bluuebunny/crossref_metadata_2025 huggingface dataset:
Elastic–plastic shear deformation of frictional granular materials
Authors: Szymanski M. B.
Published: August 2005

A theory describing plastic deformation of granular (purely frictional) materials is presented. The theory is developed from postulates for energy dissipation and for the mode of plastic deformation. The postulates are based on some restrictions for the properties of granular materials and on a frictional analogy. A distinction is made between the description of plastic behaviour of a locally homogeneous and a locally non‐homogeneous material. An interpretation of the deformation process is presented which implies that the theory accounts for the changes in the density of some local non‐homogeneities underlying a plastic hardening effect. Based on this interpretation, an analogy between elastic–plastic behaviour of granular materials and frictional, sliding of two solid bodies is assumed. In the general case, the presented constitutive equations describe two hardening (softening) effects and are capable of describing both initial and advanced plastic deformations. A special, simplest form of the constitutive equations is examined in detail and a yield condition and a stress–strain relationship are derived. An example of elastic–plastic stress–strain–strength behaviour is presented for the cuboidal loading conditions.
Some applications of the boundary element method in geomechanics
Authors: Venturini W. S. , Brebbia C. A.
Published: August 2005

This paper presents the complete formulation for the application of the Boundary Element Method to solve non‐tension material problems. The formulation is based on including an extra term due to an initial stress field into the boundary integral statement. This is then used to iterate the solution until a state of non‐tension is achieved. The resulting iteration process is very simple to apply and basically consists only of a single matrix–vector product. The applications show that accurate resultscan be obtained for boundary discretizations involving a small number of unknowns. Whenever possible, results are compared with analytical solutions or finite elements.
The consolidation problem treated by a consistent (static) finite element approach
Authors: Cividini Annamaria , Rossi Adolfo Zavelani
Published: August 2005

The consolidation problem in a plane strain porous elastic medium is treated by adopting a consistent formulation of the finite element model. To this purpose, the fluid‐phase behaviour is modelled in static terms through a piecewise linear description of the pore pressure field and the behaviour of the two‐phase medium is consistently modelled through rigorously equilibrated piec̀ewise linear stress distribution.

Incompressibility of the pore fluid and of the skeleton grains is assumed, as is linear elastic behaviour of the solid phase.

After a compact description of the model, the governing equations for the continuum problem are recalled and the solution system for the discretized problem is obtained following Galerkin's method of weighted residuals. Some examples are finally illustrated, in order to assess the reliability of the approach and to introduce possible comparisons with other methods.
A finite element model for the analysis of tailored pulse stimulation of boreholes
Authors: Swenson D. V. , Taylor L. M.
Published: August 2005

A constitutive model is described for the prediction of dynamic crack formation in geological media. The model includes a simple tensile failure criterion for crack formation and a soil plasticity model for both deviatoric and volumetric plasticity. Numerical results are presented which show that the model reproduces the observed dependence of fracture formation on loding rate for dynamic pressure loading of boreholes. The use of the model as a numerical tool for design is demonstrated through two example parameter studies.
On the solution of plane flow of granular media for jump non‐homogeneity
Authors: Michalowski Radoslaw L.
Published: August 2005

This paper deals with the plane plastic equilibrium of a cohesive frictional material in the case of a jump non‐homogeneity. Three types of interface separating rigid‐plastic bodies with different material parameters are distinguished: (i) a perfect adhesion contact, (ii) a thin layer of a material different from the adjacent bodies, (iii) a combined frictional‐adhesive contact. A sliding along the interface may occur if certain conditions are satisfied. For the first two types of joint, the direction and propagation of the velocity jump vector along the interface follow from the classical theory of plane plastic flow. In the third case, the potential sliding rule relating the velocity jump vector to the limit condition of the joint, or to the potential different from the limit condition, may be adopted. The direction of the velocity jump vector results from such a rule.

The problem of stability of a slope, being continuously non‐homogeneous in one region, and homogeneous in another, is shown in an example. The two regions of the slope are separated by the interface, a thin layer of a different material, (type ii). The associated flow law for both regions of the slope and for the material of the interface is assumed.
On the theory of consolidation with double porosity—III A finite element formulation
Authors: Khaled M. Y. , Beskos D. E. , Aifantis E. C.
Published: August 2005

We employ a finite element method to consider the numerical solution of Aifantis' equations of double porosity.1–5 The physical and mathematical foundations of the theory of double porosity were considered in two previous papers, 6,7 where analytical solutions of the relevant equations are also given. For practical purposes and for the completeness of the presentation, we re‐derive the basic equations without resorting to the more rigorous scheme of multiporosity theory.1–6 Instead, we follow the more familiar approach of Biot8,9 which we now extend from the case of single porosity to the case of double porosity. Then a general finite element formulation of the relevant eqations is thoroughly discussed and explicitly described for the two‐dimensional case where four‐node rectangular non‐conforming isoparametric elements are employed. Three numerical examples are presented in detail to illustrate the method and assess the differences between single and double porosity models in consolidation.
Rapid expansion of a cylindrical cavity in a rate‐type soil
Authors: Davis R. O. , Scott R. F. , Mullenger G.
Published: August 2005

An analytical solution for rapid (undrained) expansion of a long cylindrical cavity from initially zero radius is presented. A simple rate‐type soil model possessing the salient features of the modified Cambridge critical state model is used. Application of the solution to determination of the stress field surrounding a pile immediately after driving is discussed.
Induced anisotropy during plastic straining
Authors: Baker R. , Desai C. S.
Published: August 2005

The restrictions imposed by the form‐invariance principle on the structure of the elasto‐plastic constitutive law for small strains are examined. It is shown that the yield and plastic potential functions may depend on the joint invariants of the stress and plastic strain tensors in addition to their dependence on the direct invariants of these tensors and additional scalar hardening parameters such as the plastic work; inclusion of the joint invariants as parameters in the constitutive functions allows for induced anisotropy during plastic deformation. It is demonstrated that the physical meaning of the joint invariants is related to the deviation of the principal directions of the stress tensor from those of the plastic strain tensor. It is also shown that only three cases of anisotropy (orthorhombic, transverse and isotropy) are possible in the types of material models discussed herein. The model proposed in this paper does not imply coaxiality between the principal directions of the stress and, plastic strain increment tensors; however, implications of the assumption of coaxiality on the structure of the constitutive equations is investigated. It is shown that coaxiality does not necessarily imply isotropy, but no deviations from coaxiality can be expected in isotropic materials.
A stochastic model of soil erosion
Authors: Mossaad Mostafa E. , Wu Tien H.
Published: August 2005

The erosion model computes the rill and inter‐rill flow over a surface with random roughness, and the erosion caused by this flow. The measured roughness of a surface is analysed and used to generate random surfaces for the simulation process. Computations are carried out over a number of time intervals; the steady state condition is assumed for each interval. Changes in the surface geometry due to erosion during an interval are used to revise the surface for the subsequent interval. The model includes simplified mechanisms to simulate ponding, deposition and failure of side slopes of rills.
A finite element formulation for brine transport in rock salt
Authors: Ratigan J. L.
Published: August 2005

A set of coupled field equations is developed for transport of liquid brine in natural rock salt. The natural rock salt consists of individual crystals brought together so that only a portion of the crystal faces or grain boundaries contribute to the hydraulically connected pore space. Transport of brine inclusions within individual crystals is considered to be thermally driven; whereas transport along crystal interfaces or grain boundaries is considered to be pressure driven. The field equations for both transport mechanisms are developed and incorporated in a finite element program. An analytical solution to a one‐dimensional boundary value problem is derived and compared to the finite element solution. An application of the finite element code to radioactive waste emplacement is briefly discussed.
Slippage and re‐initiation of (hydraulic) fractures at frictional interfaces
Authors: Lam K. Y. , Cleary M. P.
Published: August 2005

The analysis of mechanisms which could control the growth of fractures in non‐homogeneous regions is of paramount importance. One such mechanism is the behavior of the fracture as it reaches a frictional interface; coupled with this is the question of re‐initiation, e.g. whether a fracture can be contained within the region of initiation. Though the problems of slippage have been dealt with by other investigators, the present paper gives a more comprehensive picture and detailed treatment: effects of various frictional models at an interface are considered for a crack which intersects it at any angle; specialization then allows comparison with existing results in the literature.

The problem of re‐initiation, after slippage has occurred at a frictional interface, is also considered, using two different models. First, by introducing microcracks in the adjacent stratum and looking at the effects on propagation criteria and, secondly, by examining the actual distribution of the stress tangential to the slip surface; detailed computations are performed and a simple criterion for re‐initiation is given, relating the re‐initiation stress dominantly to the confining stress on the interface.
Dynamic response analysis of embankment dams
Authors: Chugh Ashok K.
Published: August 2005

A one‐dimensional wave propagation method for earthquake response analysis of horizontally‐layered sites of infinite lateral extent is adapted to account for the finite cross‐sectional dimensions of an embankment dam overlying a foundation deposit which may be considered infinite in its lateral extent. The procedure is used to study the response of an existing embankment dam for an actual earthquake record. A two‐dimensional dynamic finite element analysis is also performed for this case. The records of ground acceleration at an outcropping base rock and at the crest of the dam are available for the site. The comparisons of computed and observed responses support the modified use of the simple numerical procedure.
Special finite elements for analysis of soil consolidation
Authors: Sandhu Ranbir S. , Lee Shyan Chyun , The Hwie‐Ing
Published: August 2005

Use of “singularity” elements to model pore pressures in the vicinity of free‐draining loaded surfaces, immediately after application of loads at these surfaces is discussed. One‐dimensional consolidation is considered. Comparison of numerical results with the exact solution shows that use of specially designed elements approaching “singularity” may succeed in reducing the error in pore pressures.
Singularity elements for seepage analysis
Authors: Aalto J.
Published: August 2005

A technique for locating the nodal points of standard isoparametric quadrilateral elements properly around a discharge velocity singularity point in a soil seepage flow problem is presented. It is based on the analytical solution of the problem in an infinite medium and gives simple formulae for calculating the nodal coordinates. The effectiveness of the method is justified with examples.
Three dimensional analysis of slope stability
Authors: Leshchinsky D. , Baker R. , Silver M. L.
Published: August 2005

A 3‐D mathematical approach to slope stability, which is based on limiting equilibrium and variational analysis, is presented. In the initial formulation there are three unknown functions: the slip surface, the normal stress and the shear stress direction over this surface. The minimum factor of safety is sought through variational extremization. The analysis indicates that the factor of safety is independent of the normal stress distribution over the critical slip surface. It also indicates that the direction of the elementary shear force over the slip surface depends on the slip surface function, but not on the normal stress function. The analysis yields a non‐linear first order partial differential equation, relating the slip surface and its first partial derivatives. By limiting the analysis to symmetrical problems an ordinary differential equation, governing the slip surface path on the plane of symmetry, is derived. This equation enables the development of a numerical procedure to determine the minimal factor of safety of symmetrical 3‐D slopes. Two possible failure modes are determined for homogeneous slopes. One mode consists of finite 3‐D sliding body and the second represents cylindrical failure. Numerical analyses for some simple cases, of homogencous slopes are presented.
Computing costs for FEM analysis of foundation engineering problems and possible ways of increasing efficiency
Authors: Schad Hermann
Published: August 2005

The application of finite element methods (FEM) is often restricted by the available computer capacity and the computing costs. The purpose of this paper, therefore, is, to present test results and to discuss possible ways of achieving a substantial reduction in computing times. Dividing the numerical analysis into the five levels–hardware, software, element‐mesh and element‐type, iteration technique (approximation of non‐linearity) and constitutive model–one can show that the computing time can be reduced by about 20 per cent at every level. In particular, the use of the modified Newton‐Raphson method for approximation of non‐linearity and the constitutive model–apart from the theoretical concept (elastoplastic, hypoelastic etc.)—must be formulated in a manner which does not produce substantial changes in the coefficients of the material matrix caused by small stress changes. On the whole, computing time can be reduced to about 10 per cent of present computing costs. Thus, it would even be economically viable to solve three‐dimensional non‐linear problems by FEM.
On the choice of elastic parameters for sand
Authors: Loret B.
Published: August 2005

When soils are considered as elastoplastic materials the elastic moduli are much higher than the plastic one(s). However the amount of elastic strain cannot be disregarded as it appears when undrained loading occurs. Based on experimental or theoretical observations, a number of elastic models with stress dependent moduli have been proposed. Attention is focused here on the consequences of this stress dependency on the recoverability of strain and work done after a closed stress path. A necessary and sufficient condition for an elastic material to be hyperelastic is given and the way to obtain practical solutions is shown on examples. The study is restricted to isotropic material undergoing small strains.
The behaviour of an elastic non‐homogeneous half‐space. Part I‐line and point loads
Authors: Booker J. R. , Balaam N. P. , Davis E. H.
Published: August 2005

In the first part of this paper solutions are developed for the response of a non‐homogeneous half‐space subjected to either a surface point load or a surface line load. The non‐homogeneity considered is a variation in Young's modulus (E) with depth (z) which takes the form E=mEZα where mE is a constant and α is referred to as the non‐homogeneity parameter.

The variation of these solutions as the non‐homogeneity parameter α varies between the limits of zero (homogeneous soil) to unity (Gibson soil) gives some fresh insight into both these limiting cases.
The behaviour of an elastic non‐homogeneous half‐space. Part II–circular and strip footings
Authors: Booker J. R. , Balaam N. P. , Davis E. H.
Published: August 2005

Solutions developed in the first part of this paper (i.e. describing the response of a non‐homogeneous half‐space subjected to surface point and line loads) are used in this part to obtain solutions for a variety of surface loadings. Consideration is given to a distributed load acting over a circular area or strip and a rigid disk or strip subjected to applied normal load and moment.

It is established that the profiles of surface settlement due to uniformly distributed loads acting over a strip or circular area are strongly dependent on the degree of non‐homogeneity. This dependency is reduced when the footing is rigid. When α = 1 the moduli variation is identical to the Gibson soil and the equivalence with the Winkler soil model is established.
Analysis of dynamic behaviour of piles
Authors: Chow Y. K.
Published: August 2005

The finite element approach has been used to derive element matrices suitable for the analysis of the dynamic behaviour of piles. Using this method, piles with arbitrary cross‐section and soil with nonhomogeneous properties can be dealt with.
Modelling two‐dimensional heat and moisture transfer in unsaturated soils, including gravity effects
Authors: Thomas H. R.
Published: August 2005

A theoretical model is presented to predict simultaneous transient coupled heat and moisture transfer in partly saturated soils. The formulation is in terms of volumetric moisture content, is two dimensional, includes gravitational flow and takes into account latent heat of vaporization effects. The numerical solution of the problem is accomplished by means of a finite element solution algorithm. Predictions from the numerical model are used to investigate the importance of gravitational flow, for the case of a soil stratum subjected to evaporation losses at the surface. The results achieved show good qualitative agreement with expected behaviour.
Finite layer analysis of viscoelastic layered materials
Authors: Booker J. R. , Small J. C.
Published: August 2005

A method is presented for obtaining the creep settlement of strip or circular loadings applied to horizontally layered soil profiles. The solution method involves applying a fourier (strip loading) or Hankel (circular loading) transform to the governing equations, which reduces the two of three dimensional problem to one involving a single spatial demension. This leads to great savings in computer storage and data preparation time, and since an exact solution may be found for each layer of material, the method has advantages over conventional finite layer techniques where field quantities must be approximated at a number of positions within each layer.

The type of formulation presented hearein makies it possible to work in terms of the creep functions of the soil rather than the relaxation functions. This has distinct advantages, as it is often easier to measure the creep behaviour of a soil in the laboratory.

Numerical techniques are used to invert the laplace and Hankel transforms and this means that any type of creep function (which is invertible) may be used to describe the material properties of the soil.
Time dependence of axial pile response
Authors: Murff J. D. , Schapery R. A.
Published: August 2005

This communication describes an approximate method for generalizing homogeneous, linearly elastic, subgrade type solutions of axial pile response to account for soil creep behaviour. The method is very simple to apply and can be used in conjunction with either analytical or numerical elastic solutions. Exact solutions for limiting cases and finite difference solutions in both space and time are presented to confirm that errors introduced by the approximations are small. Because of the theoretical basis of this approach it is anticipated that method can be used with other pile problems, lateral and axial, for both subgrade adn continuum idealizations. Methods for generalizing the results to more complex conditions such as non‐homogeneity or time varying loads are given.
The behaviour of layered soil or rock containing a decaying heat source
Authors: Small J. C. , Booker J. R.
Published: August 2005

Solutions are presented for the behaviour of layered soil or rock deposits which contain a heat source. Such a problem arises when high level nuclear waste is placed in deep underground depositaries, as the waste continues to generate heat for many years after placement. This heating of the surrounding soil or rock may lead to expansion and cracking with subsequent contamination of ground water. Results are presented for heat soureces with different decay rates and for heat sources in layers of material with different coefficients of expansion. An example using realistic data for rock is also given.

The solution method involves applying Fourier or Hankel transforms to the field quantities and this reduces the two‐dimensional or axisymmetric problem to one involving a single spatial dimension. In cases where the soil or rock is horizontally layered, the method has great advantages over other numerical methods such as finite element or finite difference techniques, since little computer storage and data preparation time is required.

Solution of the time‐dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical means to invert the transformed solutions. This enables easy solution of problems involving time‐dependent (i.e. decaying) heat sources.
Primary potentials in cylindrical electro‐osmotic cells
Authors: Banerjee Sunirmal
Published: August 2005

A review of literature reveals that regardless of the configuration of electro‐osmotic cells, all previous laboratory investigations and interpretations have been based on the assumption of a constant potential gradient in the specimen. Appropriate solutions for electrical potentials for cylindrical cells are presented in this paper.
Interaction between jack‐up rig foundations and offshore platform piles
Authors: Chow Y. K.
Published: August 2005

This paper presents a study of the interaction between the foundations of a jack‐up rig and the pile foundations of an adjacent steel offshore platform. Parametric solutions are presented to evaluate the effect of the rig footing load on the performance of the pile foundation. Homogeneous and non‐homogeneous soil conditions have been considered. An example is used to illustrate the application of the solutions in a practical problem.
Optimal estimation of in‐situ ground stresses from displacement measurements
Authors: Feng Z. L. , Lewis R. W.
Published: August 2005

This paper presents a study on the optimal estimation of initial in‐situ stresses, in which the in‐situ stresses may be constant or linearly changing along a co‐ordinate axis, from a set of relative measurements between adjacent measuring points utilized for monitoring the stability of tunnels. Displacements occurring before installation of measuring devices can be taken into account. The approach may be used for a variety of models used to simulate the ground media through which the tunnels are being excavated and has the advantage of being easy to implement on the computer and having both good precision and calculation stability. Finally, an analysis is carried out on the stability of the algorithm and computational time for different numerical examples.
A nonlinear analysis of two‐dimensional heat and moisture transfer in partly saturated soil
Authors: Thomas H. R.
Published: August 2005

The subject of this paper is the nonlinear analysis of heat and moisture transfer in partly saturated soil. In particular, an extension of the previous work of the author to two‐dimensional applications is presented. Problems of greater complexity and engineering significance can hence be solved. The theoretical basis of the problem is first outlined before the two‐dimensional formulation of the numerical solution is given. The finite element method is employed to give the spatial distributions of the variables, with a finite difference scheme being used to predict the temporal variations. The method allows the nonlinear nature of the soil parameters to be modelled, predictions being given of the coupled transient simultaneous transfer of heat and volumetric moisture content. The two‐dimensional nature of the work is illustrated for the case of surface evaporative soil moisture losses from sloping ground. Subsoil conditions of a uniform deposit of loam are considered with values of representative material parameters assumed after a literature search. The coupled nature of heat and mass transfer is illustrated by means of an analysis of the moisture migration patterns that occur. Two‐dimensional moisture flow, out of and into the soil, is shown to take place.
A large strain theory and its application in the analysis of the cone penetration mechanism
Authors: Kiousis Panos D. , Voyiadjis George Z. , Tumay Mehmet T.
Published: August 2005

A computational method, based on an advanced elasto‐plastic large strain formulation, well suited for the analysis of the cone penetration problem, is presented.

A new approach of finite strain elasto‐plastic analysis is employed.13 The basic (non‐rate) constitutive relations are developed in a spatial reference space to preserve their physical significance. They are subsequently transformed in Lagrangian co‐ordinates, and through simple time differentiation, their rate equations are introduced. The method is computationally implemented with the finite element method and special provisions are taken to allow for the moving boundary conditions of the problem.
A semi‐analytical solution for swelling around a borehole
Authors: Carter J. P.
Published: August 2005

Previous field and laboratory studies have shown that the creation of a borehole in a saturated cohesive soil mass induces significant pore water suctions in the vicinity of the hole. The dissipation of these pore water suctions (swelling) leads to local increases in the moisture content and hence a softening of the soil around the hole. This softening may have important consequences for the stability of the hole and also for the ultimate load capacity of any foundation elements (bored piles or drilled shafts) constructed in these holes. This paper presents a semi‐analytical solution for the radial dissipation of pore water pressure around a freshly created, vertical hole. It is assumed the soil deforms elastically during the swelling process. The solutions are presented in the form of isochrones of excess pore water pressure and may be used to obtain estimates of the time required for the soil around the hole to swell and therefore to soften. Both permeable and impermeable borehole interfaces have been considered, together with either no support for the hole or partial support provided by hydrostatic pressure within the hole.
The analysis of consolidation by a quasi‐Newton technique
Authors: Borja Ronaldo I.
Published: August 2005

A quasi‐Newton algorithm is implemented for the solution of multi‐dimensional, linear consolidation problems. The study is motivated by the need to implement an efficient equation‐solving technique for the solution of large systems of equations typical in problems of consolidation of saturated porous media. The proposed procedure obviates the need to reassemble and re‐factorize the global coefficient matrix every load increment, albeit the time step may be held variable in the analysis. The method employs the combined techniques of ‘line search’ and BFGS updates applied to the coupled equations. A numerical example is presented to show that the proposed method is computationally more efficient than the conventional direct equation‐solving scheme, particularly when solving large systems of finite element equations.
Pollutant migration from deeply buried repositories
Authors: Rahman M. S. , Booker J. R.
Published: August 2005

Semi‐analytic solutions are developed for the migration of pollutants from cylindrical and spherical repositories buried deep in a homogeneous and isotropic soil in the presence of a uniform and unidirectional advection. The techniques adopted involves taking the Laplace transform of the governing equations, finding an analytic solution in transform space and then numerically inverting the transform to obtain the concentrations of the contaminants at selected positions and times. Numerical results are presented, and practical implications discussed.
A numerical and laboratory investigation into the behaviour of a dry underclay beam
Authors: Afrouz A. , Hassani F. P.
Published: August 2005

A simple and inexpensive laboratory device has been developed and used to simulate the behaviour of a dry underclay beam as the floor of an underground roadway subjected to a uniformly distributed uplift pressure. The Airy stress function method proved to be a useful means of expressing and predicting of the uplift of such beams. This method has been related to both classical beam theory and laboratory investigations. It was found that the Airy stress function method, utilizing polynomial equations, provides a closer fit to the mechanism of beam deformation and stress developments under dry laboratory conditions.
Use of the finite element method in modelling a static earth pressure problem
Authors: Bhatia S. K. , Bakeer R. M.
Published: August 2005

Results obtained with the finite element method are greatly affected by the overall dimensions of the mesh and the number and size of the elements used. Proper choice of the boundary conditions is also necessary to obtain an accurate estimate of the unknowns of the problem. This paper discusses some factors that influence the results of a finite element idealization of the problem of earth pressure behind a gravity wall with a dry, cohesionless backfill.
Initial moduli of particulated mass with frictional contacts
Authors: Chang Ching S. , Sundaram Sivanuja S. , Misra Anil
Published: August 2005

The stiffness characteristics of a packing of granules are influenced by the particle interactions at contacts, the void ratio, the co‐ordination number and the packing structure. A stress‐strain relationship for the packings of spheres is presented. The relationship explicitly includes the contact force‐displacement law and the parameters characterizing the packing structure. The initial moduli computed using this relationship are compared with experimental measurements and empirical equations for sands. The theoretical results are also compared with experimental results on packings of glass balls. Closed‐form solutions are derived for statistically isotropic packings under initial isotropic stress conditions. Numerical solutions for the stiffness properties are obtained for anisotropic initial stress conditions and anisotropic packing structures.
Formulation and application of element methods in the simulation of pressure and temperature history of geological basins
Authors: Søreng Jan
Published: August 2005

A mathematical model treating the compaction of sediments in geological basins is derived. The model is based on the principle of conservation of mass and energy, and gives a consistent and complete set of equations for compaction, pressure and temperature history of sedimentary basins.

Further, the paper describes a numerical model based on the mathematical equations, derived by using the finite element method. This derivation starts with the time‐discretized versions of the conservation laws of mass and energy. The result is the time‐discretized equations for pressure and temperature. The numerical derivation is parallel with the mathematical deductions. By integrating these time‐discretized equations spatially the element equations are obtained. Hence, the element equations are derived directly from the underlying physical laws. This approach to developing element equations in a compacting medium is believed to be new. The model has been tested successfully on some geological basins, and the results of a simulation are included at the end of the paper.
Comparison of laplace transform and finite difference solutions for an evolving permafrost region
Authors: Morland L. W. , Kelly R. J.
Published: August 2005

Laplace transform solutions are derived for an evolving permafrost region in saturated ground when the freezing interface moves with constant speed. The solution is inverse in the sense that the melting temperature at the interface and the groud surface temperature are prescribed functions of time. The solution procedure incorporates an initial temperature distribution in a domain extended above the ground surface. This allows, by asymptotic analysis, the construction of initially continuous melting and surface temperatures with bounded first and second derivatives. Solutions for two classes of initial conditions are determined by numerical inversion of the transforms. These solutions are used to test the corresponding solutions obtained by a direct finite difference algorithm developed earlier.1 Good agreements for both interface path and temperature profiles are obtained in both classes.
In‐plane vibrations of soil deposits with variable shear modulus: II. Line load
Authors: Vrettos Ch.
Published: August 2005

The dynamic response of an inhomogeneous, linear‐elastic half‐space to a time‐harmonic vertical line load on its surface is studied. The mass density and the Poisson's ratio are assumed to be constant and the shear modulus to increase continuously with depth according to a function which is bounded at infinity. This model can describe a wide range of uniformly deposited soil strata. Analytical solutions for the displacement field at the surface are obtained using the classical contour integration method by means of the residue theorem. The dependence of the displacement field on distance from the source, frequency and shear modulus variation is examined as well as the relative contribution of the higher surface wave vibration modes to the total displacement.
3D‐boundary element analysis of the lowered groundwater level for tunnels driven under compressed air
Authors: Chen Z. S. , Hofstetter G. , Mang H. A.
Published: August 2005

A direct boundary element method for the iterative analysis of the lowered groundwater level and the steady‐state airflow in porous soil for tunnels driven under compressed air is presented. The soil may be zoned and anisotropic. It is shown that disregard of the compressibility of the air leads to results for the excess air pressure and the flow of air through the surface of the soil, which are on the unsafe side. The lowered groundwater level is determined by means of an iterative procedure. During the iteration large changes of the shapes of boundary elements may occur. In order to reduce the resulting danger of divergence of the iteration, the boundary element mesh is adapted suitably in the course of the iteration process.
Computer‐aided calibration of a soil plasticity model
Authors: Anandarajah A. , Agarwal D.
Published: August 2005

A non‐linear optimization technique based on the quasi‐Newton approach is employed to back‐calculate certain model parameters of a simple, bounding surface, soil plasticity model from in situ pressuremeter data. The theoretical response corresponding to a given set of parameters is generated by finite element analysis. A semi‐analytical procedure is developed for the accurate and efficient evaluation of the gradient of objective function with respect to the model parameters of interest. The BFGS update is used to update the Hessian. Results of a series of numerical experimentation using artificial pressuremeter responses is first reported and discussed. A set of laboratory cavity expansion data is then used to calibrate the constitutive model.
Consolidation of clays subjected to three‐dimensional embankment loadings
Authors: Small J. C. , Zhang B. Q.
Published: August 2005

A Fourier transform technique is presented which may be used to analyse three‐dimensional consolidation problems for soils which are loaded by embankment shaped loadings that are rectangular in plan (or of arbitrary shape which can be divided into rectangles in plan). The introduction of a Fourier transform effectively reduces the three‐dimensional problem to one involving only two spatial dimensions and this reduces computer storage and saves computing and data preparation time. The material properties of the soil may vary arbitrarily in the plane which is perpendicular to the axis associated with the variable eliminated during the Fourier transform. Solutions obtained using the method are compared with existing solutions in order to verify the theory and assess accuracy, and illustrative examples are given for problems involving the consolidation of soils under embankment loadings.
Subsidence due to pumping from layered soil—a perturbation theory
Authors: Fallou S. N. , Mei C. C. , Lee C. K.
Published: August 2005

Persistent pumping of groundwater is known to cause subsidence of the ground surface. When the soil is composed of alternating layers of sand and clay, subsidence is, in general, a consequence of pressure change in and deformation of all layers. Even with various simplifications, the mathematical task for the mechanics of a layered soil is complex and, in the past, many idealizations have been introduced in the literature. Among the existing approximations, a well‐known approximation by Hantush1 for well‐hydraulics in leaky aquifers is intuitively attractive. He used the fact known to be strictly true for simple flows in a soil system with horizontal layers, that the flow must be mainly horizontal in a relatively porous aquifer and mainly vertical in a highly impervious aquitard, and invoked the same approximation for transient flows induced by well‐pumping. In this paper we shall apply a perturbation analysis to give a mathematical confirmation of the hydrological approximation and to show its degree of accuracy. In particular, we treat a three‐layered system, where the middle layer is a relatively soft aquitard, and the well withdraws water from the artesian aquifer at the bottom. The upper aquifer has a phreatic surface. Physically, we examine the often ignored effects of self‐weight which is important for thick aquitards. The perturbation theory is worked out for sufficiently weak pumping rates and small soil deformation. Subsidence in the vertical direction due mainly to the deformation of the soft aquitard is studied. Results show that the common assumption of constant total stress with respect to depth is valid only when the storage coefficient is very small.
Modelling of vibratory pile driving in sand
Authors: Wong Daniel , O'Neill Michael W. , Vipulanandan C.
Published: August 2005

A model for vibro‐driving of rigid piles in sand is proposed incorporating the interaction of the vibrator–pile–soil system. The vibro‐driver force and the non‐linear soil resistance (dynamic f–w and q–w relationships) have been quantified in terms ofin situstress, relative density and particle size. The influence of relative density (0·65 and 0·90), particle size (effective grain size of 0·2 mm and 1·2 mm) and in situ stress (up to 20 psi) on the vibro‐driving of a closed‐ended pipe pile was investigated experimentally using a large‐scale laboratory testing system. The vibro‐driving model predicted the observed driving history reasonably well. A computer program (UHVIBRO) has been developed to analyse vibratory pile driving using the dynamic soil resistance relationships developed along with correlation factors from the systematic laboratory study.
A consistent formulation of a dilatant interface element
Authors: Snyman M. F. , Martin J. B.
Published: August 2005

The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. The element is intended to model discontinuities with rough contact surfaces, such as rock joints, where dilatant behaviour is present. Of particular concern is the formulation of a constitutive model which fully caters for all possible histories of opening, closing and sliding (accompained by dilation or contraction) in any direction.

The non‐linear incremental constitutive equations are formulated in a manner appropriate for a back‐ward difference discretization in time along the path of loading. The advantage of such an approach is that no essential distinction need be drawn between opening, closing and sliding. Further, a convenient formulation of the constitutive equations is facilitated by representing the different contact conditions in relative displacement space. The state diagram in relative displacement space, however, changes from one time step to the next, and evolution equations for the updating must be formulated.

These concepts are illustrated for two rock‐joint models: a sawtooth asperity model and a limited dilation model. The models are based on a penalty formulation to enforce the contact constraints, and explicit equations for the tangent stiffness matrix and for the corrector step of the standard Newton–Raphson iterative algorithm are derived. These equations have been implemented as an user element into the finite element code ABAQUS7. Three examples are presented to illustrate the predictions of the formulation.
A finite element slideline approach for calculating tunnel response in jointed rock
Authors: Schwer Leonard E. , Lindberg Herbert E.
Published: August 2005

The general purpose finite element code DYNA2D is used to calculate the response of an unlined tunnel in jointed rock, with sliding interfaces used to represent the joints. The model problem selected for analysis closely follows a calculation using the discrete element code UDEC. Results for two cases [(1) jointed rock with lubricated joints (no joint friction) and (2) jointed rock with frictional resistance to joint motion] are presented and compared with each other and the UDEC results.
Analytical influence functions for displacement discontinuity and point force elements
Authors: Chan H. C. M.
Published: August 2005

The analytical influence functions for the elements of a hybridized displacement discontinuity and indirect boundary element method to model fracture propagation are presented. The influence functions are exact and in closed form and, thus, have significant advantages over their numerical counterparts.
Three‐dimensional modelling of junctions at the Channel Tunnel project
Authors: Pöttler R.
Published: August 2005

The present paper deals with a three‐dimensional FE analysis for the Channel Tunnel project. The main objective is to describe the application and the results of a FE calculation and the impact of it's results on engineering practice especially on the design of the permanent lining. The tunnel excavation was executed in accordance with the principles of the shotcrete tunnelling method (NATM). The paper represents a report from the practical engineer's point of view.
Coupled heat and mass transfer in unsaturated soil—a potential‐based solution
Authors: Thomas H. R. , King S. D.
Published: August 2005

An analysis of coupled heat and moisture movement in unsaturated soil in terms of the fundamental potentials for flow is examined. The approach adopted is based on the assumption that the total potential for liquid flow consists of two components, the elevation and the capillary potential. The fundamental potentials employed in the work are, therefore, temperature and capillary potential.

The full theoretical formulation of the problem is presented, together with full details of the solution algorithm employed. Spatial discretization is achieved via the use of the finite element method, with the time‐varying behaviour described by a finite difference technique. Soil parameter variations as functions of both temperature and moisture content are included in a one‐dimensional approach.

The work is applied to a practical engineering problem, namely heat and mass transfer in the upper layers of a soil stratum. This problem is of importance to the utilities, since many services are buried in this zone. Material parameters obtained from an associated programme of experimental work are employed. Moisture content and temperature profiles indicating the extent and rate of penetration of drying and heating fronts are produced.
A virtual surface concept for nested yield surface plasticity
Authors: Salah‐Mars Said , Kavazanjian Edward
Published: August 2005

A return mapping algorithm based on the concept of virtual surfaces is presented for stress integration in the numerical solution of boundary value problems using an elastoplastic multiple yield surface model. Both kinematic hardening and isotropic softening yield surfaces are addressed. With the implementation of virtual surfaces, the active yield surface is located before a stress update is implemented. The return mapping algorithm consists of only two steps. The first step consists of performing the intermediate update of the trial stress corresponding to the translation of all yield surfaces inside the active yield surface. Little calculation is involved in this step. The second step consists of performing the conventional explicit one‐step radial return mapping of the updated trial stress on the corresponding active yield surface. The algorithm efficiency resides in the virtual surface based return mapping which preserves the elastic predictor representation of the updated trial stress, and limits iterations to at most two steps.
A study on one‐dimensional consolidation of layered systems
Authors: Lee P. K. K. , Xie K. H. , Cheung Y. K.
Published: August 2005

A general analytical solution, which is more explicit than the one given by Schiffman and Stein,1 for the problem of one‐dimensional consolidation of layered soils is presented. A relevant computer program is developed and the computed results on some examples are included. From these results, an in‐depth study on the one‐dimensional consolidation behaviour of layered systems is then made. It is demonstrated through these examples that both the solution technique and the computer program developed are very efficient. It is found that the effects of coefficients of permeability and volume compressibility of soil on the consolidation of layered systems are different and cannot be embodied into the coefficient of consolidation of soil. The stiffness of soil layer also plays an important role on the rate of consolidation.