bluuebunny/crossref_metadata_2025 huggingface dataset:
Cramér–Rao bounds for three‐point decomposition of water and fat
Authors: Pineda Angel R. , Reeder Scott B. , Wen Zhifei , Pelc Norbert J.
Published: August 2005

The noise analysis for three‐point decomposition of water and fat was extended to account for the uncertainty in the field map. This generalization leads to a nonlinear estimation problem. The Crámer–Rao bound (CRB) was used to study the variance of the estimates of the magnitude, phase, and field map by computing the maximum effective number of signals averaged (NSA) for any choice of echo time shifts. The analysis shows that the noise properties of the reconstructed magnitude, phase, and field map depend not only on the choice of echo time shifts but also on the amount of fat and water in each voxel and their alignment at the echo. The choice of echo time shifts for spin‐echo, spoiled gradient echo, and steady‐state free precession imaging techniques were optimized using the CRB. The noise analysis for the magnitude explains rough interfaces seen clinically in the boundary of fat and water with source images obtained symmetrically about the spin‐echo. It also provides a solution by choosing appropriate echo time shifts (−π/6 + πk, π/2 + πk, 7π/6 + πk), with k an integer. With this choice of echo time shifts it is possible to achieve the maximum NSA uniformly across all fat:water ratios. The optimization is also carried out for the estimation of phase and field map. These theoretical results were verified using Monte Carlo simulations with a newly developed nonlinear least‐squares reconstruction algorithm that achieves the CRB. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Iterative decomposition of water and fat with echo asymmetry and least‐squares estimation (IDEAL): Application with fast spin‐echo imaging
Authors: Reeder Scott B. , Pineda Angel R. , Wen Zhifei , Shimakawa Ann , Yu Huanzhou , Brittain Jean H. , Gold Garry E. , Beaulieu Christopher H. , Pelc Norbert J.
Published: August 2005

Chemical shift based methods are often used to achieve uniform water–fat separation that is insensitive to Bo inhomogeneities. Many spin‐echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time‐dependent phase shifts caused by water–fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water–fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed “iterative decomposition of water and fat with echo asymmetric and least‐squares estimation” (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least‐squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2π/3, with the middle echo centered at π/2+πk (k = any integer), i.e., (–π/6+πk, π/2+πk, 7π/6+πk). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil–water phantom was observed, demonstrating that the iterative least‐squares decomposition method is an efficient estimator. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Incremental plasticity analysis of frictional soils
Authors: Christian J. T. , Hagmann A. J. , Marr W. A.
Published: August 2005

Three constitutive models of soil are used in finite element analyses of lateral earth pressure and bearing capacity. The three models are an elasto‐plastic formulation derived from the Mohr‐Coulomb law, a similar model with the plastic dilatancy removed, and a strain hardening model with a capped yield criterion. Stiffness formulations are described; the non‐dilatant model has a non‐symmetric stiffness. The results for the retaining walls are in close agreement with classical soil mechanics, but the bearing capacity analyses greatly overestimate the bearing capacity. The patterns of motion are, however, reasonable. Reasons for the discripancies in the bearing capacity case include: (a) the elements are too stiff and do not permit sliding on discrete failure planes; (b) the bearing capacity problem is itself not well settled theoretically; (c) very fine element divisions are necessary in areas of strong stress gradients and (d) rotation of principal stresses is significant.
The analysis of composite structures with prescribed frictional conditions at the interfaces
Authors: Nath P.
Published: August 2005

A method is presented for the analysis of composite structures with prescribed frictional conditions at the interfaces. The method, which can also be used for the piecewise solution of large structures, is illustrated by analyzing a test problem with two interfaces.
Measurement of flow properties of expansive clays
Authors: Uzan J. , Lytton R. L.
Published: August 2005

The paper deals with the determination of the flow properties of expansive and unsaturated clays under different conditions of stress. By choosing the moisture content as the dependent variable, the well known non‐linear diffusin equation is derived. Numerical solutions using a finite element program are presented, assuming a linear relationship between the moisture diffusivity and the concentration (the relative moisture content). These solutions are interpreted and a procedure is proposed to derive the flow properties of the clay from the sorption curves. Results of tests are presented and used to illustrate the procedure. It is found that the lower the stress applied, the smaller the initial moisture diffusivity and the stronger the dependence of the moisture diffusivity upon the concentration.
Formation of shear bands in sand bodies as a bifurcation problem
Authors: Vardoulakis I. , Goldscheider M. , Gudehus G.
Published: August 2005

The paper reports on the results of theoretical and experimental investigations on the spontaneous formation of shear bands in sand bodies. The phenomenon is considered as a bifurcation problem. Consequently, material response and configuration‐dependent loading determine the bifurcation mode. Both Coulomb's and Roscoe's solutions of inclination of the shear band can be correct theoretically and experimentally. The first one holds for non‐rotating stress axes, the second one for co‐rotating stress and strain increment axes during failure. Values in between can occur if the rotation of principal stress axes is not equal to one of these limits. If Coulomb's inclination of shear band occurs, there is a thin deforming material layer separating rigid bodies. Inside the shear band non‐coaxiality of strain increment and stress holds from the beginning. If Roscoe's inclination of shear band occurs, it is separating two deforming bodies. Inside the shear band strain increment and stress are coaxial at peak.
Plates on saturated porous elastic foundations
Authors: Tabaddor Farhad
Published: August 2005

The problem of plates on consolidating soil is considered. Biot's three‐dimensional consolidation theory, the generalization of Terzaghi's model, is employed to account for the consolidation process. A mathematical model is developed and the differential equations governing the system together with the proper boundary conditions are derived. A variational formulation of the problem and a convenient approximate method of solution are also presented.

For numerical analysis, the problem of a rectangular plate on consolidating soil under various loading conditions is numerically solved and the effects of various physical factors on the settlements and the pore pressures are studied.
Axisymmetric compression of a Mohr–Coulomb medium around a circular hole
Authors: Florence A. L. , Schwer L. E.
Published: August 2005

An analytical solution is presented for the stress and strain fields in a Mohr–Coulomb material in plane strain around a circular hole when it is compressed by an axisymmetric far‐field pressure. It is shown that several solutions arise involving one to three plastic zones depending on the values of Poisson's ratio and the friction angle. The solution chosen for presentation was obtained and used to validate the functioning of the Mohr–Coulomb yield condition that was added to the NONSAP finite element code. Stress and strain field comparisons are made.
Surface settlement of a finite elastic layer whose modulus increases linearly with depth
Authors: Brown P. T. , Gibson R. E.
Published: August 2005

An examination has been made of the behaviour of a finite layer of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which rests on a rough rigid base. Values of surface settlement at the corner of a rectangular area of uniform loading are presented for values of Poisson's ratio of \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{3} $\end{document} and 0, and for wide ranges of degree of inhomogeneity and loading breadth to depth ratio.
Numerical analysis of rafts on visco‐elastic media using eigenvector expansions
Authors: Brown P. T. , Booker J. R.
Published: August 2005

Problems of a raft on a visco‐elastic continuum may be converted to equivalent elastic problems by means of a Laplace transformation. In this paper a numerical solution of the equivalent problem is obtained by finite element or other techniques. This solution is converted into the form of an eigenvector expansion and then transformed into a numerical solution to the original problem by inverting the Laplace transform. This form of solution has the advantage of applying to any visco‐elastic model, and of requiring little additional computation as a result of changing the visco‐elastic model, the relative raft‐soil stiffness or the load pattern.

The application of the method is illustrated by results for circular rafts, strip footings of finite length and rectangular rafts, and particular attention is paid to a realistic soil creep function which is asymptotic to a linear function of log time.
Theoretical study of hydraulically fractured penny‐shaped cracks in hot, dry rocks
Authors: Abé H. , Keer L. M. , Mura T.
Published: August 2005

A simple and analytical method of solving the problem of heat extraction from a penny‐shaped crack having both inlet and outlet holes is developed by using a two‐dimensional flow model when fluid is injected at a constant flow rate. Temperature distributions in both rock and fluid are obtained by taking into account the hydraulic and thermal growth of the crack. The outlet fluid temperature and energy extraction rate versus time are shown by some illustrative examples. Although the effect of thermal, contraction of rock upon the crack width is large, its influence upon flow rate and crack tip stress intensity factor is sufficiently small within the first several years so that the crack radius can be determined mainly by the mechanical deformation of, the rock.
3D mine pillar design information from 2D FEM analysis
Authors: Pariseau W. G. , Sorensen W. K.
Published: August 2005

This paper described a technique for obtaining three‐dimensional mine design information using a two‐dimensional finite element program where the mining geometry consists of an extensive array of underground rooms and pillars. The technique is based upon a simple augmentation of forces in a two‐dimensional analysis to produce the same average pillar stress that would occur in a full three dimensional analysis. Detailed comparisons between a three‐dimensional analysis, a two‐dimensional analysis (plane stress and plane strain) and an augmented two‐dimensional analysis (also plane stress and plane strain) of stress about a typical coal mine pillar are presented. A local factor of safety is defined and then mapped over the pillar midplane, the immediate roof and immediate floor using the results from the full three‐dimensional analysis. Comparisons of roof and pillar safety factor distributions obtained by the three‐dimensional, two‐dimensional and augmented two‐dimensional analyses show that the minimum safety factors in the pillar (at the pillar sides) are predicted quite closely by the augmented two‐dimensional techniqe (plane stress). The same is true of the immediate roof, although the three‐dimensional safety factor tends to be higher in the roof (over the room) than that calculated by the augmented twodimensional technique. The augmented loading procedure appears to hold considerable promise as a very efficient and cost reducing techniqe for mine pillar design.
Finite element analyses of isotropic and anisotropic cohesive soils with a view to correctly predicting impending collapse
Authors: Toh C. T. , Sloan S. W.
Published: August 2005

One major problem encountered when using the finite element method to simulate the load–deformation behaviour of an elasto‐plastic soil mass is that the theoretical collapse load is generally exceeded, and in some cases the numerical solution fails to exhibit a collapse load. A mixed variational principle is used as the basis for developing the governing equations of deformation and the results from this are compared with those obtained from the use of the virtual power equation. The former is found to give improved results and is generalized to include description of finite deformation. An Eulerian frame of reference is used. The method of approximating configuration changes in the numerical solution procedure is found to determine the shape of the load–deformation curve. Finally, a simple method of accounting for anisotropy of yield is presented.
Numerical identification of soil‐structure interaction pressures
Authors: Gioda Giancarlo , Jurina Lorenzo
Published: August 2005

A numerical approach is presented for the ‘identification’ (or back calculation) of the earth pressure acting on embedded or retaining structures. The procedure is applicable to structures of any shape and requires a set of in situ measurements that may include displacements of points on the structure, values of concentrated forces, values of distributed loads at some locations, etc. Possible limiting values of the unknown loads, non‐linear structural behaviour, varying accuracies of the input data are accounted for in the problem formulation. Depending upon the type of problem, the solution is reached by means of the unconstrained or constrained minimization of a suitably defined error function. As an example, the proposed approach is applied to the identification of the earth pressure acting on some typical geotechnical engineering structures.
Trap‐door problem with dry sand: A statical approach based upon model test kinematics
Authors: Vardoulakis I. , Graf B. , Gudehus G.
Published: August 2005

The trap‐door problem with dry sand is treated in a statical analysis based upon model test kinematics. Integration of the equilibrium conditions along horizontal slices and introducing the mean value for the vertical stresses yields a differential equation for the trap‐door force. Concerning the constitutive response of sand a statical model of a moving shear band is proposed as an internal boundary. Solutions for the trap‐door force for the active and passive modes and for the ultimate and residual states are discussed.
Numerical prediction of collapse loads using finite element methods
Authors: Sloan S. W. , Randolph M. F.
Published: August 2005

In this paper, the ability of a displacement‐type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al.1 is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15‐noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al., 1 it is established theretically that if lower order finite elements are employed rigorously for non‐trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be.
On statistical description of stress and fabric in granular materials
Authors: Mehrabadi M. M. , Nemat‐Nasser S. , Oda M.
Published: August 2005

The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.
Limit analysis: A linear formulation of the kinematic approach for axisymmetric mechanic problems
Authors: Turgeman S. , Pastor J.
Published: August 2005

This paper deals with a numerical formulation of the kinematic limit analysis method. This formulation, based on a finite element discretization, is available for axisymmetric cases. The linearization of the yield Tresca and Von Mises criteria leads to linear programming problems. The velocity fields described here are plastically admissible only on an average. The influence of this approximation is quantified for the triaxial test problem and the stability of circular excavations.
A mapping finite element method for stress calculation in two‐dimensions
Authors: Nath B.
Published: August 2005

A mapping finite element method is proposed for the solution of elastic problems in two‐dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect‐ratio problems of this type, accurately and economically.
Finite layer analysis of consolidation. I
Authors: Booker J. R. , Small J. C.
Published: August 2005

A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini‐computer.
A critical analysis of some variational methods in slope stability analysis
Authors: Castillo E. , Luceño A.
Published: August 2005

During the last ten years the Calculus of variations technique has been applied to solve the problem of stability of slopes. All published methods are essentially based on the attainment of a functional and the search for its absolute minimum or maximum by vanishing its first variation.

Obviously this statement of the problem is valid only if such a minimum or maximum exists and can be obtained by making the first variation of the functional equal to zero. So, these implicit hypotheses must be checked.

This work analyses from this point of view the validity of the methods proposed by ‘Baker and Garber’, ‘Chen’ and ‘Castillo and Revilla’, and demonstrates that the first two methods are incorrectly stated while the third one is correct at least in the case of a frictionless soil.
Elasto‐plastic analyses of deep foundations in cohesive soil
Authors: Griffiths D. V.
Published: August 2005

The bearing capacity of deep foundations has been analysed using finite elements in conjunction with elasto‐viscoplasticity. The influence of elastic parameters, mesh size and strain conditions on computed collapse loads was observed. Axisymmetric problems in particular were of interst, because it was found that good numerical solutions could be obtained through to collapse provided reduced integration was used.
Shear vibration of vertically inhomogeneous earth dams
Authors: Gazetas George
Published: August 2005

Closed‐form solution to the problem of free vibrations of vertically inhomogeneous earth dams, modelled as truncated‐wedge‐shaped shear beams, has been obtained by implementing an inverse procedure in which the determination of the function descrbing the inhomogeneity constitutes part of the problem. The resulting cube‐root variation of the shear‐wave velocity with distance from the crest compares very favourably with measurements in two Japanese dams. The results of the method are presented in theform of natural periods, modal shapes and average seismic coefficients for a number of truncation ratios. Compared with an ‘equivalent’ homogeneous dam, the inhomogeneous experiences sharper amplification of modal displacements and greater averge seismic, coefficients near the crest and has natural periods which are closer to each other. This behaviour is in better agreement with the observed response of a 37m‐high dam during five earthquake motions.
Consequences of deviatoric normality in plasticity with isotropic strain hardening
Authors: Baker R. , Desai C. S.
Published: August 2005

For many soils experimental evidence suggests that deviation from normality between the plastic strain increments and the yield function is exhibited mainly in the volumetric behaviour, whereas the deviatoric behaviour exhibits normality. An analysis of the consequence of this observation is presented, and it leads to an expression for the plastic potential function as composed of two functions, a yield function and another dependent only on the hydrostatic pressure; the latter is considered to constitute the concept of correction functions presented recently by Desai and Siriwardane13.
Analysis of rigid pavement on viscoelastic foundations subjected to moving loads
Authors: Bandyopadhyay Sudipta S.
Published: August 2005

The dynamic behaviour of road structure has been analysed by idealizing the subgrade with different viscoelastic models having three and four elements. Complex Fourier transformation has been used to solve the resulting differential equations. The results are presented in non‐dimensional form. A detailed study has been made to determine the effect of different parameters on the deflection and moment of the pavement. Also, the relative implications of idealizing the subgrade with different viscoelastic models have been studied. A numerical example has been solved.
Factors of safety and pile load tests
Authors: Baecher Gregory B. , Rackwitz Rüdiger
Published: August 2005

The factor of safety used in designing pile foundations for vertical load should depend on three things, prior information on load capacity summarized by empirical correlations with load capacity models, site specific information derived from load tests, and an objective function reflecting economic and safety considerations. A statistical approach to factor of safety selection was developed in order to suggest improvements of current standards for driven pile design. This approach recognizes a distinction between the variability of pile load capacity within individual sites, and the global variability upon which model correlations are based. Charts have been prepared for determining the FS required to achieve specified reliability indices, as a function of the number of load tests at a particular site and their outcomes.
Plasticity model for inherently anisotropic behaviour of sands
Authors: Ghaboussi Jamshid , Monen Hassan
Published: August 2005

Most deposited sands exhibit anisotropic behaviour. A plasticity model has been proposed with the capacity for simulating such anisotropic behaviour. The proposed model contains a number of coefficients of anisotropy. Methodology for determination of the coefficients of anisotropy has been discussed. Using experimental data, the coefficients of anisotropy have been determined for a number of well‐known sands. Stress‐dilatancy has been modelled by using the ‘normalized work’ and it has been shown that the normalized work is independent of inherent anisotropy. Finally, some reasonably close comparisons between experimental results and model simulations have been reported.
Thin‐layer element for interfaces and joints
Authors: Desai C. S. , Zaman M. M. , Lightner J. G. , Siriwardane H. J.
Published: August 2005

The idea of using a thin solid element, called a thin‐layer element, in soil‐structure interaction and rock joints is proposed. A special constitutive model is used and various deformation modes such as no slip, slip, debonding and rebonding are incorporated. The shear stiffness is found from special laboratory tests and the normal stiffness is assumed to be composed of participation of the thin‐layer element and the adjoining solid elements. A parametric study shows that the thickness of the thin‐layer element can be such that the ratio of thickness to (mean) dimension of the adjacent element is in the range of 0.01 to 0.1. A number of simple and practical problems are solved to illustrate the success of the thin‐layer element for soil‐structure interaction problems.
Vibration of a homogeneous half‐space of arbitrary Poisson's ratio interrupted by a frictionless plane
Authors: Awojobi A. O.
Published: August 2005

The work presents an exact expression for the Hankel transform of the surface displacement of a rigid circular body performing harmonic vertical vibrations on a homogeneous elastic half‐space of arbitrary Poissn'S ratio interrupted at some depth by a frictionless horizontal plane. The limiting case of the uninterrupted half‐space is recovered in each of the extreme cases when the frictionless plane coincides with the surface or sinks to an infinite depth. Furthermore, the static case is derived in the limiting case of zero frequency and it is shown that the result agrees with the limiting case of zero gradient shear modulus variation for the static case of the incompressible non‐homogeneous half‐space.

It is also established that Poisson'S ratio effect is linear, and the important proposition is again sustained that only surface shear modulus dominates vibrations on elastic media whereas any other factor such as the interruption of the frictionless plane as in the present case, merely constitutes a negligible secondary parameter.
An analytical solution for axisymmetric tunnel problems in elasto‐viscoplastic media
Authors: Fritz P.
Published: August 2005

An analytical solution is presented for the time‐dependent stresses and displacements in plane strain around a circular hole when it is loaded by an axisymmetric internal and far‐field pressure. The material is assumed to be elasto‐viscoplastic with dilatant plastic deformations according to a non‐associated flow rule. Strain softening is considered by a modified St. Venant slider which is characterized by Mohr‐Coulomb yield conditions for both the peak and the residual strengths.
An improved accelerated initial stress procedure for elasto‐plastic finite element analysis
Authors: Thomas J. N.
Published: August 2005

The most flexible and generally applicable methods for elasto‐plastic analysis are those based on an incremental‐iterative form of the initial stress approach, but such methods often exhibit slow convergence. The acceleration procedure known as the alpha‐constant stiffness method is reconsidered and some modifications are proposed. The principal difference in the present approach lies in the use of a single acceleration parameter, rather than a diagonal matrix of acceleration coefficients. The new scheme shows a significant improvement in numerical stability and converges three times faster than the standard initial stress method. Some practical aspects associated with the method are discussed and a number of applications are presented.
Stresses and displacements in an elastic mass due to distributed loading by discretization technique
Authors: Sharma K. G. , Rao G.‐Venkatappa
Published: August 2005

Numerical solutions have been obtained for stresses and displacements in a linear elastic half space due to distributed loads of circular, rectangular and elliptical shapes. The technique primarily involves use of a multi‐dimensional numerical integration technique to integrate point load solutions over the distributed loading after discretizing the area into a finite number of elements. Both uniform vertical and shear loads have been considered as well as vertical conical loads and inward shear loads. The technique evolved facilitates the determination of stresses and displacements by the use of mini‐computers and is neither as tedious and cumbersome as the use of tables and charts nor as costly as FEM solutions.

A detailed comparison has been presented between the results obtained by the numerical solutions and those of the existing analytical solutions wherever they are available. It is found that the agreement between the two is within one per cent for displacements at all depths for the different cases studied. The matching is also good in the case of stresses, except at shallow depths.
The analysis of deformations caused by loading applied to the walls of a circular tunnel
Authors: Booker J. R. , Carter J. P.
Published: August 2005

An analytical solution to the problem of a load applied to a portion of the wall of a circular tunnel installed deep in a homogeneous isotropic material has been found. The solution is obtained by taking a Fourier transform, in the axial direction, of the field quantities and then representing these as a Fourier series in the polar angle. The integration which is necessary for the inversion of Fourier transforms has to be performed numerically using Gaussian quadrature.

The solution has been used to analyse the problem of uniform normal loading applied over rectangular patches of the tunnel wall. An indication of how the solution can be applied to the tunnel jacking problem is given.
A computer method for stability analysis of caverns in jointed rock
Authors: Belytschko Ted , Plesha Michael , Dowding Charles H.
Published: August 2005

A simple rigid block model has been developed for analysing the stability of caverns and tunnels in jointed rock. Rigid block interactions are idealized as linear edge‐to‐edge contacts with a zero joint tension constraint and a Mohr‐Coulomb friction law. In the method, the minimum friction angle for stability is determined by sequentially eliminating tension and then minimizing the shear. It is demonstrated through examples that the minimum joint friction angle which results in a stable configuration is independent of the stiffness of the joint, and depends only upon the loading and geometry of the jointing and cavern. This insensitivity of stability to the normal and tangential joint stiffnesses, which can be difficult to obtain, is very useful for design purposes.
A differential slice approach to the problem of retaining wall loading
Authors: Michalowski Radoslaw L.
Published: August 2005

A differential slice technique is applied in order to obtain the solution for the pressure distribution on rigid retaining walls. The technique is based on a statical analysis of a plane differential slice, for which only the global equilibrium is required. An analytical solution to the problem is found for a non‐cohesive material and a linear slip surface. For more complicated cases the numerical solution is required.
F. E. analysis of field consolidation curves obtained with the modified borehole shear device (BHSD)
Authors: Demartinecourt Jean Pierre , Bauer Gunther E. , Soulié Michel
Published: August 2005

A modified version of the bore hole sheat device (BHSD) was used to obtain field consolidation curves in a soft sensitive clay. The Porewater pressure dissipation was monitored at the centre of one of the shear plates.

This paper describes briefly the in situ device employed and demonstrates the basic features of the linearelastic F. E. program ‘SOL’. A detailed study is made to simulate the field behaviour with the finite element approach. Comparisons are made between the field and analytical consolidation behaviour. Difficulties in predicting the value of the coefficient of consolidation of a sensitive clay using the BHSD consolidation curves are discussed.
Visco‐damage tension model for rocks in ground‐shock applications
Authors: Whitman Lorraine
Published: August 2005

A simple rate‐dependent tension model, tailored primarily for rocks in ground‐shock calculations, has been constructed. It is formulated as an internal state variable theory with spherical void development taken to approximate the underlying dissipative micromechanism. This simplifying assumption of ductile, rather than brittle, damage growth has been made to enhance the practicality of the model for large‐scale problems. The model has been restated within the fromework of (strain‐softening) viscoplastcity to associate it with the desirable mathematical properties of the latter theory. The tension option, extended to include healing in the post‐damage compressive phase, has been implemented in a standard cap constitutive routine and is referred to as the visco‐damage tension model. Model parameters are selected for a shale‐like material. Results of uniaxial shock‐loading strain‐rate calculations exhibit desired characteristics in tension. Damage‐related hysteretic effects are illustrated through cyclic loading calculations. It is planned to develop more effecient computational procedures to facilitate adoption of the model into large‐scale ground shock calculations. Anisotropic extensions of the model will then be considered.
Stability and bifurcation of undrained, plane rectilinear deformations on water‐saturated granular soils
Authors: Vardoulakis I.
Published: August 2005

Stability and bifurcation of plane‐strain, undrained, rectilinear deformations on water‐saturated granular soil specimens are discussed. The soil, sand or normally consolidated clay, is described by a 2D‐flow theory of plasticity for frictional material with non‐associated flow rule. Contractant material become unstable (liquefies) at the state of maximum deviatoric stress. For dilatant material the dominant failure mode is shear banding that occurs close to the state of maximum principal effectivestress ratio. The theoretical findings are supported by and are used to explain existing experimental results.
Simple model for transient soil loading in earthquake analysis. II. Non‐associative models for sands
Authors: Pastor M. , Zienkiewicz O. C. , Leung K. H.
Published: August 2005

This paper extends the bounding surface, generalized plasticity, model of Part I to reproduce the behaviour of sands under both static and transient loading.

The essential features of the first model are preserved but the following changes are introduced:

The shape of the yield surface is modified.

A non‐associative flow rule is introduced.

The hardening parameter of the bounding surface includes not only volumetric but also deviatoric plastic strain.

Plastic volumetric and deviatoric strains are introduced during unloading.

Each of these modifications can be introduced separately in a hierarchical manner to model in an improved way the behaviour of sands. Good comparison with experimental observations is recorded. The simplicity of the original model is preserved with modifications being introduced progressively to model rising complexity of the phenomena.
Response of porous beds subjected to random waves
Authors: Layas F. M. , Rahman M. S.
Published: August 2005

A general analysis procedure is developed for the evaluation of the effective stress response of a porous ocean bed subjected to random waves. The ocean floor soil is treated as a saturated porous elastic medium and Biot's theory is used to formulate the coupled flow and deformation. The waves are treated as a random process which is described by Pierson–Moskowitz spectrum. The derived statistical properties of the response are used to evaluate the probability of failure in ocean bed.
Mixed time integration for the transient analysis of jointed media
Authors: Plesha Michael E.
Published: August 2005

A constitutive operator split method with implicit‐explicit time integration is presented for the transient analysis of rigid block models of jointed media. The linear portion of the joint constitutive law is integrated by an implicit method and the non‐linear, time dependent portion is integrated by an explicit method. The method features the stability of implicit procedures as well as the flexibility of explicit procedures for non‐linear problems. The solutions obtained with this method are compared to the solutions obtained by the explicit central difference method; in all cases there is good to excellent agreement. For some problems, particularly for those with low frequency excitation, it is shown that the implicit‐explicit method can result in a substantial savings over more conventional explicit methods.
Analysis of excavations in jointed rock of infinite extent
Authors: Sofianos A. I. , Watson J. O.
Published: August 2005

The subject of this work is the development of a code to study the behaviour of stratified and jointed rock masses around underground excavations. The rock mass is divided into two types of regions, one which is supposed to exhibit linear elastic behaviour and which may extend to infinity, and the other which will include discontinuities that behave inelastically. The former has been simulated by a symmetric direct, boundary integral, plane strain, quadratic, orthotropic module, and the latter by quadratic plane strain, membrane and inelastic joint elements. The two modules are coupled in one program. Sequences of loading include static point, pressure, body and residual loads, construction and excavation sequences, and quasi‐static earthquake load. The programe is interactive, with graphics. A numerical example is presented to illustrate the method.
An integral method for predicting hydraulic fracture propagation driven by gases or liquids
Authors: Nilson R. H.
Published: August 2005

Hydraulic fracture propagation is predicted by a general numerical procedure which satisfies the transport equations in a global or integral sense over the entire fracture and over a small control volume near the leading edge. At each discrete time step the pressure distribution is selected from a four‐parameter family of profiles such that the stress intensity is equal to the critical value at the tip of the fracture and the integral equations are satisfied. Comparisons with previous analytical and, numerical solutions indicate accuracy within 10 per cent for a variety of test problems include wedge‐shaped and envelope‐shaped fractures, laminar and turbulent flows, incompressible liquids and ideal gases, permeable and impermeable media, prescribed inlet pressure and prescribed flow rates. CPU time is typically a few seconds for a tenfold increase in fracture length. The method has been applied to explosively driven and propellant‐driven gas fracturing problems as well as the traditional pump‐driven hydraulic fracturing problem.
Stability analysis of an advanced vault excavation with unlined invert according to the finite element method
Authors: Wittke W. , Feiser J. , Krieger J.
Published: August 2005

This paper attempts to present questions associated with the stability of advanced vault excavations which are driven according to the New Austrian Tunnelling Method (NATM) without lining of the temporary invert. The dimensions of the investigated cross‐section correspond to those of the tunnels driven on the new high‐speed tracks for the German Federal Railways. Two possible modes of failure are investigated with the aid of continuum mechanics analyses according to the finite element method. Reference is made to structural measures which may positively influence the stability of this construction stage. Furthermore, the manner in which the stress‐strain behaviour of a horizontal alternating sequence with open vertical discontinuities may be taken into consideration in a continuum mechanics analysis is also demonstrated. The analysis results presented clearly show that the load‐carrying action of the rock mass which characterizes the NATM may be better described by rock mechanics analyses according to the finite element method than by conventional procedures.
The behaviour of an impermeable flexible raft on a deep layer of consolidating soil
Authors: Booker J. R. , Small J. C.
Published: August 2005

Analytic solutions to the problem of the time‐settlement behaviour of raft foundations have been limited in the past to flexible or rigid loadings, and have treated the foundation as being completely permeable. In this paper, solutions are presented for smooth circular rafts of any flexibility causing consolidation of a deep homogeneous clay layer, where the raft may be considered permeable or impermeable.

Results for the time‐dependent behaviour of contact stresses, pore pressures, raft displacements and moment in the raft are presented.
A boundary integral equation technique for visco‐elastic stress analysis
Authors: Carini Angelo , Gioda Giancarlo
Published: August 2005

On the basis of the correspondence principle of visco‐elasticity, an application is discussed of the boundary integral equation method to the solution of time‐dependent stress analysis problems. The adopted solution technique, in addition to the time‐dependent stress and strain distributions, enables the determination of a measure of the error affecting the numerical results. The governing equations for the plane strain visco‐elastic problem are derived with reference to a generalized Kelvin model consisting of the series of any number of simple kelvin elements, having both volumetric and deviatoric components. To get some insight into the overall performance of the technique, the results obtained in the solution of some test examples are discussed and compared with those dering from the available closed from solutions.
Adaptive methods to solve free boundary problems of flow through porous media
Authors: Chung Kyoon Yang , Kikuchi Noboru
Published: August 2005

Grid adaptive methods combined with domain adaptation are discussed for two‐dimensional seepage flow problems with free boundaries through porous media. Examples of grid and domain adaptive methods are presented to demonstrate several ways to predict grids and shapes of free boundaries using an iterative scheme. Finally, the combined adaptive methods are applied to obtain smooth non‐oscillatory shape of a free boundary of seepage flow through non‐homogeneous porous media.
Elastic consolidation around a point sink embedded in a half‐space with anisotropic permeability
Authors: Booker J. R. , Carter J. P.
Published: August 2005

The complete solution is presented for the transient effects of pumping fluid from a point sink embedded in a saturated, porous elastic half‐space. It is assumed that the medium is homogeneous and isotropic with respect to its elastic properties and homogeneous but anisotropic with respect to the flow of pore fluid. The soil skeleton is modelled as a linear elastic material obeying Hooke's law, while the pore fluid is assumed to be incompressible with its flow governed by Darcy's law. The solution has been evaluated for a particular value of Poisson's ratio of the solid skeleton, i.e. 0.25, and the results have been presented graphically in the form of isochrones of excess pore pressure and surface profile for the half‐space. The solutions presented may have application in practical problems such as dewatering operations in compressible soil and rock masses.
Numerical Laplace–Fourier transform inversion technique for layered soil consolidation problems; II, Gibson soil layer
Authors: Harnpattanapanich T. , Vardoulakis I.
Published: August 2005

The numerical Laplace–Fourier transformation technique previously presented by the authors11 is used here for solving the consolidation problem of a finite inhomogeneous soil layer whose shear modulus is increasing linearly with depth. Parametric studies are performed and the results are critically discussed.
One‐dimensional advective–dispersive transport into a deep layer having a variable surface concentration
Authors: Booker J. R. , Rowe R. K.
Published: August 2005

Two analytic closed form solutions for the one‐dimensional advection–dispersion equation are presented. These solutions take account of changes in surface concentration with time as mass is transported into the soil. The first solution is developed for the case of rapid landfill construction. The second solution considers a time‐dependent mass input to the landfill. The use of these solutions is illustrated by a number of examples and it is shown that consideration of the finite mass of contaminant within the landfill can significantly affect the concentration profiles beneath the landfill.
Computation of gas pressure profiles relevant to outbursting in coal mines
Authors: Schlanger Harry P. , Paterson Lincoln
Published: August 2005

High gas pressure gradients in coal seams play an important role in the occurrence of outbursts during underground coal mining. Excess stress resulting from body forces due to high pressure gradients contributes to the structural failure of coal. We present a one‐dimensional model of a dry, rigid coal seam with a moving mine face and determine gas pressures by solving the nonlinear equation for gas flow in a porous medium. An implicit finite difference scheme is used. Since the structure of coal has a dual porosity nature, we consider flow through both the macropores and the micropores. We investigate the effect of changes in mining velocity, idle mining periods and coal properties on the pressure profile in the coal seam. When the yield zone behind the moving mine face is taken into account, the greatest body force occurs on the least competent section of the coal seam.
Plastic collapse of long piles under inclined loading
Authors: Murff J. D.
Published: August 2005

A method is detailed for the plastic collapse analysis of long piles typical of offshore foundations, subjected to inclined loading. The method is based on the upper bound method of plasticity. It easily incorporates both axial and lateral variable soil resistance and variable pile cross section properties. The incorporation of plastic yield interaction between axial load and moment for the pile is a key feature of the method. The solution can itself be cast in the form of a curve representing axial and lateral load interaction and is amenable to incorporation in the analysis of foundation systems such as pile groups.