bluuebunny/crossref_metadata_2025 huggingface dataset:
Examples of embedded eigenvalues for the Dirichlet Laplacian in perturbed waveguides
Authors: Witsch K. J.
Published: August 2005

It is shown that there exist domains Ω ⊂ ℝN, which outside of some ball coincide with the strip ℝN − 1 × (0, π) and for which the Dirichlet Laplacian – Δ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, ∞).
Blow‐up in non‐linear three‐dimensional thermoelasticity
Authors: Racke Reinhard
Published: August 2005

It is shown that solutions of the equations of thermoelasticity in general will develop singularities in finite time.
Radially symmetric Poisson–Boltzmann equation in a domain expanding to infinity
Authors: Krzywicki A. , Nadzieja T.
Published: August 2005

The electric potential u in a solution of an electrolyte around a linear polyelectrolyte of the form of a cylinder satisfies

We study the problem when R → ∞.
On the exponential convergence of theh–pversion for boundary element Galerkin methods on polygons
Authors: Babuška I. , Guo B. Q. , Stephan E. P.
Published: August 2005

This paper applies the technique of theh–pversion to the boundary element method for boundary value problems on non‐smooth, plane domains with piecewise analytic boundary and data. The exponential rate of convergence of the boundary element Galerkin solution is proved when a geometric mesh refinement towards the vertices is used.
Some new fundamental solutions
Authors: Ortner Norbert , Wagner Peter
Published: August 2005

The fundamental solutions of non‐decomposable evolution operators are represented by multi‐dimensional parameter integration formulae. The method is applied to operators occurring in the theories of elasticity, magnetohydrodynamics and heat conduction.
Steady states in plasma physics—the Vlasov–Fokker–Planck equation
Authors: Dressler Klaus
Published: August 2005

In this paper we investigate the non‐linear Vlasov–Fokker–Planck (VFP) equation, a both physically and mathematically interesting modification of Vlasov's equation, which describes a plasma in a thermal bath. We prove existence, uniqueness and representation results for steady states of the VFP equation both in the case of a mollified interaction potential and for the VFP–Poisson system. The uniqueness and representation results are of special interest since they distinguish special solutions of the Vlasov equation.
Control of continuous sedimentation of ideal suspensions as an initial and boundary value problem
Authors: Bustos María Cristina , Paiva Freddy , Wendland Wolfgang
Published: August 2005

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.
Convergence analysis for a multiplicatively relaxed EM algorithm
Authors: Iusem Alfredo N.
Published: August 2005

The expectation maximization (EM) algorithm is an iterative procedure used to determine maximum likelihood estimators in situations of incomplete data. In the case of independent Poisson variables it converges to a solution of a problem of the form min ∑[〈ai,x〉 −bilog 〈ai,x〉] such thatx⩾0. Thus, it can be used to solve systems of the formAx=b,x⩾0 (withAstochastic andbpositive.) It converges to a feasible solution if it exists and to an approximate one otherwise (the one that minimizesd(b,Ax), wheredis the Kullback–Leibler information divergence). We study the convergence of the multiplicatively relaxed version proposed by Tanaka for use in positron emission tomography. We prove global convergence in the underrelaxed and unrelaxed cases. In the overrelaxed case we present a local convergence theorem together with two partial global results: the sequence generated by the algorithm is bounded and, if it converges, its limit point is a solution of the aforementioned problem.
Scattering theory for hyperbolic equations of order 2m
Authors: Pickett Douglas
Published: August 2005

Given self‐adjoint operators Hj, on Hilbert spaces ℋ︁j, j = 0,l, and J ∈ ℬ︁ (ℋ︁0, ℋ︁1) (where ℬ︁ (ℋ︁0 ℋ︁1) denotes the set of bounded linear operators from ℋ︁0to ℋ︁1), define the wave operators magnified image where P0 is the projection onto the subspace for absolute continuity for H0. We use (i) to study the scattering problem associated with a pair of equations each of the form magnified image where L is a positive, self‐adjoint operator on a Hilbert space X, m is a positive integer and the αj are distinct positive constants. Methods patterned after those of Kato are used to study two equations (that is for L = L0 and L = Ll) each of the form (ii). We show that they are equivalent to equations of the form magnified image where each Ĥk is a self‐adjoint operator on an associated Hilbert space ℋ︁k. Now suppose∼he‐wave operators W±,(L1 L0) exist and are complete. Then we can find a J ∈ ℬ︁(H1 H0) such that W+(Ĥl, Ĥ0,J) exists. In the case where Lo and L1 have the same domain, ℋ︁1 and ℋ︁0 are equal as vector spaces, and under certain conditions (on Li, i = 0, 1) ℋ︁0 and ℋ︁1 have equivalent norms. Assuming these conditions, let J'∈ ℬ︁(ℋ︁1' ℋ︁0) be the identity map. We show that (with an additional assumption on L0 and L1) W+(Ĥ1Ĥ0,J) exists andisequal to W+(Ĥl,Ĥ0, J).
Attenuation correction in positron emission tomography
Authors: Natterer F. , Herzog H.
Published: August 2005

We describe a mathematical method for computing the attenuation distribution from Positron emission tomography (PET) data. The method renders possible the correction of PET data for attenuation without a transmission scan. It can be applied if the attenuation distribution is sufficiently simple (abdomen and bead). We give the results for computer‐generated data and for data on patients.
Spatially localized free vibrations for a non‐linear string model
Authors: Feireisl Eduard
Published: August 2005

We prove the existence of infinitely many non‐zero time‐periodic solutions (breathers) to the dispersive wave equation of the form magnified image which are localized in the spatial variable, that is magnified image

The main tool employed is the concentration compactness principle of P. L. Lions.
A numerical method for some initial‐value problems of one scalar hyperbolic conservation law
Authors: Kunik Matthias
Published: August 2005

We examine the existence and regularity results for a scalar conservation law with a convexity condition and solve its weak solution with shocks by using a special method of characterization combined with a representation formula for the weak solution.
Multicriteria optimization in antenna design
Authors: Angell T. S. , Kirsch A.
Published: August 2005

We formulate certain problems in the optimal design of radiating structures such as multicriteria optimization problems. We review the basic background of such problems, prove the existence of Pareto optimal points, and give necessary conditions. We apply the latter to the numerical computation of optimal surface currents for the problem of simultaneously optimizing both the quality factor and the signal‐to‐noise ratio of a conformal antenna.
Boundary integral solution of the two‐dimensional heat equation
Authors: Hsiao George C. , Saranen J.
Published: August 2005

Here we consider initial boundary value problems for the heat equation by using the heat potential representation for the solution. Depending on the choice of the representation we are led to a solution of the various boundary integral equations. We discuss the solvability of these equations in anisotropic Sobolev spaces. It turns out that the double‐layer heat potential D and its spatial adjoint D′ have smoothing properties similar to the single‐layer heat operator. This yields compactness of the operators D and D′. In addition, for any constant c ≠ 0, cI + D′ and cI + D′ are isomorphisms. Based on the coercivity of the single‐layer heat operator and the above compactness we establish the coerciveness of the hypersingular heat operator. Moreover, we show an equivalence between the weak solution and the various boundary integral solutions. As a further application we describe a coupling procedure for an exterior initial boundary value problem for the non‐homogeneous heat equation.
The NMR spectra and conformations of cyclic compounds–VIII. Car‐3‐ene
Authors: Abraham R. J. , Cooper M. A. , Whittaker D.
Published: August 2005

The 220 MHz PMR spectrum of car‐3‐ene (3,7,7‐trimethylbicyclo[4,1,0]hept‐3‐ene) is interpreted and a conformation deduced. In contrast to previous work, which has discussed a highly buckled structure for the 6 membered ring, the present work finds this ring to be essentially planar.
Stéréochimie de β‐diols et de leurs dérivés cycliques–VI. Calcul empirique des déplacements chimiques en série dioxannique. Détermination et discussion des incréments de calcul
Authors: Maroni Pierre , Cazaux Louis , Gorrichon Jean‐Pierre , Tisnes Pierre , Wolf Jean‐Gérard
Published: August 2005

Afin de calculer empiriquement les déplacements chimiques des protons de dioxannes‐1,3 méthylés, nous avons tout d'abord dégagé les valeurs de base du déplacement chimique de chaque proton du dioxanne‐1,3. ensuite, en utilisant des dérivés méthylés en conformation chaise, nous avons établi une systématique effets Δδ des groupes méthyles en position quelconque.

Pour certaines molécules, présentant notamment des interaction gauches, ces divers effts peuvent être modifiés, et nous avons é ces perturbations. L'analogie de Δδ entre les deux séries dioxannique et cyclohexanique a été rapprochée d'une similitude de gémétrie des cycles. Cependant la présence des atomes d'oxygène introduit des différnces parfois importantes.
Stéréochimie de β‐diols et de leurs dérivés cycliques—VII. Calcul empirique des déplacements chimiques en série dioxannique. Application a l'analyse conformationnelle de dérivés alkyles
Authors: Maroni P. , Cazaux L. , Gorrichon J. P. , Tisnes P. , Wolf J. G.
Published: August 2005

Le calcul empirique des déplacements chimiques de méthyl dioxannes‐1,3 conduit à des résultats cohérents. L'écart avec la valeur expérimentale a pu être corrélé à la déformation du cycle dioxannique. La méthode a été étendue aux substituants éthyle, isopropyle et tertibutyle en position 4 ou 6 sur ce cycle.

En l'bsence de substituant en 5, le groupe tertiobutyle n'induit pas plus de déformation du cycle en position 4 qu'en 2 ou 5. Les interactions particulières de ce groupement avec un ou deux méthyles en 5 sont mises en relief.
Solvent effects on the proton magnetic resonance spectra of p‐substituted phenyltin chlorides
Authors: Matsubayashi Gen‐Etsu , Koezuka Hiroshi , Tanaka Toshio
Published: August 2005

A PMR study of solvent effects on some p‐substituted phenyltin chlorides (substituents = CH3, (CH3)3C, CH3O) is reported. Co‐ordination of solvent molecules to the tin atom leads to an unusual low field shift of the o‐ring protons. The results for p‐tolytin trichloride have been compared with those for p‐tolylsilyl trichloride and discussed. In o‐, m‐ and p‐tolyltin trichlorides long range spin‐spin couplings between the ring methyl protons and the tin atom have been observed. The order of magnitude is o‐ > p‐ > m‐methyl protons.
Non‐empirical calculations of NMR indirect spin–spin coupling constants. Part 13: configurational assignment of aminosulfonylamidines
Authors: Krivdin Leonid B. , Larina Lyudmila I. , Chernyshev Kirill A. , Rozentsveig Igor B.
Published: August 2005

Carbon–carbon coupling constants have been experimentally measured using the INADEQUATE pulse sequence in the series of N‐[1,2‐bis(dialkylamino)‐2‐arylethylidene]arylsulfonamides obtained from N‐(1‐aryl‐2,2,2‐trichloroethyl)amides of arylsulfonic acids. Comparison of the experimental J(C,C) in this series with those calculated at the SOPPA (Second‐Order Polarization Propagator Approach) level in the model aminosulfonylamidine provided an unambiguous assignment at the CN bond of the eight‐title aminosulfonylamidines to E‐configuration, while the unknown J(C,C) couplings in their inaccessible diverse Z isomers have been predicted with high reliability. The established marked difference between J(C,C) of the corresponding carbon–carbon bonds in cis and trans orientations to the nitrogen lone pair in aminosulfonylamidines provides a powerful tool in the configurational assignment at the CN bond in a wide series of the related systems containing the CNSO2R moiety. Copyright © 2005 John Wiley & Sons, Ltd.
Variable‐density one‐shot fourier velocity encoding
Authors: DiCarlo Julie C. , Hargreaves Brian A. , Nayak Krishna S. , Hu Bob S. , Pauly John M. , Nishimura Dwight G.
Published: August 2005

In areas of highly pulsatile and turbulent flow, real‐time imaging with high temporal, spatial, and velocity resolution is essential. The use of 1D Fourier velocity encoding (FVE) was previously demonstrated for velocity measurement in real time, with fewer effects resulting from off‐resonance. The application of variable‐density sampling is proposed to improve velocity measurement without a significant increase in readout time or the addition of aliasing artifacts. Two sequence comparisons are presented to improve velocity resolution or increase the velocity field of view (FOV) to unambiguously measure velocities up to 5 m/s without aliasing. The results from a tube flow phantom, a stenosis phantom, and healthy volunteers are presented, along with a comparison of measurements using Doppler ultrasound (US). The studies confirm that variable‐density acquisition of kz‐kv space improves the velocity resolution and FOV of such data, with the greatest impact on the improvement of FOV to include velocities in stenotic ranges. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Analytical approach to the MR signal
Authors: Ibrahim Tamer S.
Published: August 2005

In this work, an analytical evaluation of the MR signal is presented using the principle of reciprocity for any transmit and receive probe(s) with general geometrical structure(s). It is shown that the excitation of the spins cannot be explained using the principle of reciprocity in its standard form due to the asymmetry in the permeability tensor of the transverse magnetization. In the reception problem, the standard form of the principle of reciprocity is then utilized to calculate the NMR signal. As expected, the analysis shows that the strength of the NMR signal is a function of the receive coil's (fictitious) circularly polarized component of the field that poses an opposite sense of rotation to that corresponding with the excitation field, produced by the same coil, if it were to be used for excitation. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Selective excitation of myelin water using inversion–recovery‐based preparations
Authors: Travis Adam R. , Does Mark D.
Published: August 2005

T1 and T2 relaxation of excised frog sciatic nerve water was characterized at 7 T. Based on these findings, optimal timings for multiple inversion–recovery magnetization preparations were determined to selectively excite the so‐called myelin–water T2 component. Subsequent double inversion–recovery and triple inversion–recovery preparations were used in combination with CPMG acquisitions to experimentally determine optimal timings and effect of the preparation. Using double inversion–recovery, optimal timings were found to excite magnetization that is predominantly (≈93%) derived from the myelin–water component. Greater selectivity (≈96%) was found by extending the preparation to triple inversion–recovery, at the price of decreasing SNR by a factor of ≈ 2. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Evaluation of Nørsett methods for integrating differential equations in time
Authors: Smith I. M. , Siemieniuch J. L. , Gladwell I.
Published: August 2005

Some recently developed implicit time discretizations are discussed whose main application is to solving ordinary differential equations arising from finite element approximations to partial differential equations. Their theoretical properties, computer implementation and numerical behaviour, as observed in tests on simple examples, are compared with well‐known discretizations such as the Crank‐Nicholson method.
Numerical performance of some finite element schemes for analysis of seepage in porous elastic media
Authors: Sandhu Ranbir S. , Liu Honho , Singh Kamar J.
Published: August 2005

Several finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs. Their numerical performance is evaluated by comparison with the exact solution for Terzaghi's problem of one‐dimensional consolidation.
Time‐dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses
Authors: Zienkiewicz O. C. , Pande G. N.
Published: August 2005

A new model for rocks and rock‐like material with multiple planes of weakness is proposed. The behaviour of the assembly applies tensile and Mohr‐Coulomb shear limits on each such plane with possible strain dependence of frictional properties. The visco‐plastic algorithm which allows the incorporation of time effects is used to obtain static solutions.

The model is illustrated in actual context by applications to stability of rock slopes and behaviour of tunnels.

A generalization of the model to include arbitrary three‐dimensional distribution of laminae in ‘quasi‐plane strain’ is included. The effect of various flow rules adopted for plastic straining is indicated.
Large strain analysis of some geomechanics problems by the finite element method
Authors: Yamada Yoshiaki , Wifi Abdalla S.
Published: August 2005

This paper presents a rational approach to the finite strain analysis of elastic‐plastic materials. An updated incremental finite element technique was applied to problems of shallow foundations of homogeneous as well as multilayer soils. This was based on a variational principle which is suitable for such problems.
A mathematical model for predicting coupled heat and water movement in unsaturated soil
Authors: Dempsey Barry J.
Published: August 2005

An investigation was conducted to develop a comprehensive moisture model for predicting non‐isothermal moisture conditions in soils. An extensive literature review indicated that a model based on the Philip and de Vries equations for non‐isothermal moisture movement and heat conduction would give the best results. By using numerical methods, the implicit finite difference approximations to the moisture movement and heat‐transfer equations were programmed for computer solution of water content and temperature in the soil with time.

Validation studies indicate that the moisture model can be used to predict accurately moisture conditions in the soil. The model was validated by using hydraulic data from laboratory studies conducted on soil columns compacted with AASHO A‐3 and AASHO A‐4 soil.

The application of the moisture model to the study of non‐isothermal moisture movement in the field is demonstrated. The influence of parameters such as water table depth, precipitation, and soil hydraulic properties on soil moisture content are shown by use of the moisture model. The model is shown to be applicable to a wide range of boundary conditions and that it predicts the moisture‐temperature regime with time in soils utilizing climatic input data.
Approximate time‐dependent analysis of tunnel support structure considering progress of tunnel face
Authors: Sakurai Shunsuke
Published: August 2005

The pressure acting on tunnel support structures generally increases with lapse in time. The pressure increase may be caused by not only the time‐dependent mechanical properties of the underground medium, but also by the progression of the tunnel face. In order to clarify these two effects, three‐dimensional analysis is required. In this study, however, a method which takes into account the three‐dimensional effects of the tunnel face progression in two‐dimensional plane strain analyses is proposedby introducing the ‘equivalent intial stress’. The proposed method can be easily applied to time‐dependent analyses of the behaviour of tunnel support structures installed in a visco‐elastic medium.

The tunnels considered here are circular in shape, being driven in homogeneous isotropic linear visco‐elastic media having hydrostatic initial stresses.

In the first part of this paper, detailed discussions of the proposed equivalent initial stress are given. The second deals with the mathematical formulations for obtaining closed‐form solutions for the pressure acting on tunnel support structures. In the third, numerical results and discussions are given, and special attetion is paid to the effects of both the time‐dependent mechanical properties of the material and the tunnel face progression. Finally, the theoretical results obtained here are utilized for interpretation of field measurements.
An anisotropic hardening model for soils and its application to cyclic loading
Authors: Mrǒz Z. , Norris V. A. , Zienkiewicz O. C.
Published: August 2005

An anisotropic hardening model for soils is proposed by applying the concept of a field of hardening moduli developed previously for metals. Besides the yield surface, a set of nesting surfaces in the stress‐space specifies the variation of hardening moduli during the deformation process. Both drained and undrained soil behaviour can be treated and distortional as well as volumetric strain cycles can be considered. The model can be applied in studying soil behaviour under cyclic loading and in particular to describe densification or liquefaction phenomena.
A rate‐type constitutive model for soil with a critical state
Authors: Davis R. O. , Mullenger G.
Published: August 2005

A continuum representation for soil which incorporates the concepts of hypoelasticity and critical state theory is proposed. General, three‐dimensional constitutive equations are formulated to relate specific volume, stress, rate of deformation and rate of change of stress, resulting in a mathematical material model which exhibits phenomenological features typical of soil response. The general constitutive equations are specialized to represent the particular cases of isotropic compression, constant, volume deformation, uniaxial compression and biaxial deformation. Methods are suggested for determining the model parameters to represent a specific soil using conventional triaxial test data. Comparisons of stress‐strain response with published experimental data are shown.
Effects of driving and subsequent consolidation on behaviour of driven piles
Authors: Desai C. S.
Published: August 2005

The effects and simulation of driving of structures (piles) into saturated soil media are discussed, and procedures for numerical simulation of driving are proposed. Consolidation caused by changes in stresses and in pore water pressures in the soil mass due to the driving is solved by using a finite element procedure. The changes in stresses and pore water pressures due to driving are obtained on the basis of the cavity expansion approach, and are introduced in the finite element procedure as initial conditions. Stresses and deformations around a pile as consolidation proceeds are plotted and related to the quantities such as a wall friction, and point and total loads relevant to analysis and design.
Finite element free surface seepage analysis without mesh iteration
Authors: Bathe Klaus‐Jürgen , Khoshgoftaar Mohammad R.
Published: August 2005

An effective solution procedure for the finite element analysis of free surface seepage problems is presented. The solution algorithm employs a non‐linear permeability description of the material and avoids iteration with the finite element mesh. The results and experiences obtained in the analyses of some problems are presented to demonstrate the usefulness of the technique.
A method of analysis for horizontally embedded anchors in an elastic soil
Authors: Rowe R. K. , Booker J. R.
Published: August 2005

A general method is presented for the analysis of horizontally embedded anchors in an elastic soil. Provision is made in the analysis for the consideration of anchor shape, layer depth, anchor–soil interface condition, breakaway of the anchor from the underlying soil and interaction between groups of anchors.

Application of the analytical technique is illustrated for strip and circular anchors, and these solutions are presented in the form of influence charts which may be used directly in hand calculations to predict the elastic load deflection behaviour, of anchor plates for a wide variety of material and geometric conditions.
On the estimation of the deformability characteristics of an isotropic elastic soil medium by means of a vane test
Authors: Selvadurai A. P. S.
Published: August 2005

The conventional use of the shear vane test is primarily restricted to thein‐situmeasurement of the undrained shear strength characteristics of saturated cohesive soils. Scant attention has been devoted to the use of this test as a means of measuring further properties of geotechnical interest. This paper presents an analytical study which illustrates the possible use of a shear vane test as a technique for the measurement ofin‐situdeformability characteristics of a soil medium. Certain plausible assumptions have been invoked for the analytical treatment of the shear vane problem. The vane blades are represented as elliptical shapes, the soil disturbance associated with the vane penetration is neglected and the soil mass enclosedwithin the swept boundary of the vane is represented as a rigid region. These, together with assumptions of classical isotropic elastic soil behaviour, enable the development of certain exact solutions for the torque–twist relationships of vanes fully or, partially embedded in the soil. The results indicate that the elastic deformability characteristics of a soil medium can be directly recovered from an examination of the initial stages of an experimental torque–twist curve. In particular, the measured parameter would correspond to the linear elastic shear modulus of the soil medium.
Finite element models for rock fracture mechanics
Authors: Ingraffea Anthony R. , Heuze Francois E.
Published: August 2005

A finite element model for the prediction of discrete fracture propagation in rock structures loaded in compression is presented. The model integrates any one of three theories for mixed‐mode fracture initiation; it contains an energy balance algorithm for predicting crack increment length, and incorporates recent developments in finite element stress‐intensity factor computation. The predictions of the model are compared with the observed fracture response of a real rock structure. Results show that the model accurately predicts both stable and unstable fracture progagations observed experimentally.
Settlement of inhomogeneous consolidating soils—I: The single‐drained layer under confined compression
Authors: Mahmoud M. S. , Deresiewicz H.
Published: August 2005

The settlement and excess pore pressure are calculated for a column of water‐saturated clay in which the permeability and/or shear modulus vary with depth. Several fairly general laws of variation are investigated. In each case, the soil is assumed to have a permeable top surface and to rest on an impervious substrate.

For all the variations examined, in which the shear modulus increases with depth below the surface but the permeability of the soil remains constant, the deflection at a given instant after imposition of the load decreases and the degree of settlement increases with increasing rate at which the change with depth takes place. It is found that, when the variation over the height of the column is one order of magnitude or less, the curve of degree‐of‐consolidation versus time is reasonably wellapproximated by the curve for a homogeneous soil whose modulus equals the depth‐averaged value. When, in addition, the permeability decreases with depth, the approximation becomes less accurate.

The same approximation, for moderate increase in shear modulus with depth, predicts satisfactorily the process of dissipation of excess pore pressure at a given depth, but breaks down when the variation in modulus is large.

Finally, it is shown that the effect of variable modulus on the settlement is greater than of a comparable variation in permeability.
Shear band inclination and shear modulus of sand in biaxial tests
Authors: Vardoulakis I.
Published: August 2005

The spontaneous shear band formation in the biaxial test on dry sand samples with constant cell pressure is treated as a bifurcation problem. The constitutive response of sand is described in terms of mobilized friction and dilatancy. Dilatancy is looked upon as an internal constraint and the hardening rule is expressed in terms of an adequate dimensionless stress measure. Owing to fail of normality in sand, localization always occurs in the hardening regime. The theoretical solution of the shear band inclination is a geometrical mean of the classical Coulomb and Roscoe solutions and is in good agreement with the experimental data. The incipient shear modulus is proportional to the stress level and can be estimated to be also proportional to these cant modulus.
Vertical and horizontal land deformation due to fluid withdrawal
Authors: Safai Nader M. , Pinder George F.
Published: August 2005

A non‐linear distribution of vertical displacement versus aquifer depth is calculated in the case of a partially penertrating well. For a fully penetrating well, however, a linear distribution is observed. The solution exhibits a vertically uniform horizontal displacement in the case of a fully penetrating well and, for a partially penetrating well, the maximum horizontal displacement occurs at the elevation of the well bottom.
Stability properties of the Newmark, Houbolt and Wilson θ methods
Authors: Gladwell Ian , Thomas Ruth
Published: August 2005

This paper analysis the stability of several methods for obtaining numerical solutions of second‐order ordinary differential equations. The methods are popular in structural and geotechnical engineering applications and are direct, that is they do not require the transformation of the second‐order equation into a first‐order system. They include Newmark's method in both implicit and explicit forms, Wilson's θ‐method, Houbolt's method and some variants on this latter method. We shall examine the stability of the methods when applied to the second‐order scalar test equation

where a and c are real.
Vertical vibrations of a rigid circular body on a non‐homogeneous half‐space interrupted by a frictionless plane
Authors: Awojobi A. O.
Published: August 2005

An exact formulation is presented for the problem of a rigid circular body performing harmonic vibrations on an elastic half‐space whose shear modulus increases linearly with depth and is interrupted at some finite depth by a frictionless horizontal plane. The static case is derived in the limit of zero frequency vibrations while the known result for the uninterrupted half‐space is recovered in either extreme limit of the horizontal frictionless plane coinciding with the surface or when it is pushed down to an infinite depth.

It is shown that the maximum effect of the interruption occurs when the frictionless plane is at a depth where the shear modulus is about 1·6 times the surface shear modulus. Furthermore, this maximum effect is equivalent to a reduction of about 5 per cent of the surface shear modulus or a reduction of about 2½ per cent in the natural frequency of the rigid body on an uninterrupted half‐space. The important conclusion, therefore, is that irrespective of the depth at which a half‐space isso interrupted, the surface shear modulus is still the dominant parameter and that both the increase in shear modulus with depth and the interruption are not only secondary but also opposing effects.
Stress analysis of a deep rigid axially‐loaded cylindrical anchor in an elastic medium
Authors: Luk V. K. , Keer L. M.
Published: August 2005

The elastostatic problem of an infinite elastic medium containing an axially‐loaded rigid cylindrical inclusion is investigated. This problem is of interest in connection with the geotechnical study of the time‐independent, load‐deflection characteristics of deep rigid anchors embedded in cohesive soil or rock media. The problem is formulated by means of Hankel integral transforms and reduced to a system of four coupled sing ular integral equations, where the unknown quantities are the normal and the shear stresses acting on the entire surface of the anchor. Numerical solutions are investigated for various Poisson's ratios and several values of the aspect ratio of radius to length of the cylindrical anchor.
A finite element method for studying the transient non‐linear thermal creep of geological structures
Authors: Anderson C. A. , Bridwell R. J.
Published: August 2005

A finite element theory, suitable for describing the long‐term transient thermal creep of geomechanical structures where the material obeys an arbitrary type of creep law, is presented. The method takes into account large deformation effects, is stable for the large time steps required to model geophysical phenomena and accurately simulates changing, incompressible, plastic flow fields. Applications of the theory to the prediction of long‐term creep and creep rupture of simple engineering structures, are given. The theory is also applied to predict the thermal creep of layered media to study the mechanics of folding and rift formation.
The elastic response of multiple underream anchors
Authors: Rowe R. K. , Booker J. R.
Published: August 2005

A technique is developed for the analysis of multiple underream anchor systems resting in an elastic soil. This technique may be used to consider anchor systems involving arbitrary anchor inclination and depth beneath the soil surface, as well as arbitrary number, shape, size and spacing of underreams. The approach is largely analytical in nature and involves only a fraction of the computation required for a finite element analysis.

Consideration is given to the effects of anchor depth and inclination to the soil surface, and the spacing and number of underreams upon the elastic response of anchor systems. On the basis of the result from this study, a simple, approximate method for estimating the response of multiple underream anchors is proposed. This approach involves the use of several interaction charts, which are presented in the paper, and can be used as a hand method for estimating the load–displacement behaviour of quite general anchor systems to sufficient accuracy for most practical purposes. The use of the approximate approach is illustrated by an example.
A general basis for yield, failure and potential functions in plasticity
Authors: Desai C. S.
Published: August 2005

A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three‐dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.
A novel finite element method for seepage analysis
Authors: Nath B.
Published: August 2005

A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately.

The validity of the method has been demonstrated by means of a number of examples including anisotropy and non‐linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.
Mathematical model for one‐dimensional desiccation and consolidation of sedimented soils
Authors: Casteleiro Manuel , Krizek Raymond J. , Edil Tuncer B.
Published: August 2005

A mathematical model has been developed to represent the physical phenomena that occur during the desiccation and one‐dimensional consolidation of successive layers of hydraulically transported sediments as they are periodically deposited in a containment area. The governing boundary value problem, defined in terms of pore water pressures, consists of two field equations (one for the saturated domain and one for the unsaturated domain), a drainage boundary condition, an evapotranspiration boundary condition and a series of continuity conditions at the interfaces between different layers. A number of simplifying assumptions were made to render the field equations tractable, and a step‐by‐step numerical procedure was used to solve the linearized boundary value problem; at the end of each step, the errors introduced by the simplifying assumptions were corrected. Based on a thorough study of the convergence and stability conditions associated with the numerical approximation employed, a system of automatic corrections was incorporated into the computer program to reduce the time increment if stability problems originate during the solution. Based on the results of a parameter study, it was found that, although drainage conditions at the bottom of the, layer do exert some influence on the consolidation rate during deposition of the dredgings, the evapotranspiration potential renders this effect almost negligible when desiccation takes place at the surface. In contrast, transpiration plays an important, role on the consolidation rate during the early stages of desiccation, but its effect is reduced considerably as the water table approaches an equilibrium position.
Non‐linear analysis of a joint element and its application in rock engineering
Authors: Xiurun (Ke Hsu‐Jun) Ge
Published: August 2005

In this paper models are given for analysis and description of non‐linear properties of joints, weak intercalations and interfaces in rock masses.

Models for analysis consist of four parts, i.e. shear displacement model, normal deformation model, shear strength model and a relationship between unit shear stiffness and normal stress.

The method of non‐linear analysis given in this paper is based on an incremental procedure.

The proposed method is available for different types of shear‐displacement curves, and also adapted to the complicated process of loading‐unloading‐reloading.

The results of computer simulation of an in‐situ shear test obtained by this method gave a good fit to the measured data.

The method of non‐linear analysis of joint elements has been used in some practical rock engineering problems, and some interesting results and conclusions have been obtained.
Finite element method for time‐dependent problems of frozen soils
Authors: Klein Joachim
Published: August 2005

Ground freezing technology is favoured in civil engineering, mainly in tunnelling. The time‐dependent material characteristics in the form of creep control the bearing capacity of any frozen earth support system. The finite element method in connection with an initial strain algorithm is able to include these effects. The information about stress redistribution and deformation rate is important for an economic design. Case histories of different tunnel linings in frozen soil and two other examples of realized projects show the usefulness of such a procedure.
Non‐linear elastic finite element analysis of lateral earth pressures against basement wall
Authors: Roth W. H. , Crandall Leroy
Published: August 2005

Perhaps the most widely used non‐linear elastic soil behaviour law uses the hyperbolic functions to define tangent modulus and Poisson's ratio versus strain.1,2 This paper presents the results of analytical studies with the hyperbolic elastic finite element technique for the prediction of static earth pressures against a 10‐story basement wall. Carefully performed laboratory tests of the backfill material and measurements of earth pressures during backfilling provided the basis fora, refinement of the current hyperbolic elastic method. The refined analysis resulted in closer agreement of calculated earth pressures with measured values.
Finite element analysis of problems with infinitely distant boundaries
Authors: Booker J. R. , Small J. C.
Published: August 2005

A method allowing for the presence of infinitely distant boundaries in prismatic bodies is developed. The method is closely related to the consistent boundary concept used in dynamic applications but the development presented is algebraic and context free and is thus applicable to a wide variety of geotechnical problems both static and dynamic.
A theoretical estimate of the tilt of a surface foundation due to an inclined anchor load applied at the interior of the soil medium
Authors: Selvadurai A. P. S.
Published: August 2005

This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.
The consolidation of a soil stratum, including self‐weight effects and large strains
Authors: Lee Kuantsai , Sills G. C.
Published: August 2005

A layer of fill deposited in a soft wet condition will consolidate under its own weight and will commonly undergo comparatively large strains in the process. Neither of these aspects of behaviour can be modelled by traditional consolidation theories. In this paper, a consolidation model is developed from the theory proposed by Gibson et al.5 and is applied here to soil consolidation during and after soil deposition. No restriction is made on the magnitude of strain, so that the boundaries are not taken as being fixed in space, but are allowed to move as required by the process of consolidation. However, perhaps the more important aspect is the consideration of self‐weight, since in many instances, the surface loading applied to soft, soils is small, and the majority of the compression of the layer occurs while the effective stresses reach equilibrium with the weight of the soil. Although some idealizations have to be made in assuming relationships between soil parameters, it is shown that the self weight effects in consolidation can be significant, and fundamental to an understanding of soft soil behaviour.
Inexpensive but technically sound mine pillar design analysis
Authors: Pariseau William G.
Published: August 2005

A simple algorithm (PILLR) for obtaining by two‐dimensional analysis thee essential results that would be obtained in an actual three‐dimensional finite element analysis of stress about mine pillars in flat‐laying stratified rock is presented. A series of comparisons between the distributions of the local factor of safety calculated from the results of three‐dimensional analysis and that obtained in the PILLR two‐dimensional analyses for pillars of length/width ratio ranging from 0.33 to 8.0 shows the algorithm to be quite effective. The average vertical stress over the horizontal mid‐plane of the pillar in the PILLR two‐dimensional analyses is always within 0.5 per cent of the exact average; the local safety factor distribution is always within 10 per cent of the three‐dimensional result. The ratio of the computer core x time product for the 2D' to 3D analyses is approimately 1/150. Additional improvements ard possible, although with the current PILLR algorithm 3D analyses require less than 1 minute for execution. This fact makes technically sound 3D mine pillar design analyses economically feasible on a routine basis.
Vibrational characteristics of soil deposits with variable wave velocity
Authors: Gazetas George
Published: August 2005

The paper studies certain dynamic characteristics of soil deposits with wave velocities increasing with depth according to (1 + μz)m, where m = 1, 2/3, 1/2, 1/4 and 0. Analytical solutions are presented for the fundamental periods, mode shapes and amplification functions due to vertically propagating shear waves and the effects of type (m) and rate (μ) of heterogeneity are systematically investigated. The analytical–numerical techniques are used to study the attenuation with depth in a deposit of the vertical and horizontal displacements due to travelling of Rayleigh waves. Differences attributed to different heterogeneities are discussed in connection with the machine isolation problem and the steady‐state vibration technique for soil exploration. Finally, the dependence on soil heterogeneity of the time–distance response curves, obtained during seismic refraction surveys, is graphically illustrated.
On the non‐linear ‘squeezing’ effects around circular tunnels
Authors: Gioda Giancarlo
Published: August 2005

An analysis is presented of the non‐linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time‐dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.
Incremental constitutive law for sands and clays: Simulations of monotonic and cyclic tests
Authors: Darve F. , Labanieh S.
Published: August 2005

An incremental formulation of constitutive laws is first presented and the fundamental notion of incremental non‐linearity, necessary for the description of cyclic behaviour of soils, is emphasized.

The incremental constitutive law for soils and its principal assumptions, which make it more general than the classical elastic–plastic models are detailed.

The constitutive parameters of Hostun sand and Grundite clay are then given, as well as a comparison of theoretical results with experimental axisymmetrical and true triaxial measurements (Hostun sand tests at Grenoble and Grundite clay tests at Berkeley). Different cyclic behaviour simulations are presented, as well as an example of cyclic liquefaction of Monterey loose sand. Finally, a simple shear test is simulated.
The prediction of frost penetration
Authors: Bell Graham E.
Published: August 2005

The effectiveness of the heat balance integral approach in determining the extent of frost penetration of the ground is illustrated.
Two‐surface versus multi‐surface plasticity theories: A critical assessment
Authors: Prevost Jean H.
Published: August 2005

It is the objective of this note critically to assess the merits and shortcomings of two‐surface and multi‐surface plasticity theories.