bluuebunny/crossref_metadata_2025 huggingface dataset:
Rheological analysis of tunnel excavations by means of coupled finite element (FEM)–boundary element (BEM) analysis
Authors: Swoboda G. , Mertz W. , Beer G.
Published: August 2005

To facilitate the practical numerical analysis of tunnel structures by means of the finite element method in the case of viscoplastic properties of the rock mass and viscoelastic properties of the shotcrete, this method is coupled to boundary elements. In this way, the unchanged properties of the boundary element region provide enormous savings in computing time. In order to improve the numerical stability of such calculations, a variable time‐step analysis was employed for each time step with an iterative correction method. Characteristic values are obtained from measured values by back‐analysis.
Heat extraction through a geothermal reservoir on an oblique fault plane
Authors: Shibuya Y. , Sekine H. , Takahashi Y.
Published: August 2005

The heat extraction through a geothermal reservoir on an oblique fault plane in the earth's crust is considered. The fault could be modelled mechanically as a frictional contact interface of two elastic bodies. The heat is recovered by circulating fluid through the reservoir, and then the surface of the reservoir is cooled by the fluid. The analysis is based on the two‐dimensional theory of quasi‐static thermoelasticity. It is concluded from numerical calculations that a geothermal reservoir can be created on an oblique fault plane, and the opened region, i.e. the fluid‐filled region, increases gradually with time during the heat extraction. Also discussed are the effects of the fluid pressure and the coefficient of friction on the behaviour of the reservoir.
Wave‐induced displacements in seafloor sands
Authors: Siddharthan R.
Published: August 2005

The stability and deformation of the seafloor in response to storm wave loading is an important consideration in the design of pipelines, anchors, and offshore structures such as gravity‐and pile‐supported platforms. Two quite different approaches have been proposed for investigating the effects of storm waves on seafloor sands. These approaches derive from quite different considerations of soil‐water interaction.

In one of these approaches (exemplified by Yamamoto and Madsen) the seafloor is visualized to be a porous elastic or Coulomb‐damped porous nonlinear medium. In this approach, the response of the seafloor, i.e. the displacements, stresses and porewater pressures, are computed for a given wave. The response is transient and is, therefore, related to the largest wave in the storm wave group.

On the other hand, in the approach proposed by Seed and Rahman, only the development of residual porewater pressures (for estimating liquefaction potential) due to the storm wave group are considered. The effects of transient porewater pressures and stresses on the seafloor sands are ignored. The residual porewater pressures are computed using properties based on initial effective stresses through a porewater generation‐dissipation model.

The application of these techniques to problems of offshore structures such as pile‐supported platforms has led to considerable uncertainty and confusion. In this paper, both of these approaches are combined to investigate seafloor response to a storm wave group. For typical storm wave conditions that exist in the North Sea, it appears that the inclusion of damping, inertia and anisotropic permeabilities in the study is not important relative to ocean sands. Parametric studies show that, for a given wave, the thickness and the stiffness properties of the soil deposit dictate the response of the deposit. The displacements in the deposit are, therefore, affected by the generation of residual porewater pressures.
Expansion of cavities in layered elastic system
Authors: Sayed S. M. , Hamed M. A.
Published: August 2005

Theoretical formulations to the problem of expansion of spherical and cylindrical cavities in a layered elastic system are presented. The medium surrounding the cavity is assumed to consist of several layers, and each is idealized as a linear elastic solid. The solutions are expressed in matrix forms and can be obtained using a programmable calculator. The developed solutions are of some importance in geomechanics. The spherical cavity solution can be used to compute the settlement of single axially loaded piles. The predicted settlement using the analysis outlined herein agrees reasonably well with one case of field measurements. The cylindrical cavity solution can be used to manifest the effect of disturbed mass at the cavity wall on the stress–strain and deformation characteristics of the intact mass.
The time–deflection behaviour of a rigid under‐reamed anchor in a deep clay layer
Authors: Small J. C. , Booker J. R.
Published: August 2005

The behaviour of an under‐reamed anchor in a consolidating soil is examined by approximating the anchor as an impermeable circular plate embedded in a deep soil layer. Hankel and Laplace transforms are applied to the equations governing the consolidation process, and this greatly simplifies the equations, allowing a solution to be obtained for the transformed variables. Numerical inversion of both the Hankel and Laplace transforms is used to obtain the solution at any time.

A particular feature of the solution method is that the unknown contact stress between the anchor and the soil and the unknown flows in the plane of the anchor are approximated as a series of simple functions with unknown coefficients. By determining the coefficients of the terms in the series, the complete solution may be found.

Computations have been carried out using the method proposed, and results are presented for the time–settlement behaviour of an impermeable anchor. These results are compared with some published and some recomputed finite element data, and this highlights some of the difficulties encountered in using such numerical techniques.
Implicit integration of elastoplastic relations with reference to soils
Authors: Runesson Kenneth
Published: August 2005

The stress solution in plasticity with an associated or a non‐associated flow rule is considered. Upon fully implicit integration of the relevant constitutive relations the stress is obtained as the projection of the (fictitious) elastic stress onto the yield surface for given values of the hardening softening variables. This projection is defined, for a general non‐associated flow rule, in adjusted complementary elastic energy, which becomes exactly the complementary energy when the flow rule is associated.

Isotropic elasticity and mean‐stress dependent isotropic yield criteria (pertinent to soil) are considered and the implications of a certain class of non‐associated flow rules are evaluated. This class relates to dilatant (or contractant) materials and involves non‐associated plastic volume change. The corresponding stress solutions are shown to be strongly influenced by Poisson's ratio and by the dilation angle.
A boundary element solution to land subsidence above 3‐D gas/oil reservoirs
Authors: Gambolati Giuseppe , Sartoretto Flavio , Rinaldo Andrea , Ricceri Giuseppe
Published: August 2005

A linear boundary element (BE) model is proposed for the uncoupied simulation of land subsidence due to gas, oil and hot water production over three‐dimensional (3‐D) arbitrarily shaped reservoirs. The pore pressure decline is assumed to be specified in advance, e.g. via a numerical model of flow. Use is made of the fundamental solution derived in 1885 by Boussinesq for a vertical load acting upon the traction‐free surface of a semi‐infinite medium. A straightforward application of Betti's (1872) reciprocal theorem allows for the development of a boundary integral whose numerical execution yields directly the downward settlement over the point of interest.

The new procedure is applied to assess land sinking caused by an uniform pore pressure decline occurring within fields of elliptical shape and to explore the influence of the assumption of small reservoir thickness which underlies the ‘tension center’ or ‘strain nucleus’ approach previously developed by Geertsma in 1966. The results emphasize the numerical efficiency of the solution and the promising features of the BE method for the evaluation of ground subsidence in 3‐D problems.

The present model is based on the theory of the linear poroelasticity and is implemented for a mechanically homogeneous and isotropic half‐space. It allows for any arbitrary geometry of the reservoir and for a non‐uniform distribution of the pore pressure decline. It may easily be extended to other physical settings for which a vertical surface point load solution is available.
An elastoplastic constitutive model for cyclic behaviour of sands
Authors: Hirai Hiroyoshi
Published: August 2005

The constitutive model of sands is proposed to describe the characteristics of plastic behaviour for cyclic loadings. A non‐associated flow rule is used and both yield function and plastic potential are generalized forms of the Modified Cam clay model. The hardening parameter is represented by the plastic work related to different portions of volumetric and deviatoric changes. The boundary surface is employed to describe the plastic strain within the yield surface. The directional independency of yield condition in triaxial compression and extension tests is extended to that in general stress states. Several drained and undrained cyclic tests are predicted and the comparison is made with experimental results. The proposed model is capable of representing the monotonic and cyclic behaviours of sands with reasonable accuracy. The simulation is performed for both included and excluded membrane penetration effects and it is suggested that the membrane penetration causes the significant influences on the results of undrained cyclic tests.
Modelling the elastic behaviour of granular materials
Authors: Lade Poul V. , Nelson Richard B.
Published: August 2005

A review of the literature indicates that the elastic behaviour of granular materials is isotropic and that Poissony's ratio is constant, whereas Young's Modulus, the bulk modulus and the shear modulus vary with the mean normal stress and the deviatoric stress. A nonlinear, isotropic model for the elastic behaviour is developed on the basis of theoretical considerations involving the principle of conservation of energy. Energy is therefore neither generated not dissipated in closed‐loop stress paths or in closed‐loop strain paths. The framework for the model consists of Hooke's law, in which Poission's ratio is constant and Young's modulus is expressed as a power function invlving the first invariat of the stress tensor and the second invariant of the deviatoric stress tensor. The characteristics of the model are described, and the accuracy is evaluated by comparison with experimental results from triaxial tests and three‐dimensional cubical triaxial tests with a variety of stress paths. Parameter determination from unloading–reloading cycles in conventional triaxial compression tests is demonstrated, typical parameter values are given for granular materials and extension of the model to soils with effective cohesion is described.
Back analysis procedures for the interpretation of field measurements in geomechanics
Authors: Gioda Giancarlo , Sakurai Shunsuke
Published: August 2005

A survey is presented of some recent developments of the numerical techniques for back analysis in the field of geomechanics, with particular reference to tunnelling problems. In the spirit of Terzaghi's observational design method, these techniques are seen as practical tools for interpreting the available field measurements, in order to reduce the uncertainties that in many instances affect the parameters governing the solution of complex geomechanics problems. Both deterministic and probabilistic viewpoints are considered and some significant applications to practical problems are illustrated.
Flow through porous media: A procedure for locating the free surface
Authors: Lacy Sara J. , Prevost Jean H.
Published: August 2005

A finite element procedure is developed to accurately locate the free surface of unconfined seepage flow through porous media. The free surface is taken as the boundary between wet and dry soils, with flow in the saturated region characterized by Darcy's law. The method involves equations and meshing which are fully consistent with a general formulation for geotechnical engineering problems involving simultaneous solution of pore fluid pressures and soil skeleton displacements. Accuracy and versatility of the proposed procedure are demonstrated by solving various unconfined seepage flow problems through earth structures. Free surfaces and flownets are presented for the calculated flow fields.
Stress waves in laterally loaded piles
Authors: Wang M. C. , Liao W. P.
Published: August 2005

The behaviour of single vertical piles subjected to lateral loading at the pile head was analysed. Based on the assumption of beam on elastic foundation, the analysis was made by using the method of direct analysis which is a numerical approach making direct use of governing physical laws without explicitly utilizing the differential equation of vibration. The analysis provides short‐time pile response to pulse loadings. These results indicate, among others, that an interaction between the dilatation and shear waves results in a stress discontinuity of considerable magnitude which may deserve special attention in pile design.
Dynamic stress analysis of a class of geomechanics problems by the boundary element method
Authors: Ahmad Shahid
Published: August 2005

This paper presents the application of an advanced BEM for periodic and transient dynamic stress analyses of a class of geomechanics problems. For transient dynamic analysis, the problem is first solved in the Laplace transform space, which happens to be similar to the periodic dynamic analysis, and then the time domain solution is obtained by numerical inversion of transform domain solutions. The numerical implementation of the BEM used to present the results in this paper is complete and most general available to date. It is capable of treating very large, multi‐layered problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring, capability problems related to layered media and soil–structure interaction have been analysed. A number of examples are presented and through comparisons with available analytical and numerical results, the applicability and usefulness of the present analysis to real geomechanical problems are established.
A simple model for isotropic non‐linear elasticity of frictional materials
Authors: Molenkamp F.
Published: August 2005

A simple isotropic nonlinear elastic model has been developed to describe the behaviour of granular materials immediately after stress reversal. Its three parameters can be measured in the same drained triaxial test.
Prediction of pile capacity from stress‐wave measurements: Some numerical aspects
Authors: Chow Y. K. , Wong K. Y. , Karunaratne G. P. , Lee S. L.
Published: August 2005

The analysis of measured stress waves for the prediction of static pile capacity is described. The usual method of using the measured velocity record as the input boundary condition in a wave equation analysis with a finite element model, if not properly implemented, can lead to significant numerical errors. An alternative scheme using an accurate prescribed displacement procedure with the measured displacement record (obtained from the integration of the velocity) is proposed, and is shown to be very efficient. These aspects of the numerical modelling procedure are illustrated by a case study.
Numerical studies of vibratory pile driving
Authors: Smith I. M. , To P.
Published: August 2005

The processes underlying pile installation by vibratory loading rather than impact loading are complex. However, numerical studies using simple models for soil behaviour do throw some light on the basic dynamic processes involved. As better soil models become widely used, quantitative analyses using the techniques described, or simplifications of them, should be feasible.
Slope stability analyses for materials with a non‐linear failure envelope
Authors: Collins I. F. , Gunn C. I. M. , Pender M. J. , Yan Wang
Published: August 2005

Upper bound techniques are used to analyse the stability of slopes of material failing according to a non‐linear failure criterion, such as closely jointed rocks. The global, extremal nature of upper bound calculations is discussed, as is the inverse use of such procedures for obtaining safe lower bound estimates for material strength properties in back analyses. Specific results are presented for the material model proposed by Hoek and Brown.
Three‐dimensional fracture propagation under specified well‐bore pressure
Authors: Lam K. Y. , Cleary M. P.
Published: August 2005

Results are presented for three‐dimensional planar fracture propagation in the presence of variations in confining stress, reservoir properties and frac‐fluid viscosity when the well‐bore pressure is constant throughout the frac‐job. Solid rock deformation during the frac‐job is described by the dislocation method with singular integral equations, and the fluid flow in the fracture is represented by the finite element method. A convergence study is undertaken on the three‐dimensional numerical model, and good agreement is obtained with results from laboratory tests and from the simpler circular model.
Numerical simulation of shear band formation in soils
Authors: Shuttle D. A. , Smith I. M.
Published: August 2005

Zones of localized shear strain, called bands, are initiated numerically within idealized cohesive and frictional soil specimens both by inhomogeneities and by imperfect boundaries. Qualitatively the results agree with experimental evidence, and give promise of quantitative analyses using better soil models, when the presence of porewater pressures will be of particular significance.
Comparison of dynamic stiffnesses of rigid square and rectangular foundations by DBEM and IBEM
Authors: Ahmad S. , Israil A. S. M. , Chen K.
Published: August 2005

In this work, the Direct and Indirect Boundary Element Methods as applied to dynamic soil structure interaction problems, are compared. Both the methods are used to find the dynamic stiffnesses of rigid surface and embedded foundations. For surface foundations, the results obtained by the two methods were very close for the frequency range considered, but for embedded foundations at higher frequencies, the Indirect Boundary Element Method produced erroneous values for the real part of vertical compliance. The possible reasons for this discrepancy are also studied in this paper.
Upper bound limit analysis using finite elements and linear programming
Authors: Sloan S. W.
Published: August 2005

This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive‐frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory.

The computational procedure uses three‐noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem.

Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure.
Performance of flexible retaining walls supporting dry cohesionless soils under cyclic loads
Authors: Siddharthan Raj , Maragakis Emmanuel M.
Published: August 2005

A finite element model is proposed for studying the seismic response of a flexible retaining wall/soil system. The model accounts for nonlinear hysteretic soil behaviour, and also for the increase in lateral stresses and settlement related to grain slip caused by cyclic loads. The response computed by the proposed method was compared with responses recorded at the Cambridge centrifuge facility, and found to be in reasonable agreement. The model was then used to identify the importance of factors such as flexibility of the wall and relative density of the backfill. The study reveals that the maximum bending moments given by current design procedures are nonconservative for stiffer walls. Deflections of flexible walls are of major concern. Flexible walls supporting a sand of medium density yield the greatest deflection.
Undrained and partially drained behaviour of end bearing piles and bells founded in untreated calcarenite
Authors: Murff J. D.
Published: August 2005

The subject paper1 details finite element analyses of underreamed footings installed at the tips of deeply embedded pipe piles. The analysis model incorporated a double‐hardening constitutive law and was calibrated using extensive field and laboratory test results. The results of the study were used to judge the relative effects of various aspects of the design, such as partial drainage and layering. Ultimately, this analysis was used to assess the adequacy of the footings as a remedial strengthening measure for a major offshore platform.
Numerical analysis of anchors in soils
Authors: Siriwardane Hema J.
Published: August 2005

An understanding of soil‐structure interaction effects is a key element in innovative design and analysis of various earth‐retaining structures. The purpose of this brief is to examine the application potential of a general three‐dimensional procedure for the analysis of anchors presented by Desai et al1.
Deformation analysis of sands in cubical and hollow cylinder devices
Authors: Chang Ching S. , Misra Anil , Weeraratne Saroj P.
Published: August 2005

For discrete materials like sands, the continuum field variables, stress and strain, are defined in terms of micro‐level quantities by considering the deformation mechanism of granular soils from a microscopic point of view. Under the application of load, soil is considered to deform due to the movement relative to each other of clusters of particles. Based on this deformation mechanism, the kinematics of soils are developed and a strain tensor for granular soils, in terms of local displacements and geometric measures, is introduced. A local constitutive law relating local displacements and local tractions is defined. Using the local constitutive law, the relationships between stress and strain for the media are developed. The developed model incorporates the influence of strain hardening and material anisotropy on the deformation behaviour of the media. Comparisons of the model predictions and experimental results from tests conducted in cubical and hollow cylinder devices are presented.
A semi‐analytic model for contaminant migration in a regular two‐ or three‐dimensional fractured network: Conservative contaminants
Authors: Rowe R. K. , Booker J. R.
Published: August 2005

A new semi‐analytical solution for the transport of a conservative contaminant species in a fractured medium having a regular two‐ or three‐dimensional fracture network is presented. The application of the technique and some of the practical implications arising from an examination of contaminant migration in fractured systems is discussed. Particular consideration is given to the effects of Darcy velocity, fracture spacing, matrix porosity, dispersivity and the mass of contaminant available for transport. The implications of uncertainty with respect to fracture opening size and ground‐water velocity is also discussed and it is shown that provided one can obtain a reasonable estimate of the hydraulic gradient and hydraulic conductivity for the rock mass, uncertainty regarding the magnitude of the opening size and the groundwater velocity does not have a significant effect on predicted contaminant migration for the class of problems being considered.
Horizontal soil stress changes around displacement piles
Authors: Sayed Sayed M. , Clemente Jose L. M.
Published: August 2005

A simplified analysis of the problem of horizontal soil stress changes around circular displacement piles, caused by pile placement, is presented. Pile installation is assumed to cause soil displacements in the horizontal direction only, thus yielding an axisymmetric problem. The soil surrounding the pile is modelled as a weightless non‐linear elastic material. Material non‐linearity is handled in a simplified manner by adopting secant shear moduli defined in terms of a proportionality coefficient and a softening factor. The resulting equilibrium equation is solved analytically and an expression is obtained which is also conveniently presented in graphical form. The derived expression can be used to estimate horizontal soil stress changes and is incorporated into a simple procedure to estimate the ultimate load or the efficiency of pile groups. Comparisons are made between efficiencies calculated according to this procedure and efficiencies measured in full‐scale group load tests in sand.
A mapping technique for steady‐state unconfined seepage analysis
Authors: Morland L. W. , Gioda G.
Published: August 2005

An approach is presented for the analysis of the unconfined steady‐state seepage through homogeneous trapezoidal dams based on a bijective mapping between the flow domain, having an unknown shape, and a fixed triangular domain. It is shown that the geometrically non‐linear unconfined analysis is equivalent to the problem of determining the unknown distribution of permeability, within a triangular domain with known shape, that satisfies the set of transformed boundary conditions. The flow problem in the triangular domain is solved through a finite‐element technique analogous to that adopted for confined analyses and, on the basis of this solution, the shape of the free surface in the physical space is evaluated. The proposed approach is applied to the determination of the influence of the water levels in the upper and lower reservoirs on the elevation of the free surface seepage point.
Finite element analysis of two cylindrical expansion problems involving nearly incompressible material behaviour
Authors: Burd H. J. , Houlsby G. T.
Published: August 2005

The displacement formulation of the finite element method is well suited to the analysis of elasto‐plasticity problems involving compressible material behaviour, but it is well known that numerical difficulties occur when the material is incompressible or nearly incompressible. The effect of these additional constraints depends on both element formulation and mesh topology. A two‐dimensional plane strain finite element formulation suitable for the solution of problems involving large strains and displacements (but small rotations) based on the isoparametric approach is described. The kinematics of deformation are defined in terms of the Eulerian strain rates that are invariably used in small strain analysis; the formulation therefore retains some of the character of small strain theory but includes additional geometrically non‐linear terms. The results of a series of plane strain finite element analyses of two cylindrical expansion problems are presented. These results confirm the previously observed trend that as Poisson's ratio approaches 0·5 then the quality of the calculated stress deteriorates. The study also indicates that the solution quality depends increasingly on mesh topology as perfect incompressibility is reached.
Estimation of geometrical parameters of key discontinuities within an engineering rock region
Authors: Xing Zhang
Published: August 2005

Discontinuities that have unfavourable orientation and are continuous within overall engineering rock regions can have a dominant effect on the strength, deformability and permeability of the rock mass. The concepts of geometrical parameters of basic discontinuities and engineering discontinuities are proposed in this communication. Further, the engineering discontinuities are divided into key discontinuities and non‐key discontinuities. Within any region of the rock mass, the spacing, trace length and probability of engineering discontinuities can be estimated from the geometrical parameters of the basic discontinuities. In general, the geometrical parameters are different from those of the basic discontinuities. Finally, two examples are given to illustrate how to apply these parameters to rock engineering problems.
Primary and remote fracture around underground cavities
Authors: Carter B. J. , Lajtai E. Z. , Petukhov A.
Published: August 2005

The development of fractures around cavities in rock is examined using physical and numerical models. In uniaxial compression, fracture proceeds from primary through remote to compressional (slabbing) fracture. There is a wide stress interval where the only event is the stable propagation of the primary fracture. When the crack length becomes equal to about the size of the diameter of the cavity, the critical stress condition shifts to either side of the primary fracture, leading to the nucleation of remote fractures. Almost simultaneously, failure at the compressive stress concentration follows. With increasing stress, fracture in the remote region is seen to extend away from and towards the compressive region, eventually merging with the slabbing fractures. Increasing the confining pressure shortens the stress interval during which primary fracture is the only process and shifts failure to the remote and the compressional fracture zone.
Embankment reliability versus factor of safety: Before and after slide repair
Authors: Wolff Thomas F.
Published: August 2005

Probabilistic slope stability analyses incorporate more information regarding the input variables than do traditional deterministic analyses. Consequently, more information is contained in the results. A probabilistic method for slope stability analysis for very general problems was presented by Wolff and Harr.1 The method allows analysis of a broad range of slope stability problems. In this Application Brief, the method is reviewed and used to illustrate the significant change in reliability of a dam slope from the time of an actual slide to the time the slide was repaired by the construction of a rock toe berm.
Application of numerical analyses for tunnelling
Authors: Duddeck H.
Published: August 2005

The paper reviews the application of numerical methods in tunnelling, the achievements and the shortcomings, hence also the future tasks for closing the gap between real ground behaviour in critical tunnelling situations and the present approaches by numerical models. After discussing the role of the structural model within the entire design procedure for a tunnel project, problems are mentioned where numerical methods are essential. This is explained for soft ground tunnelling as well as for tunnels in rock. A special section is devoted to the kind of numerical models needed for the interpretation of field measurements. There is still much to do, especially in covering failure modes of tunnels by numerical analysis. The paper is a shorter version (e.g. without photographs of the actual tunnelling work) of a lecture presented at the Innsbruck Conference on Numerical Methods in 1988.
Determination of asperity damage parameters for constitutive models of rock discontinuities
Authors: Plesha Michael E. , Hutson Robert W. , Dowding Charles H.
Published: August 2005

Dilatancy and contact surface damage are important phenomena affecting the behaviour of rock joints and other geological discontinuities. Effective constitutive laws that incorporate these behaviours have recently been developed but require the specification of new material parameters that govern damage of asperity surfaces. Determination of the parameters that control damage is currently a difficulty that confronts practitioners. This brief will summarize the findings of Hutson and Dowding's investigation of joint surface asperity degradation and elaborate on the implications for application.
Interface elements for singular plasticity points
Authors: Van Langen H. , Vermeer P. A.
Published: August 2005

Zero‐thickness interface elements are applied to solve plasticity problems involving singular points where stresses and displacements are non‐unique. Singular points occur in soil–structure interaction, e.g. at the ridges of footings, buried structures and foundation piles. Here the introduction of potential displacement discontinuities appears to give quite accurate finite element solutions. This is demonstrated for indentation problems both for plane strain and axisymmetric situations. In all problems the soil behaviour is modelled by the elastic–plastic Mohr–Coulomb model.
Wave‐induced stresses and pore pressures in sloping seabeds
Authors: Gatmiri Behrouz
Published: August 2005

By using the Mellin transform, a general solution is obtained for the total stresses and pore pressure distribution in an infinite wedge under fairly general conditions of loading. The results for the particular case in which each surface is subjected to static sinusoidal pressures are given in an explicit form. The infinite integrals can be evaluated by numerical integration methods. This analytical method is verified by different cases. The results of this study could be used to determine the total stresses and pore pressures induced by a wave on a sloping seabed.
An interpretation of initial stress and strain methods, and numerical stability
Authors: Stolle Dieter F. E.
Published: August 2005

This paper explores similarities and differences between initial stress and initial strain methods of analyses. The author takes the position that both methods, although perhaps conceptually different, are actually numerically the same. A simple approach for providing closed‐form stability criteria for explicit and implicit time‐marching procedures is described. For the case of associated, non‐hardening viscoplasticity the approach provides criteria which are identical to those of Cormeau for explicit schemes. An implicit time‐marching scheme which avoids the compliance matrix inversions at the constitutive level is also presented. Like many other implicit methods, this implicit time‐marching scheme is unconditionally stable for θ≥½.

The connection between initial strain plasticity and an explicit viscoplastic time‐marching scheme is also addressed.
A comparison of field‐monitored and numerically predicted moisture movement in unsaturated soil
Authors: Thomas H. R. , Rees S. W.
Published: August 2005

This paper presents the results of the application of a numerical model of flow of water in unsaturated soil to simulate real field behaviour. Numerical predictions are compared with field‐monitored results as part of an assessment of the approach adopted.

The numerical approach is based on a finite element solution of Richards' theoretical formulation, adopting a finite difference recurrence relationship to model the transient nature of the problem. The field results have been collected by British Gas in Kimmeridge clay at a site in Swindon.

The simulation addressed the autumn wetting of the soil during 1983. Comparisons of volumetric moisture content readings from the field and numerical predictions give good correlation. It is concluded that the numerical model has adequately represented field behaviour over the depth of interest. Taken in conjunction with previous results, it is claimed that the model should now be capable of use in a predictive mode.
Stability of openings in jointed rock
Authors: Vaughan David K. , Isenberg J.
Published: August 2005

The slide line approach is combined with the finite element method to represent the action of a removable block on a lined tunnel. The present paper examines the strength and ductility required of the tunnel liner to resist the forces imposed by a block when the surrounding rock mass is subjected to explosive loading. Key block theory developed by Goodman and Shi provides the conceptual framework for simplifying a general jointed domain to a manageable size for analysis with finite element models.
A semi‐discrete procedure for dynamic response analysis of saturated soils
Authors: Chohan Harpal S. , Sandhu Ranbir S. , Wolfe William E.
Published: August 2005

Biot's equations of wave propagation through fluid‐saturated porous elastic media are discretized spatially using the finite element method in conjunction with Galerkin's procedure. Laplace transformation of the discretized equations is used to suppress the time variable. Introducing Laplace transforms of constituent velocities at nodal points as additional variables, the quadratic set of equations in the Laplace transform parameter is reduced to a linear form. The solution in the Laplace transform space is inverted, term by term, to get the complete time history of the solid and fluid displacements and velocities. Since the solution is exact in the time domain, the error in the calculated response is entirely due to the spatial approximation. The procedure is applied to one‐dimensional wave propagation in a linear elastic material and in a fluid‐saturated elastic soil layer with ‘weak’, ‘strong’ as well as ‘moderate’ coupling. With refinement of the spatial mesh, convergence to the exact solution is established. The procedure can provide a useful benchmark for validation of approximate temporal discretization schemes and estimation of errors due to spatial discretization.
Probabilistic analysis of an impulsively loaded deep‐based structure
Authors: Harren S. V. , Fossum A. F.
Published: August 2005

A deep‐based (i.e. deeply buried) structure subjected to stress wave loading is analyzed probabilistically. The finite element method, coupled with a fast probability integration technique, is used to perform the analysis. Randomness due to uncertainties in loading and stratum material properties is addressed. The results presented, although for an idealized linear elastodynamic problem, clearly demonstrate that more realistic probabilistic analyses of impulsively loaded deep‐base structures are feasible.
Coupling versus uncoupling in soil consolidation
Authors: Lewis R. W. , Schrefler B. A. , Simoni L.
Published: August 2005

Coupling and uncoupling between the equilibrium and mass balance equations in soil consolidation problems in investigated in detail. A procedure for judging the strength of coupling is indicated. In the applications, particular emphasis is given to subsidence problems where the coupled nature of the problem is still sometimes questioned. It is shown that even in the case of a single pumped aquifer most situations are coupled.
Efficient multigrid solution of boundary element models of cracks and faults
Authors: Peirce A. P.
Published: August 2005

We consider the multigrid solution of a discretized singular integral equation whose solution represents the displacement discontinuity distribution across a pressurized crack or the slip on a fault subjected to a prescribed shear stress. The multigrid technique reduces the operation count for a crack model having N degrees of freedom from O(N3) operations for standard stationary iterative methods to O(N2) operations. In the numerical simulations performed the multigrid approach proves to be extremely efficient even for small values of N. We use Fourier analysis to determine the spectral properties of the coarse grid correction process and the effect of a number of different interpolation operators on the multigrid algorithm. We show that the multigrid technique can be combined with the process of lumping remote influences to yield an algorithm that involves O(N) operations. The performance of multigrid iteration in a nonlinear environment is explored by considering seams filled with nonlinear material. For this purpose a segmented multigrid algorithm is developed that allows for different seam constitutive relations to be used along different line segments. The O(N2) operation count characteristic of linear multigrid iteration is shown to persist in this nonlinear environment and the segmented multigrid approach is shown to provide significant computational savings for values of N well within the range for typical problems that occur in practice.
Analysis of subsidence due to a point sink in an anisotropic porous elastic half space
Authors: Tarn Jiann‐Quo , Lu Cheer‐Chung
Published: August 2005

Analytical solutions of the long‐term consolidation deformation and excess pore water pressure due to fluid withdrawal from a saturated anisotropic porous elastic half space are presented. In the analysis, both the permeability and the elastic properties are considered cross‐anisotropic. Cases of pervious and impervious half‐space boundary are studied. The consolidation settlements as effected by the anisotropy and boundary conditions for pore water are illustrated and discussed.
Computer‐aided design of constitutive laws
Authors: Kolymbas D.
Published: August 2005

In this paper a method is presented which helps to develop and to check constitutive laws by means of computer experiments. The exposition has been carried out along the formalism of hypoplasticity, which has been introduced as a generalization of hypoelasticity. Several results of computer experiments are graphically represented.
Implementation of hierarchical single surface δ0 and δ1 models in finite element procedure
Authors: Desai C. S. , Sharma K. G. , Wathugala G. W. , Rigby D. B.
Published: August 2005

Hierarchical single surface (HISS) δ0 and δ1 models are briefly discussed. An algorithm for the implementation of δ0 and δ1 models in a finite element code and the associated subroutines, written in FORTRAN 77, are presented. The algorithm is general and can be adopted for other computer codes with minor changes. Detailed steps and subroutines are included for easy implementation of the models in specific codes. Two example problems are also presented to enable the user to verify the implementation.
Elastostatic deformation of a half‐space under conical loading
Authors: Hemsley J. A.
Published: August 2005

In the idealised modelling of ground distortion induced by a freely deposited heap of granular material, consideration is given to a fundamental problem in classical elasticity whereby an axisymmetric distribution of vertical conical loading is applied to the surface of a half‐space. Closed‐form expressions are derived for the deformed shape of the surface, and three variations of the integral transform method are described for determining stresses and displacements within the half‐space. Extensive numerical results are presented in graphical form.
Finite layer analysis of laterally loaded piles in cross‐anisotropic soils
Authors: Lee C. Y. , Small J. C.
Published: August 2005

This paper presents a finite layer method for the analysis of laterally loaded piles in isotropic and cross‐anisotropic layered soils. Excellent agreement is found between the isotropic solutions computed by the finite layer method and the more rigorous finite element method. Some theoretical solutions are presented to demonstrate the effect of soil anisotropy. Two full scale field case histories have been analysed by the method using isotropic and cross‐anisotropic soil models.
Pile group settlement: A probabilistic approach
Authors: Quek S. T. , Phoon K. K. , Chow Y. K.
Published: August 2005

The uncertain settlement response of pile groups is determined using a ‘hybrid’ formulation and a first‐order perturbation technique. The spatially varying soil modulus, which gives rise to the uncertainties in the pile group settlement, is modeled as a homogeneous random field. The random field is assumed to be one‐dimensional since the ‘hybrid’ formulation does not account for horizontal variation in the soil properties. Using the proposed method, the coefficient of variation of the pile group settlement is computed. The single‐pile solutions obtained compare favorably with the solutions from a conventional stochastic finite element analysis. Pile groups of sizes ranging from two to twenty‐five piles are studied. It is observed that the coefficient of variation is not significantly affected by the pile spacing as well as the group size. By defining an appropriate performance function, the reliability index of a pile group system is also found to be approximately the same as that of a single‐pile system. These observations suggest that the solutions for a single pile may be used to estimate the uncertainties in the settlement response of pile groups.
Application of non‐linear elastic model
Authors: Molenkamp F.
Published: August 2005

The properties of a previously published isotropic non‐linear elastic model with an elastic potential are illustrated in detail. Its parameter determination is elaborated and a parameter list is composed on the basis of published experimental data. The formulation with the elastic potential is shown to enable the minimization of numerical drift in incremental calculations of the deformation for alternating loading.
An updated reference configuration formulation for large‐deformation problems
Authors: Stolle D. F. E. , Schad H.
Published: August 2005

This paper examines difficulties encountered when using the Green‐Nagdi rate and presents an updated configuration formulation for problems dealing with large deformations. It is shown that a natural link can be established between the updated reference configuration and linearized updated Lagrangian formulations, if Truesdell's objective stress rate is used. Owing to this connection, any limitations associated with the described formulation would be expected to also apply to an updated Lagrangian formulation and vice versa. It is pointed out that, if second‐order effects are induced, the Truesdell rate appears in the rate equation for equilibrium even when strains are infinitesimal. By examining a simple‐shear problem, where hypoelastic material behaviour with ‘Hooke's law’ is assumed, it is shown that the spherical state of stress is coupled with the shear stress when using the Truesdell or Green‐Nagdi stress rate. It is suggested that objective stress rates, introduced in large‐deformation formulations, may contribute to erroneous predictions if a constitutive law is developed independent of the adopted stress rate.
Accuracy of four‐node standard finite element
Authors: Molenkamp F. , Kidger D. J. , Smith I. M.
Published: August 2005

In this note the accuracy of the elastic standard 4‐node plane‐strain finite element is investigated by comparing numerically calculated eigenvalues of the element stiffness matrix to those according to higher‐order algebraic approximations. From this study it may be concluded that the ‘hourglass’ eigenmodes are the only inaccurate ones. For selective reduced numerical integration the hourglass eigenvalues may be expected to be of the order of 1/2 to 2/3 of the analytical values.
Numerical treatment of progressive localization in relation to borehole stability
Authors: Papanastasiou Panos C. , Vardoulakis Ioannis G.
Published: August 2005

Results of large‐scale finite element computations are presented for the problem of borehole failure due to the high stresses at great depths. Rock is modelled by an extension of the Mohr–Coulomb flow theory of plasticity for material with Cosserat micro‐structure. The introduction of internal length (grain size) improves the computational stability and allows for robust post‐localization computations. The presented results show clearly a progressive failure mechanism and the computed failure modes are in a good qualitative agreement with laboratory and field observations.