bluuebunny/crossref_metadata_2025 huggingface dataset:
Two practical examples of numerical approaches for solving discontinuity problems in dam design
Authors: Lima V. Souza , Abrahão R. A.
Published: August 2005

This paper draws attention to the great influence certain types of discontinuities in foundation rock masses can have on dam design. By means of two practical examples, the role of numerical procedures in the solution of stability and deformation problems posed by foundation heterogeneities is discussed and emphasized. Some basic theoretical considerations regarding the limit‐states and the concept of safety to be used in dam design are also presented as a complement to the analyses description.

The case of the Ãgua Vermelha dam, recently built in southern Brazil, is the subject of the first example. Here, a major joint in the basaltic foundation was the decisive geological feature for the stability analyses which were performed by means of the finite element method. The second example refers to the Itaipu dam, a record‐breaking Brazilian–Paraguayan hydroelectric development. Marked sub‐horizontal discontinuities between lava flows, greatly reducing the strength and stiffness of the basaltic rock masses, were of main concern in this case. The results of the foundation studies, with due help of numerical procedures, called for the construction of concrete shear keys, in order to achieve a satisfactory margin of structural safety.
Modelling microcrack kinetics in rocks
Authors: Stout R. B. , Thigpen L.
Published: August 2005

Mathematical concepts of statistical mechanics are use here to formulate the problem of microcrack kinetics. A stochastic distribution function is defined to characterize some modelling parameters of microcracks. This formalism results in an integral–differential equation of the Boltzmann type. A functional form for the microcrack production rate is imposed to model dilatancy and failure under shear‐loading histories. This simple model illustrates some concepts of this theoretical approach.
Two‐dimensional stresses in a saturated poro‐elastic foundation beneath a rigid structure—part. I. An impervious dam in a river
Authors: Mei Chiang C. , Mynett Arthur E.
Published: August 2005

The problem of an impervious dam on a poro‐elastic foundation is solved analytically. Using the known solution for the fluid pressure in the pores, the elastostatic stress field in the solid skeleton is analysed by reduction to two simpler problems whose solutions can be obtained by complex variable techniques. For welded contact, the rotation of the dam base is then found along with the stresses and strains in the ground. Modification for finite friction along the base is outlined in the appendix.
A numerical solution for the stability of a vertical cut in a purely cohesive medium
Authors: Cascini Leonardo
Published: August 2005

The problem of the critical height of a vertical cut in a purely cohesive medium has been repeatedly dealt with by several authors and, in spite of its apparent simplicity, the characterization of satisfactory solutions has presented, for a considerable period, notable difficulties. The present paper supplies the results obtained with a numerical method, which has so far been applied successfully to a considerable number of problems.
Application of a Cam–Clay model to overconsolidated clay
Authors: Amerasinghe S. F. , Kraft L. M.
Published: August 2005

The yield locus governing the stress–strain response of a soil may degrade during rebound at high overconsolidation ratios. The cause can be attributed to a breakdown in bonding. A Cam–Clay model is applied to account for the degrading yield locus, and the influence of this degradation is assessed using a theoretical approach for friction pile capacity. Stress changes in the soil continuum due to pile installation and setup are simulated by cylindrical cavity expansion and radial consolidation, anda segment loading model is used to determine the effective stress change in the soil at peak load transfer under undrained conditions. The results indicate that plastic rebound affects peak load transfer to at least the same extent as shear strength.
Fundamental results concerning the settlement of a rigid foundation on an elastic medium due to an adjacent surface load
Authors: Selvadurai A. P. S.
Published: August 2005

This paper examines the interaction between a rigid circular foundation resting in smooth contact with an isotropic elastic halfspace and a concentrated surface load which acts at a finite distance from the foundation. Owing to the action of the external load the rigid foundation experiences an extra settlement and a tilt. The expressions for the extra settlement and the tilt are evaluated in exact closed form. It is also shown that these deformations due to the external load satisfy Betti's reciprocal theorem. The auxiliary solution required for the application of the reciprocal theorem is derived from the analysis of the problem of a rigid circular foundation resting in smooth contact with an elastic medium and subjected to an eccentric load. The, results developed for the interaction between the rigid circular foundation and the external concentrated load are utilized to generate, among others, solutions for the settlement and tilt induced at a rigid foundation due to its interaction with uniformly or non‐uniformly distributed loads with circular and square plan shapes.
Three‐dimensional analysis of Infiernillo dam during construction and filling of the reservoir
Authors: Justo J. L. , Saura J.
Published: August 2005

A three‐dimensional finite element program has been prepared to study the behaviour of Infiernillo dam during construction and filling of the reservoir. A linear stress‐strain behaviour of materials has been assumed. The parameters are deduced from the movements measured during construction, checked with the results of oedometer tests at the laboratory. The no tension strength of granular materials has been introduced following Zienkiewicz et al.9 Collapse of the upstream shell is introduced into the calculation in a simple way from the settlement observed upon flooding under constant stress at the oedometer.

A good agreement is found between measured and calculated movements.
A note on indirect boundary element methods for the diffusion equation
Authors: Sharp S.
Published: August 2005

This paper corrects an impression, created by a recent contribution to the International Journal for Numerical and Analytical Methods in Geomechanics, that the mathematical equivalence of the direct and indirect boundary element methods for the diffusion equation implies that their respective computational needs with regard to the body integral terms are equal. It is shown that in a stepwise implementation of the numerical procedure for solving a finite body problem, indirect methods requirean integration over an infinite region and not merely over the body as is the case for the direct version.
A constitutive model for sand with anisotropic hardening rule
Authors: Mróz Z. , Pietruszczak St.
Published: August 2005

An anisotropic hardening model for sand or other granular materials is presented. The state of initial densification is represented by a configuration surface and the state of loading by a loading surface in the stress space. The domain of elastic response may not exist and the irreversible strain is assumed to occur for both active and reverse loading. The derived constitutive equations are applicable both for dense and loose sands. Some model predictions are compared with available experimental data for triaxial compression and extension under undrained condition.
A family of Houbolt methods for dynamic vibration problems
Authors: Thomas R. M. , Addison C. A. , Gladwell I.
Published: August 2005

We extend the well‐known Houblt method for dynamic vibration problems to a class of methods suitable for a variable‐order variable‐step computer program implementation. We discuss the numerical stability properties of these methods and derive a family of extensions with improved stability properties. Finally we present some numerical results which compare a variety of Houbolt methods with other well‐known Backward Differentiation methods, demonstrating in passing the practical value of the stability, concepts.
A simple contact–friction interface element with applications to buried culverts
Authors: Katona Michael G.
Published: August 2005

A simple friction–contact interface element is introduced which simulates frictional slippage, separation, and re‐bonding of two bodies initially mating at a common interface and subsequently deforming with an arbitrary static loading schedule. Constraint equations between initially mating node pairs and the general principle of virtual work are used to formulate the interface element for a finite element solution procedure. Some advantages of the interface element include; easy implementation intostandard finite element programs, direct determination of interface forces without round‐off problems, and the generality afforded by the virtual work formulation to include other non‐conservative models in the system.

The application of the interface element to an idealized buried culvert problem illustrates that the model behaves properly. A second application, for a long‐span culvert installation with incremental soil loading, demonstrates the importance of modelling slippage at the culvert–soil interface in order to conform with experimental observations.
Multi‐laminate model of clays—a numerical evaluation of the influence of rotation of the principal stress axes
Authors: Pande G. N. , Sharma K. G.
Published: August 2005

A new framework for the development of constitutive models based on certain aspects of physical theories of plasticity is proposed. The resulting Multi‐laminate model of clays has the same response as the Critical state model provided no rotation of principal stress axes takes place during plastic flow.

The influence of rotation of the principal stress axes on the volumetric and deviatoric plastic strains has been numerically evaluated. In undrained saturated, normally consolidated clays considerable excess pore pressure may build up due to rotation of the principal axes only. Numerical studies of the collapse of footings indicate that significant rotations do not take place in this class of problems and consequently the collapse load is only marginally reduced.
A material model for inelastic rock deformation with spatial variation of pore pressure
Authors: Smith M. B. , Pattillo P. D.
Published: August 2005

This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic‐plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.
Dynamic behaviour of saturated porous media; The generalized Biot formulation and its numerical solution
Authors: Zienkiewicz O. C. , Shiomi T.
Published: August 2005

The basic equations of motion for porous media were established by Biot and despite many subsequent rederivations, are, with minor modifications, relevant today. However, some changes of variables and approximations are on occasion useful, and this paper discusses the alternative forms available and their relative efficiency of solution in the numerical context. Here penaity methods prove once again useful. The paper is illustrated with examples covering phenomena of different periods ranging froms hock excitation to slow consolidation which are treated in a single unified program.
Localization of deformations in elastic‐plastic solids
Authors: Prevost Jean H.
Published: August 2005

Localization of deformation in elastic‐plastic solids subject to plane strain deformation are investigated numerically. It is shown that the localization may be captured accurately in finite element models by employing (1) the elastic‐plastic material stiffness to form the global stiffness, (2) in the case of symmetrical configurations, an imperfection in the form of a weak element, and (3) in the case of incompressible materials, a reduced selective integration scheme which alleviates mesh ‘locking’. Accuracy of the technique is demonstrated by applying it to analyse the classical punch and slope stability problems. Its versatility is illustrated by applying it to analyse finite deformation problems and shear bands formations in associative and non‐associative elastic‐plastic solids.
Trapezoidal footings on non‐linear subgrades
Authors: Chandra S. , Madhav M. R. , Iyengar N. G. R.
Published: August 2005

The pressure versus settlement response is highly non‐linear for soils, in general. In the present study, a cubic equation of the type p = K1w − K2w3 is suggested to incorporate the non‐linear behaviour. A trapezoidal footing with constant depth resting on a subgrade having non‐linear response is analysed. The resulting fourth order non‐linear differential equation with variable coefficients is solved by using the Galerkin technique and beam characteristic functions are employed to obtain faster convergence. The results are presented in the form of non‐dimensional charts for valid ranges of footings and soil parameters.
Comparison of finite and infinitesimal strain consolidation by numerical experiments
Authors: Meijer Karel L.
Published: August 2005

A number of computations have been performed in order to gain an insight into whether or not the non‐linear finite deformation theory must be applied in consolidation problems. These numerical experiments were preluded by tests to determine the correct model size and the fineness of the discretization. For this an analytical solution served as a gauge. The conclusion is that with stiffnesses of the order of ten times the external load, moderate deviations appear in both the effective stresses and the pore pressures.
Consolidation around a point heat source
Authors: Booker J. R. , Savvidou C.
Published: August 2005

When a heat source such as a canister of radioactive waste is buried in a saturated soil the temperature changes that occur will cause the pore water to expand a greater amount than the voids of the soil. The temperature change will thus usually be accompanied by an increase in pore pressure. If the soil is sufficiently permeable these pore pressures will dissipate. This paper develops an analytic solution for the fundamental problem of a point heat source buried deep in a saturated soil.
The effect of pore‐fluid compressibility on failure loads in elasto‐plastic soil
Authors: Griffiths D. V.
Published: August 2005

The influence of pore‐fluid compressibility on failure loads in certain soil mechanics problems is investigated. The results are tested using a finite element approach treating the soil as an elasto‐plastic material. A limiting value for the pore‐fluid compressibility to give satisfactory solutions and numerical stability is suggested.
Effect of stone column yield on settlement of rigid foundations in stabilized clay
Authors: Balaam N. P. , Booker J. R.
Published: August 2005

In this paper the settlement of a rigid foundation supported by a layer of clay which has been stabilized with stone columns is considered. The results of an analytic solution for the settlement, assuming no yield occurs in the clay or columns, have been presented in a previous publication. This solution is now used to develop an interaction analysis which takes account of yielding within the stone columns.

This interaction analysis is based on a number of plausible assumptions regarding the behaviour of the clay and columns. In order to check the validity of these assumptions elasto‐plastic finite element analyses have been performed and the agreement between the two methods is very good. However, the computational effort required for the finite element analyses is many orders of magnitude greater than that for the interaction analysis.

This analysis has been used to generate a number of parametric solutions which provide a basis for estimating the reduction in settlement of the foundation due to the stabilization of the clay.
Condensation of elastic half space soil stiffness matrix considering symmetry
Authors: Sharma K. G.
Published: August 2005

The finite element formulation for deriving the soil stiffness matrix by idealizing the foundation as an elastic half space is presented. The procedure for condensation of the soil stiffness matrix taking symmetry into consideration is discussed. Computation time is considerable reduced when a condensed soil stiffness matrix is used for the finite element analysis of rafts resting on an elastic half space.
Torsional stiffness of non‐uniform and hollow rigid piers embedded in isotropic elastic media
Authors: Rajapakse R. K. N. D. , Selvadurai A. P. S.
Published: August 2005

This paper examines the torsional response of a rigid pier type foundation, with a non‐uniform or hollow cross‐section which is embedded in bonded contact with a layered elastic half space. The tractions which act at the axisymmetric boundary surface between the pier and the surrounding elastic medium are represented by discretized regions of uniform traction. The compatibility of deformation at the boundary is used to determine the interface stress distribution. The torque‐rotation response for the, rigid pier foundation is obtained for different choices of the pier geometry and shear modulus mistnatch between the layer and the underlying half space.
Two dimensional discontinuous deformation analysis
Authors: Shi Gen‐Hua , Goodman Richard E.
Published: August 2005

This paper explains a novel ‘back‐analysis’ shceme to determine rock mass behaviour modes from an array of deformational measurements. The input will be the locations of data points and the set of measured displacements, as well as description of the locations and orientations of planes of discontinuity, and the blocks they determine. The output, drawn by the computer, will be the set of block displacements, rotations, and strains that determine the behavioural mode of the mass.
Analysis of vertically loaded pile groups
Authors: Chow Y. K.
Published: August 2005

An approach is presented for the analysis of linear and non‐linear responses of vertically loaded pile groups. The soil behaviour of individual piles in modelled using load‐transfer curves and the pile‐soil‐pile interaction is determined based on Mindlin's solution. Good agreement between the present method of analysis and the rigorous boundary integral method is observed for the computation of the response of pile groups embedded in a homogeneous, isotropic elastic half‐space. The computed non‐linear response of pile groups compares favourably with measured results from field load tests.
Dynamic stability analysis of undrained simple shear on water‐saturated granular soils
Authors: Vardoulakis I.
Published: August 2005

Dynamic stability of undrained, simple‐shear deformations on water‐saturated granular soil specimens is discussed. The soil is described by a 2D‐flow theory of plasticity for frictional and dilatant material. Contractant material becomes unstable (liquefies) at the state of maximum shear stress, whereas dilatant material becomes unstable after the state of maximum effective stress obliquity is reached in the softening regime of the background drained behaviour. In both cases the correct evolution equations for the growth coefficient of the instability are derived and compared with the results of the inertia‐free formulation of the problem.
Dynamics of fluid‐saturated soils—variational formulation
Authors: Sandhu Ranbir S. , Hong Soon J.
Published: August 2005

Variational principles governing dynamics of fluid‐saturated linear elastic porous media are derived. Complementary as well as direct formulations are discussed. Discontinuities in the field variables, the approximation space and the excitation are allowed for. Extensions of the variational principles to relax smootheness requirements on certain field variables are introduced along with some specizalizations convenient for finite element applications.
A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms
Authors: Booker J. R. , Small J. C.
Published: August 2005

A method is presented for obtaining the consolidation behaviour of a layered soil subjected to strip, circular, or rectangular surface loadings, or subjected to fluid withdrawal due to pumping. The solution method involves applying a Fourier or Hankel transform to the field quantities along with a Laplace transformation. The effect of the Fourier or Hankel transform is to reduce a two‐ or three‐dimensional problem or one involving axial symmetry, to one involving only a single spatial dimension. In cases where the soil is horizontally layered, this has great advantages over conventional methods, such as finite element or finite difference methods, since very little computer storage and data preparation time is required. Solution of the time dependent problem is achieved by applying a Laplace transformation to the field variables, obtaining solutions in Laplace transform space, and then numerically inverting the transformed solutions to obtain the real time behaviour. This eliminates the need for ‘marching type’ schemes where a solution is found from one at a previous time. By direct inversion of the Laplace transform, a solution may be obtained directly at any given time.
Shakedown in frictional materials under moving surface loads
Authors: Collins I. F. , Cliffe P. F.
Published: August 2005

Elastic/plastic deformations in frictional materials under moving surface loads are investigated. The static and kinematic shakedown theorems are used to obtain estimates of the critical shakedown load for plane strain deformations under trapezoidal surface load distributions and for three‐dimensional deformations under loads distributed over circular areas. It is shown that the material can fail either by incremental collapse or in cyclic or alternating collapse modes.
A method of time‐dependent analysis using elastic solutions for nonlinear materials
Authors: Chua Koon Meng , Lytton Robert L.
Published: August 2005

The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time‐dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi‐elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress‐strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time‐dependent stress‐strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis.
Rapid evaluation of the critical slip surface in slope stability problems
Authors: Li K. S. , White W.
Published: August 2005

Existing approaches for locating the critical slip surfaces are briefly reviewed. A number of techniques and strategies are proposed whereby the efficiency and robustness of some of the existing approaches can be enhanced. A new solution scheme is also developed for rapid calculation of the factor of safety. The new solution scheme requires only one level of iterations in contrast to the conventional solution scheme which invoives two levels of iterations. It is also applicable to a variety of stability models. A new compound iterative procedure is developed whereby the factor of safety can be calculated to a high accuracy within a few iterations. This reduces greatly the total computer time required for locating the critical slip surfaces.
Parameter identification in a damage model for rock mechanics
Authors: Resende L. , Martin J. B.
Published: August 2005

Attention is focused on the mechanical behaviour of rock‐like materials. Developments and applications of a constitutive model based on damage theory are presented. The internal damage model is calibrated for a hard brittle rock, Bushveld Norite, and through this process the identification of the material parameters is carried out. Emphasis is placed on the identification of the material parameters in the damage evolution law. The uniqueness of solutions in the softening regime is investigated through finite element mesh sensitivity studies of non‐uniform deformation triaxial compression tests.
Bifurcations in finite element models with a non‐associated flow law
Authors: De Borst R.
Published: August 2005

A numerical approach to bifurcation problems in soil mechanics is described. After locating the bifurcation point by a combination of an incremental‐iterative loading procedure and an eigenvalue analysis of the tangent stiffness matrix, the solution is continued on the localization path by a suitable combination of the fundamental solution and the eigenvector belonging to the lowest eigenvalue. The procedures are applied in a bifurcation analysis of a cohesionless soil in a biaxial testing device. The results suggest that a diffuse bifurcation mode with a short wavelength is encountered whereupon a shear band gradually develops. The inclination angle of the shear band compares well with analytical formulae and with empirical data.
Modelling and simulation of load transfer in reinforced soils: Part 1
Authors: Juran I. , Guermazi A. , Chen C. L. , Ider M. H.
Published: August 2005

Results of both triaxial and direct shear tests on reinforced soil samples performed by different investigators have shown that soil dilatancy and extensibility of the reinforcements have a significant effect on the generated tension forces in the inclusions. An appropriate soil‐‐reinforcement load transfer model, integrating the effect of soil dilatancy and reinforcement extensibility is therefore needed to adequately predict forces in the inclusions under expected working loads. This paper present a load transfer model assuming an elastoplastic strain hardening behaviour for the soil and an elastic‐‐perfectly plastic behaviour for the reinforcement. This model is used to analyse the response of the reinforced soil material under triaxial compression loading. A companion paper present the application of this model for numerical simulations of direct shear tests on sand samples reinforced with different types of tension resisting reinforcements. The model allows an evaluation of the effect of various parameters such as mechanical characteristics and dilatancy properties of the soil, extensibility of the reinforcements, and their inclination with respect to the failure surface, on the development of resisting tensile stresses in the reinforcements. A parametric study is conducted to evaluate the effect of these parameters on the behaviour of the reinforced soil material. An attempt is also made to verify the proposed model by comparing numerical predictions with available experimental results of both triaxial and direct shear tests on reinforced soil samples. This model can be used for analysis and design of reinforced soil walls with different types of tension resisting inclusions to predict tension forces under expected working loads.
Effects of voids and volume changes on the behaviour of frictional materials
Authors: Lade Poul V.
Published: August 2005

Development of constitutive models for engineering materials is often based on a framework of elasticity and plasticity theories as developed for metals. Prsented here is a review of some of the basic differences in the experimentally observed behaviour of metals and frictional materials. Two of the distinguishing characteristics between metals and frictional materials are the absence or presence of voids and the tendency to change or maintain constant volume during compression and shear. These differences must be recognized in order to develop reasonable constitutive models for frictional materials.
A three‐dimensional finite element program for brittle bimodular rock‐like materials
Authors: Khan Akhtar S. , Yuan Si
Published: August 2005

The present paper models the behaviour of bimodular materials (materials with different tensile and compressive moduli) by using a three‐dimensional finite element method. Since there is no explicit and definite expression for the shear modulus G of bimodular materials, the analysis starts with a 3 × 3 elasticity matrix in the principal stress coordinate system, and then uses a transformation from principal to Cartesian coordinates to obtain the 6 × 6 elasticity matrix. A corresponding iterative technique is proposed, and multiloading sequences in non‐proportionate loading—which need more iterations because of the non‐linear elastic property—are also discussed. Numerical examples are presented which show good agreement with analytical results.
Finite element analysis of strain localization in frictional materials
Authors: Leroy Y. , Ortiz M.
Published: August 2005

Numerical examples are given which illustrate the poor performance of conventional finite elements in problems involving strain localization in frictional materials. In one of the cases investigated, that of granular media subjected to plane strain biaxial loading, isoparametric elements are seen to inhibit localization altogether. With these examples by way of motivation, the performance of a recently proposed finite element method in the context of strain localization in frictional materials is assessed, with particular emphasis on three‐dimensional problems. In passing, some issues pertaining to the post‐bifurcation response of biaxial specimens are examined. In particular, the numerical simulations suggest that the observed softening is a geometrical effect not attributable to constitutive behaviour.
Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties
Authors: Savvidou C. , Booker J. R.
Published: August 2005

A solution is derived for the heat flow and consolidation which occur when a heat source is buried deep in a porous thermoelastic soil having anisotropic flow properties. This solution is used to examine the pore pressure generation and dissipation near both point and cylindrical heat sources. An increase in temperature will tend to generate an increase in excess pore pressure. However, the pore water will tend to flow from regions of high excess pore pressure to regions of low excess pore pressure, and so consolidation will occur, and temperature‐generated excess pore pressures will tend to dissipate. Many natural soils exhibit horizontal layering and so have a higher horizontal than vertical permeability. It is shown that in soils the excess pore pressure generated by a heat source is significantly less than that in an isotropic soil having an equal vertical permeability.
The key blocks of unrolled joint traces in developed maps of tunnel walls
Authors: Shi Gen‐hua , Goodman Richard E.
Published: August 2005

This paper presents a general method of key block analysis for cylindrical surfaces with numerous real or statistically produced joint traces. General tunnel curves, analytically represented, are unrolled to yield a ‘developed view’ on which the joint traces are continuous curves. Then, using extended block theory, the maximum key block regions are delimited from the curved polygons of the unrolled joint trace map. The methods discussed here apply to a cylindrical tunnel of any shape in section and in any orientation, including inclined tunnels and shafts. The trace maps for which the method applies can be generated statistically, as described herein, or surveyed from real traces on exposed tunnel walls. A brief introduction to the basic theory about tunnel key blocks is provided here so that this paper can be understood without reference to other papers on block theory.
Fracture toughness of geomaterials
Authors: Siriwardane Hema J. , Layne Abbie W.
Published: August 2005

An understanding of the fracture mechanics of geomaterials is important for the solution of many problems in geomechanics. One of the most important material properties involved in fracture mechanics is the fracture toughness, KIc. The short‐rod test configuration proposed by Barker1 has significant potential for becoming a standard test for fracture toughness determination in geomechanics. The purpose of this brief is to examine the application potential of the short‐rod test for geomechanics problems.
Numerical simulation of excavation in elastoplastic soils
Authors: Borja Ronaldo I. , Lee Seung R. , Seed Raymond B.
Published: August 2005

A finite element method for simulating excavation in elastoplastic soils which produces a ‘unique’ solution for any number of excavation stages is presented. The proposed method satisfies the uniqueness principle for elastic materials postulated by Ishihara,1 and degenerates to the methods presented in the ADINA code2, 3 and by Brown and Booker4 and Ghaboussi and Pecknold5 for the simple elastic cases. The non‐linear (elastoplastic) finite element equations are derived from a variational formulation which accounts for time‐varying problem domain and boundaries. The roots of these non‐linear equations are solved by Newton's method, using the notion of the consistent tangent operator proposed by Simo and Taylor6 in conjunction with a numerical algorithm based on the ‘radial‐return’ concept for integrating stresses.7–9 Numerical examples demonstrate that in the elastic case the solution to problems involving a ‘shrinking’ (excavation) or ‘expanding’ (fill) domain is superposable and does not depend on the number of construction stages. For a monotonically shrinking elastoplastic domain and the von Mises and Drucker—Prager yield models, it is shown that the proposed method also produces a ‘unique’ solution independent of the number of excavation stages. Finally, the asymptotic quadratic convergence exhibited by the proposed method is demonstrated to show the efficiency engendered by the technique described.
On hypo‐elastic analogues of the dilatant double‐sliding model
Authors: Kruyt N. P.
Published: August 2005

The relation between the hypo‐elastic constitutive law and Mehrabadi and Cowin's dilatant double‐sliding model for cohesionless granular materials is studied. Conditions that must be satisfied by hypo‐elastic analogues of the double‐sliding model are derived constructively, and a simple example is given.
Strain‐path analyses for arbitrary three‐dimensional penetrometers
Authors: Huang An‐Bin
Published: August 2005

A numerical technique has been implemented to perform strain path analyses for arbitrary three‐dimensional (3D) penetrometers. The technique is based on that developed in aeronautical engineering for the calculation of incompressible potential flows about arbitrary 3D, non‐lifting bodies. It uses a source‐density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. The surface of a 3D body is approximated by a series of plane quadrilaterals, and the integral equation for the source density is replaced by a set of linear algebraic equations which are then solved for the source densities on the quadrilaterals. The displacements and strains are eventually derived based on these source densities. A series of strain‐path analyses have been performed for cone and flat dilatometer penetrations. Results show that the soil responses to these two types of penetrometers are fundamentally different.
Effects of geometrical and material properties on the vertical vibration of three‐dimensional foundations by BEM
Authors: Israil A. S. M. , Banerjee P. K.
Published: August 2005

The dynamic response of foundation is influenced by various mechanical properties of soil as well as the geometrical properties of the foundation. In this paper, the effects of Poisson's ratio and material damping, as well as the influences of aspect ratio and embedment depth on the dynamic stiffness of rectangular foundations are studied. Studies are also conducted to investigate the influence of the type of contact at the soil–foundation interface and the soil layer overlaying a half‐space. These studies were conducted using an advanced algorithm of the boundary element method incorporating isoparameteric quadratic boundary elements. Higher‐order elements (quadratic) were used since they can model the wavy nature of the dynamic problem accurately.
Probabilistic modelling of joint orientation
Authors: Kulatilake Pinnaduwa H. S. W. , Wu Tien H. , Wathugala Deepa N.
Published: August 2005

Observed frequencies of joint orientations are subject to error due to sampling bias. This error should be corrected before statistical inference is made on the distribution of orientation. Corrections (weighting functions) are developed for sampling bias in orientation for finite joints of different sizes and shapes intersecting rectangular exposures. Chi‐square goodness‐of‐fit procedures available for hemispherical normal and bivariate normal distributions are modified to make them applicable for both raw data and data corrected for sampling bias. The aforementioned corrections and procedures were applied to a joint orientation cluster to study the effect of (a) joint orientation, (b) joint size and (c) joint shape, on the statistical distribution of the orientation. The influences of all these aforementioned factors were found to be significant. However, at present, joint sizes and shapes are not measured in field joint surveys. Therefore, it is suggested to make attempts to obtain joint sizes and shapes in field joint mapping surveys. Since the currently available probability distributions are not adequate to represent all joint orientation distributions, it is suggested either to look for new probability distributions or to develop procedures to use empirical distributions in modelling orientation distributions.
Stress and couple stress in a layered half plane with surface loading
Authors: Mühlhaus Hans‐Bernd
Published: August 2005

In this paper the stress and moment stress distribution in a periodically layered half plane due to an arbitrary surface loading are derived. The bending stiffness of each layer is considered within the framework of Cosserat's continuum theory. Special emphasis is given to the case when the shear modulus of the one type of layer is much smaller than that of an adjacent layer. Results are illustrated for the case of a strip loading.
Finite element analyses of soil plug response
Authors: Leong E. C. , Randolph M. F.
Published: August 2005

Open‐ended pipe piles are often used in offshore foundations. The response of the soil plug inside a pipe pile is poorly understood, and only limited work has been performed to quantify the response under the different loading conditions relevant to offshore platforms. This paper describes numerical analyses that have been carried out in order to assess the end‐bearing capacity of the soil plug under loading conditions which range from undrained to fully drained. The soil plug has been modelled as either elastic, elastic–perfectly‐plastic or elastoplastic. The soil–pile interface, an important aspect of the problem, has been examined critically. Comparison with experimental data from model test at laboratory scale indicates that the load–deformation behaviour of the soil plug is modelled well using an elastoplastic model for the soil plug, and an elastic–perfectly‐plastic joint element to model the soil–pile interface. The finite element analyses show that, under typical loading conditions, adequate end bearing may be mobilized by the soil plug, largely by high effective stresses in the bottom 3–5 diameters of the soil plug.
Theory of the collapsed zone at the front of a coal seam and its effect on translatory rock bursting
Authors: Lippmann H.
Published: August 2005

If the slope of the uniaxial stress–strain diagram in the post‐failure regime is steep enough, it is shown, using a simplified (‘elementary’) theory, that the frontal zone of a coal seam close to a cavity may suddenly collapse. This collapse, well known from in situ, evidence, is also shown to reduce in most cases the danger of initiation or the strength of a subsequent coal mine bump.
A thermomechanical analysis of the G‐Tunnel heated block experiment using a compliant‐joint rock‐mass model
Authors: Costin L. S. , Chen E. P.
Published: August 2005

The results of two‐dimensional finite element analyses of several thermal/mechanical loading cycles of the G‐Tunnel heated block experiment are presented. The deformations of the block resulting from thermal loading under constant biaxial stress were determined using a recently developed compliant‐joint rock‐mass model. The results of the finite element calculations were compared to experimental results reported by Zimmerman et al. Qualitative agreements between the experimental and numerical results were obtained in all cases while quantitative agreements were achieved in some cases. The results of this evaluation are discussed.
Modelling heat and fluid flow in sedimentary basins by the finite element method
Authors: Wangen Magnus
Published: August 2005

In this article we solve the equations for a 2D model of compaction of sedimentary basins saturated with water by the finite‐element method. This compaction model considers the rock described by the porosity as a function of effective stress, and both the anisotropic permeability and the anisotropic heat conductivity as functions of porosity. The water density is approximated linearly in the water pressure and temperature, and the water viscosity is a function of temperature. The main variables in the model are the water excess pressure and the temperature, and we account for an implicit solution scheme where we solve for both main variables simultaneously. The non‐linearities in the model are either dealt with by the Newton method or by fixed‐point iterations. We compare the coupled solution of temperature and pressure with the same decoupled equations. Then we study the contribution to the temperature by convection, the effect of the non‐constant water density, and some anisotropic case examples.
Pore‐pressure response due to penetration through layered media
Authors: Elsworth Derek
Published: August 2005

A solution is developed for a point dislocation traversing a slab of saturated porous material under prescribed upper and lower hydraulic boundary conditions as an analogue to penetration in a layer of finite thickness. Pressure response is conditioned by geometrical parameters and those of dimensionless penetration rate UD, dimensionless time following penetration initiation tD, and dimensionless time following penetration arrest t′D. The extended set of dimensionless parameters controlling the response makes parameter determination problematic and questionably non‐unique. Pressure response in the proximity of a lower permeable or impermeable boundary is indistinguishable from the homogeneous case for coefficients of consolidation c in excess of 2 cm2/s. Below this threshold, penetration‐generated pore pressures are visibly modified in the presence of a discrete boundary. In situ parameters inferred directly from pressure magnitudes, without due consideration for the influence of layering, may therefore be in considerable error. In the hydraulically visible range, the influence of layering on the generated tip pressures is apparent at a separation of the order of 1·5 cm for standard penetration. Although absolute pressure magnitudes are strongly modified in the presence of boundaries, dissipation rates remain relatively unaffected and are consistent with those recorded in the absence of boundaries. The monitoring of dissipation rates, post‐arrest, is suggested as the most reliable and accurate method of extricating parameters, in situ.
Dynamic response of concrete gravity dams including dam–water–foundation interaction
Authors: Valliappan S. , Zhao Chongbin
Published: August 2005

In this paper, the gravity dam–water–foundation system including the physical and mechanical properties of the sediment at the reservoir bottom is modelled using a finite element and infinite element coupling model. The sediment at the reservoir bottom has been assumed to be a viscoelastic solid medium. The effects of thickness, elastic modulus, Poisson's ratio and material damping of the sediment on the response of the dam have been studied. The related numerical results from this study illustrated that the existence of the sediment at the bottom of the reservoir has significant effects on the response of concrete gravity dams since the soft layer of the sediment plays two main roles in the dam–water–foundation system, the energy dissipation of the system and the amplification of the incident wave on the water–sediment interface. It is the amplified acceleration on the water–sediment interface that results in different mechanisms of the effect of the sediment on the response of the dam. Therefore, apart from the incident wave, the thickness, the softness and the damping ratio of the sediment can also affect the response of the dam.
Finite‐element analysis of time‐dependent large‐deformation problems
Authors: Chopra Manoj B. , Dargush Gary F.
Published: August 2005

An updated Lagrangian finite‐element formulation has been developed for time‐dependent problems of soil consolidation involving finite deformations. Large plastic strains as well as rotations occur in such problems and nominal stress measures are introduced in the formulation to redefine stresses. This leads to corrective terms for equilibrium and yield violations in addition to geometric stiffening terms in the governing integral equations. The soil is considered to be either a linear elastic or an elastoplastic, critical‐state material. Some simple numerical examples are studied to validate the formulation, followed by a detailed analysis of the problem of penetration of a pile into soil. The results of this problem are viewed with emphasis on the physical interpretation and practical significance.