

An approximate step‐by‐step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non‐approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint.
A statistically based numerical model for heat conduction in fractured rock masses
Authors: Gartling David K. , Thomas Robert K.
Published: August 2005

A computational procedure for simulating heat conduction in fractured rock masses is proposed and illustrated within the context of the finite element method. The procedure makes use of simple local models for conduction in the vicinity of a single open fracture. The local models allow effective thermal properties for fractured rock to be expressed in terms of fracture characteristics such as spacing, orientation and aperture. The distributions of fractures and fracture properties within the finiteelement model are derived from a statistical representation of geological field data. The procedure is demonstrated to satisfactorily reproduce heat transfer results across single fractures and provide an efficient means of representing conduction in formations with multiple fractures.
A critical assessment of methods of correcting for drift from the yield surface in elasto‐plastic finite element analysis
Authors: Potts D. M. , Gens A.
Published: August 2005

The analysis of elasto‐plastic boundary value problems using the finite element method involves many discretizations. These lead to the problem of yield surface drift in which the stress state predicted at the end of an elasto‐plastic increment of loading does not lie on the current yield surface. As such discrepancies are comulative it is important to ensure that the stresses are corrected back to the yield surface during each increment of loading.

In this paper five methods of accounting for this drift are examined. These involve correcting the stresses by projecting back along the plastic flow, the total strain increment and the accumulated effective stress direction. In addition a ‘correct’, method which accounts for the changes in elastic strains which accompany any stress correction is considered. This method is theoretically more sound than the other approximate approaches. All five methods have been used in finite element analyses of the stress changes that occur adjacent to a single pile installed in a uniform deposit of soil on pile loading. The soil was assumed to be normally consolidated and was modelled using a form of modified Cam Clay. Comparison of these results with an analysis, in which yield surface drift was negligible indicated that only the ‘correct’ method and the method involving projecting back along the plastic flow direction give accurate predictions. Substantiai errors occur if the other methods of correcting for yield surface drift are employed. It is recommended that the ‘correct’ method be adopted for finite element calculations.
A coupling scheme for boundary and finite elements using a joint element
Authors: Mitsui Y. , Ichikawa Y. , Obara Y. , Kawamoto T.
Published: August 2005

A coupling scheme for boundary and finite elements using a joint element is proposed. The scheme is based on the finite element discretization (i.e. the equivalent FE procedure). Footing problems founded on multiple layers are solved. Furthermore, the scheme is extended to a non‐linear analysis.
An application of the calculus of variations to rectilinear flow of granular materials
Authors: Spencer A. J. M. , O'Mahony T. C.
Published: August 2005

The calculus of variations is an attractive tool for the determination of critical slip surfaces, but there are unresoived difficulties in its application to plane strain problems. Here we consider the simpler problem of rectilinear flow under gravity or other constant body force. In particular we investigate the stability of an infinitely long slope of finite width for material with cohesion and internal friction. From a variational formulation, the differential equation of the critical slip surface is formulated. An explict solution of this equation is obtained, and hence we determine the critical slope angle in terms of the width of the slope and the material properties. The results are compared with those of an earlier limit analysis treatment.
Viscoelastic analysis of piles and pile groups
Authors: Ahmad S. , Davies T. G. , Manolis G. D.
Published: August 2005

The axial and lateral load–displacement response of single piles and pile groups during the secondary consolidation (creep) phase of deformation is obtained by idealizing the soil as a linear viscoelastic material. The boundary element method is used to model the soil halfspace and the piles, which are assumed to behave elastically, are idealized as beam‐columns. By using the correspondence principle, the problem is solved in the Laplace transform domain and the final solution is obtained by numerical inversion of the transformed data. The salient features of the viscoelastic response are identified in several non‐dimensional plots which encompass the spectrum of geometrical and material parameters commonly encountered in practice. The results of the analysis compare favourably with the limited data available in the literature.
Linearization of in situ stress change formulae for gauges at arbitrary down‐hole orientation
Authors: Pariseau William G.
Published: August 2005

The vibrating wire stress gauge is a borehole device for measuring stress changes in situ. Three gauge arrays are required for determining changes in the secondary principal stresses. Standard data reduction formulae that use the principal axes for reference are in error because of possible changes in the principal directions. Data reduction formulae that allow for such changes and for arbitrary gauge orientations within an array are presented here. This is of considerable practical importance when installing gauges because of scheduling restrictions and hole irregularities that may preclude installation at the planned angles for which data reduction formulae exist. Linearization and thus direct inversion of the resulting system of equations, is achieved in a fixed but otherwise arbitrarily oriented Cartesian system of reference.
Transfer matrix approach for nonlinear pile group response analysis
Authors: Nogami Toyoaki , Paulson Stephen K.
Published: August 2005

A transfer matrix method is applied for the analysis of non‐linear pile group responses. The expression for the transfer matrix is obtained by idealizing the non‐linear pile group as a group of piles attached to a piecewise linear “Winkler model for a pile group”. This Winkler idealization is essential to apply a transfer matrix method for the pile group response analysis. The parameters of this Winkler model can be defined from unit load transfer curves obtained for a single pile. In the limited studies carried out, it is found that the present approach predicts the response of pile groups reasonably well.
Finite element simulation of time dependent fracture and fragmentation processes in rock blasting
Authors: Digby P. J. , Nilsson L. , Oldenburg M.
Published: August 2005

Two constitutive models for the simulation of fracture and fragmentation processes in rapidly loaded rocks are studied. The models were included in a wave propagation finite element code. The results obtained from the two models were compared by a study of the intensity and extent of fracturing obtained from two different configurations of explosive charge and reflecting surfaces in a plane strain problem. The evolution of the time dependent fracture pattern and fragmentation process is also presented.
Dynamic analysis of piles and pile groups embedded in non‐homogeneous soils
Authors: Senm R. , Kausel E. , Banerjee P. K.
Published: August 2005

A hybrid boundary element formulation for the steady state analysis of piles and pile groups embedded in a soil stratum in which the modulus increases linearly with depth is presented. The piles are represented by compressible columns or flexible beams and the soil as a hysteretic, layered medium. The explicit Green's function corresponding to dynamic loads in the interior of a layered stratum, developed earlier by Kausel is used in the study.

The governing differential equations for the pile domain are solved for a distributed periodic loading intensity and those for the soil domain by a system of boundary elements at the pile‐soil interface. These are then assembled into a system of algebraic equations by satisfying interface equilibrium and compatibility.

The results of the analysis have been compared against those from alternative formulations, e.g. finite elements, and confirm the accuracy of the proposed formulation. Representative results for single piles and pile groups are presented.
Some aspects of coupled FEBEM analysis of underground openings
Authors: Varadarajan A. , Sharma K. G. , Singh R. B.
Published: August 2005

The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM.
Geotechnical aspects of remedial design for a gold tailings dam
Authors: Sully J. P.
Published: August 2005

Remedial measures were required for a gold tailings dam in South Africa which had undergone a minor slope failure. Information from laboratory and field measurements was used for evaluation of the present and future stability as the height of the dam increased. To aid the design process, numerical methods were used for prediction of in situ conditions. Stability analyses by computer were then used to optimize the type of remedial measure.
A variational inequality approach to free surface seepage in an inhomogeneous dam
Authors: Westbrook D. R. , Gilmour Grant J.
Published: August 2005

The current work uses Baiocchi's transformation to obtain heuristically a formulation of the inhomogeneous dam problem. When finite element methods are applied the finite dimensional problem is a variational inequality which may be solved to obtain approximate solutions. The main advantage of the method is that it uses a fixed mesh.

The finite dimensional problem is solved by means of succesive overrelaxation with projection. Although the standard convergence theory1 for this method does not apply in this case, because the stiffness matrix is not symmetric, satisfactory and rapid convergence was obtained in all of our examples.

Numerical results are given for some examples.
Numerical Laplace‐Fourier transform inversion technique for layered‐soil consolidation problems: I. Fundamental solutions and validation
Authors: Vardoulakis I. , Harnpattanapanich T.
Published: August 2005

A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro‐elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace‐Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique.
Analysis of axial pile‐soil interaction in clay
Authors: Heydinger Andrew G. , O'Neill Michael W.
Published: August 2005

A method for predicting the maximum mobilized side resistance and unit shaft resistance‐displacement curves (load transfer functions) on piles in clay is described. The method was derived using a numerical solution to model pile installation effects and a finite element scheme to model pile loading. Results of three well‐documented pile load tests on steel piles were used to develop intermediate steps and final solutions, and the method was verified by comparing predicted results to two other load tests. An expression is proposed to represent load transfer functins for use by practitioners for the design of bridge and other foundations in clay.