Showing papers in "International Journal for Numerical and Analytical Methods in Geomechanics in 1977"
TL;DR: In this article, a new model for rocks and rock-like material with multiple planes of weakness is proposed and the behavior of the assembly applies tensile and mohr-coulomb shear limits on each such plane with possible strain dependence of frictional properties.
Abstract: A new model for rocks and rock-like material with multiple planes of weakness is proposed. The behaviour of the assembly applies tensile and mohr-coulomb shear limits on each such plane with possible strain dependence of frictional properties. The visco-plastic algorithm which allows the incorporation of time effects is used to obtain static solutions. The model is illustrated in actual context by applications to stability of rock slopes and behaviour of tunnels. A generalization of the model to include arbitrary three-dimensional distribution of laminae in 'quasi-plane strain' is included. The effect of various flow rules adopted for plastic straining is indicated.(a) /TRRL/
230 citations
TL;DR: In this article, a general analytical model was proposed to describe the anisotropic, elasto-plastic, path-dependent, stress-strain strength properties of inviscid saturated clays under undrained loading conditions.
Abstract: The proposed general analytical model describes the anisotropic, elasto-plastic, path-dependent, stress-strain-strength properties of inviscid saturated clays under undrained loading conditions. The model combines properties of isotropic and kinematic plasticity by introducing the concept of a field of plastic moduli which is defined in stress space by the relative configuration of yeidl surfaces. For any loading (or unloading) history, the instantaneous configuration is determined by calculating the translation and contraction (or expansion) of each yield surface. The stress-strain behaviour of clays can thus be determined for complex loading paths and in particular for cyclic loadings. The stress-strain relationships are provided for use in finite element analyses. The model parameters required to characterize the behaviour of any given clay can be derived entirely from conventional triaxial or simple shear soil test results. The model's extreme versatility is demonstrated by using it to formulate the behaviour of the Drammen clay under both monotonic and cyclic loading conditions. The parameters are determined by using solely the results from monotonic and cyclic stain-controlled simple shear experimental tests, and the model's accuracy is evaluated by applying it to predict the results of other tests such as (1) cyclic stress-controlled simple shear tests, (2) monotonic triaxial loading compression and unloading extension tests, and (3) cyclic stress- and strain-controlled triaxial tests on this same clay. The theoretical predictions are found to agree extremely well with the experimental test results. /Author/
202 citations
TL;DR: In this paper, finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs and evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
Abstract: Several finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs. Their numerical performance is evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
76 citations
TL;DR: In this article, a series of finite element analyses were performed to study the behavior of two parallel and adjacent tunnels and various sequences of excavation of the two tunnels and installation of tunnel liners have been simulated in the analyses.
Abstract: A series of finite element analyses were performed to study the behaviour of a system of two parallel and adjacent tunnels. Various sequences of excavation of the two tunnels and installation of tunnel liners have been simulated in the analyses. Influence of various parameters on the behaviour of the two parallel tunnels has been investigated. The important parameters considered in this study are: the width of the pillar separating the two tunnels; the tunnel depth; support condition; sequence of excavation; and, to some extent, the influence of plastic yielding in the medium surrounding the two tunnels.
63 citations
TL;DR: The use of discrete models for the dynamic analysis of a contiuum requires the existence of a finite domain with well defined boundaries as mentioned in this paper, which may be necessary to apply appropriate conditions on forces or displacements at the boundary nodes to reproduce the physical behaviour of the actual problem.
Abstract: The use of discrete models for the dynamic analysis of a contiuum requires the existence of a finite domain with well defined boundaries. When these boundaries do not exist naturally but have to be artificially imposed it may be necessary to apply appropriate conditions on forces or displacements at the boundary nodes to reproduce the physical behaviour of the actual problem. In the solution of soil structure interaction problems these conditions are simulated through the use of transmitting boundaries. In this paper several of these boundaries are evaluated comparing the results they produce in the amplification of seismic motions, the determination of foundation stiffnesses and the structural response. The distance of the boundaries to the zone of interest, the level of excitation (influencing the amount of internal soil damping), the geometry of the problem (finite soil layer versus a half-space) and the relative frequency of the structure with respect to the soil and the specified motion are all parameters which must be taken into account for this evaluation.
54 citations
TL;DR: In this paper, a formulation and a numerical solution method for problems which involve finite deformations of an elasto-plastic material is presented and the governing equations are cast in rate form and the constitutive laws are formulated in a frame indifferent manner.
Abstract: SUMMARY Presented in this paper is a formulation and a numerical solution method for problems which involve finite deformations of an elasto-plastic material. The governing equations are cast in rate form and the constitutive laws are formulated in a frame indifferent manner. Particular reference is made to the finite deformation of soil. Plastic failure is described by a general yield condition and plastic deformation by an arbitrary flow rule. Several examples are treated numerically. INTRODUCI'ION In the formulation of theories in applied mechanics and in particular soil mechanics, it has been a common practice to assume that strains, both elastic and plastic are infinitesimal and, that the initial geometry of a deforming body is not appreciably altered during the deformation process. These assumptions are less justified for soil than for such materials as steel and concrete. Theories of finite strain that relax some of these restrictive assumptions have been developed and there exists a considerable body of literature on what might be called the classical elastic large strain theory'-5 (e.g. the large deformation of materials like rubber has been In contrast to the methods of these early investigators, many more recent studies have preferred an incremental appr~ach"~ to facilitate the analysis of the more general class of inelastic materials whose constitutive laws are expressible in terms of incremental or rate quantities. For such formulations the solution of a given problem is found by following a specified loading path. In most cases the governing equations cannot be solved analytically and it is necessary to adopt an approximate numerical technique." Much recent work has been devoted to formulating analyses for plate and shell problems involving large displacement but small strains (a survey is given by Marcal"). As has been noted'* these formulations are inappropriate for applications to bulky geometries such as occur in many problems in soil mechanics. Several attempts have been made to formulate a finite deformation theory suitable for use with soils. An example is that of Thoms and Arman13 who directly applied a technique of ArgyrisI4 to the problem of an embankment constructed on soft clay. The analysis was restricted to an elastic material and theoretical results were compared with results from photo-elastic model tests. Davidson and Chen" have given some solutions for the problem of footings on clay while Fernandez and Christian16 examined flexible footing and retaining wall problems. In this paper a formulation is given for the solution of problems of finite elasto-plastic flow without restricting deformation magnitude. Plastic failure is described by a general yield condition and plastic deformation by an arbitrary flow rule. The theory is developed for a general constitutive law which relates an objective stress rate to the strain rate. This theory has applications to such problems as: the penetration of embankments into very soft soil; the behaviour of layers of normally consolidated clay in which both elastic modulus and undrained
47 citations
TL;DR: In this paper, a finite element study is presented of the short-term effects that develop when a tunnel is driven in a ground showing viscous behaviour associated with the deviatoric deformations.
Abstract: A finite element study is presented of the short-term effects that develop when a tunnel is driven in a ground showing viscous behaviour associated with the deviatoric deformations. Axisymmetric conditions around the tunnel centreline are assumed and the process of excavation is simulated by means of a step-by-step time incremental technique. The Kelvin model is used to approximate the medium creep behaviour and a simple procedure is presented that allows the determination of the creep model constants from the laboratory test data. Various rates of advancing the presence of an unsupported zone close to the tunnel face and the temporary interruption of the excavation process are considered. For the viscous model and the anlaytical technique used, simple, approximate relationships are presented for the displacements around the tunnel and the overexcavation volume as functions of the rate of excavation advancing. /Author/
39 citations
TL;DR: In this article, a comparison study with a finite element consolidation model was conducted in the Polesine region in the northeast of Italy, showing that the model is capable of simulating the field behaviour during production and also after the closure of the wells.
Abstract: The Polesine, a region in the northeast of Italy, has experienced considerable surface subsidence due to the withdrawal of water and gas from the underlying reservoir sediments. These settlements have been well documented and form the basis of a comparison study with a finite element consolidation model. It is shown that the model is capable of simulating the field behaviour during production and also after the closure of the wells. /Author/
30 citations
19 citations
TL;DR: In this paper, three constitutive models of soil are used in finite element analyses of lateral earth pressure and bearing capacity: an elasto-plastic formulation derived from the Mohr-Coulomb law, a similar model with the plastic dilatancy removed, and a strain hardening model with a capped yield criterion.
Abstract: Three constitutive models of soil are used in finite element analyses of lateral earth pressure and bearing capacity. The three models are an elasto-plastic formulation derived from the Mohr-Coulomb law, a similar model with the plastic dilatancy removed, and a strain hardening model with a capped yield criterion. Stiffness formulations are described; the non-dilatant model has a non-symmetric stiffness. The results for the retaining walls are in close agreement with classical soil mechanics, but the bearing capacity analyses greatly overestimate the bearing capacity. The patterns of motion are, however, reasonable. Reasons for the discrepancies in the bearing capacity case include: (a) the elements are too stiff and do not permit sliding on discrete failure planes; (b) the bearing capacity problem is itself not well settled theoretically; (c) very fine element divisions are necessary in areas of strong stress gradients; and (d) rotation of principal stresses is significant. /Author/
18 citations
TL;DR: A semi-empirical creep law is derived from thermodynamic principles and experimental results in this article for a cavity with the shape of a prolate spheroid in dome salt with emphasis given to the excavation phase.
Abstract: The stress field and flow characteristics are studied for a cavity with the shape of a prolate spheroid in dome salt with emphasis given to the excavation phase. A semi-empirical creep law is derived from thermodynamic principles and experimental results. In this paper, an elementary non-linear form is used in the kinetic relation. A finite element solution procedure is discussed which incorporates the creep law, excavation sequence, and arbitrary non-homogeneous initial stress field.
TL;DR: In this paper, a tow-dimensional finite difference wave propagation code was used to analyse the impact of a rigid, ogival-nosed penetrator with a target consisting of thin alternating layers of silt, sand, and clay.
Abstract: A tow-dimensional finite difference wave propagation code was used to analyse the impact of a rigid, ogival-nosed penetrator with a target consisting of thin alternating layers of silt, sand, and clay. The response of the idealized target was described with an elastic-plastic constitutive model depending upon two stress invariants and the history of plastic deformation. Interfacial friction between the penetrator and target was assumed to be negligible.
Comparisons are made of calculated results and those of nominally similar experiments conducted at the Watching Hill test site in Alberta, Canada. Analysis of these comparisons reveals that numerical methods like the one employed in this study can yield insight into penomena, as well as suggesting possible improvements in the calculation technique.
TL;DR: Some recently developed implicit time discretizations are discussed whose main application is to solving ordinary differential equations arising from finite element approximations to partial differential equations.
Abstract: Some recently developed implicit time discretizations are discussed whose main application is to solving ordinary differential equations arising from finite element approximations to partial differential equations. Their theoretical properties, computer implementation and numerical behaviour, as observed in tests on simple examples, are compared with well-known discretizations such as the Crank-Nicholson method.
TL;DR: In this article, the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi, and an approximation theory, including a priori error estimates, is developed using finite element methods and an associated numerical scheme is given.
Abstract: The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h1.25-δ), 0 < δ < 0.25, respectively, if the permeability is constant.
TL;DR: In this paper, an incremental finite element technique was applied to problems of shallow foundations of homogeneous as well as multilayer soils, based on a variational principle which is suitable for such problems.
Abstract: This paper presents a rational approach to the finite strain analysis of elastic-plastic materials. An updated incremental finite element technique was applied to problems of shallow foundations of homogeneous as well as multilayer soils. This was based on a variational principle which is suitable for such problems.
TL;DR: In this article, an approximate method, using a simplified soil model, for predicting the behavior of raft foundations subjected to applied vertical forces and moments is outlined, and results obtained for circular rafts of finite rigidity are compared with those obtained, from more rigorous solutions, by other authors.
Abstract: An approximate method, using a simplified soil model, for predicting the behaviour of raft foundations subjected to applied vertical forces and moments will be outlined. Results obtained for circular rafts of finite rigidity are compared with those obtained, from more rigorous solutions, by other authors. Satisfactory agreement is obtained for the surface settlements and raft bending moments over a wide range of soil inhomogeneity. Finally, the versatility of the method of analysis is illustrated for an unusual asymmetrical structure. Computed total and differential settlements are shown to be in reasonable agreement with measured values and those predicted by an independent plane strain finite element analysis.
TL;DR: Both of these texts should be of value to geomechanics engineers, particularly in the areas of storage efficiency, linear equation solution accuracy and eigenvalue algorithm choice.
Abstract: The types of analytical problem facing the present-day geomechanics engineer, apart from limit equilibrium calculation, tend to fall into three categories, namely equilibrium, eigenvalue and propagation problems. The sets of equations which have to be solved are usually generated by finite difference or finite element approximations to differential equations. Since it is of the greatest importance that the equations are economically and accurately solved, these two texts on this theme are timely. Both caver much of the same ground, but from somewhat different standpoints. The first two chapters of both books introduce the reader to the concepts of linear algebra and matrix notation. Thereafter Jennings writes in general terms, whereas Bathe/Wilson orientate their presentation specifically towards finite element approximations. Their Chapters 3 to 6 cover formulation of the FEM, isoparametric elements, variational formulations and implementation of the FEM by means of an in-care static analysis program STAP. A feature of Jennings’s book is the presentation of parallel subroutine algorithms in ALGOL and FORTRAN for matrix handling and equilibrium equation solution, for example by Gaussian elimination and by Choleski’s method for variable bandwidth equations, in Chapters 3 to 6. In Chapters 8 and 9 of Bathe/Wilson, solution of propagation (initial value) problems is discussed, with a good discussion of algorithm performance. The final chapters of both books, 7 to 9 of Jennings and 10 to 12 of Bathe/Wilson deal with eigenvalue problems which are less familiar ground for geomechanics specialists, although assuming greater importance daily in connection with earthquake and offshore engineering for example. Here the scope for inefficiency in algorithm choice is much wider than in linear equation solution and the reader’s attention is rightly directed to Sturm sequence and subspace/simultaneous iteration processes. Bathe/Wilson include program coding for such a method. Both of these texts should be of value to geomechanics engineers, particularly in the areas of storage efficiency, linear equation solution accuracy and eigenvalue algorithm choice.
TL;DR: In this paper, the surface settlement due to the shield tunnel opening in the relatively shallow diluvium deposit is analyzed using the finite element method and a simplified numerical method for computing the surface settlements due to tunnelling.
Abstract: When shallow tunnels are constructed under streets and buildings, surface settlement due to the tunnelling and its control becomes essential to prevent any environmental problems. This paper deals with finite element analysis and a simplified numerical method for computing the surface settlement due to tunnelling. The computed results are compared with the observations made during the construction of the shield tunnel through the diluvium deposit. The surface settlements due to the shield tunnel opening in the relatively shallow diluvium deposit are analyzed using the finite element method. The surface settlement computed from the elastic finite element analysis are added to the one from the empirical equation based on the lowering panel test. Non-linear finite element analysis was also carried out in order to account for the non-linearity of the soil. The analytical results are compared with the observed surface settlement obtained from the field measurement at the shield tunnelling site. In the sandy ground, it was noted that the elastic and plastic deformations occurred rapidly and that 95% of the final settlement was reached within 2 weeks. It was also noted that the non-linear finite element analysis using the hyperbolic representation of stress-strain relation gave a good estimate of the pattern of surface settlement. Finally, when only the final surface settlement due to the tunnel opening is required, it can be easily estimated from the summation of the elastic settlement and the settlement caused by local yielding.
TL;DR: In this paper, a numerical step-by-step procedure analogous to the initial stress method is presented for the analysis of a single-layer jointed rock beam subjected to gravity loads and in-plane in situ formation pressure.
Abstract: A numerical step-by-step procedure, analogous to the ‘Initial Stress Method,’ is presented for the analysis of a single-layer jointed rock beam subjected to gravity loads and in-plane in situ formation pressure. The joints are permitted to open at locations where the flexural stresses exceed flexural strength. The material properties may be different for each rock block and joint. A detailed algorithm is given for the solution of the problem. The results of several analyses indicating the relative effects of initial formation pressure, transverse load, stiffness of the joint material, and joint spacing on the response of a jointed beam are presented. The convergence characteristics of the numerical procedure are included. The joint material is assumed to be ‘no-tension’ type. Both the geometric and material non-linear effects are considered.
TL;DR: A method is presented for the analysis of composite structures with prescribed frictional conditions at the interfaces that can also be used for the piecewise solution of large structures.
Abstract: A method is presented for the analysis of composite structures with prescribed frictional conditions at the interfaces. The method, which can also be used for the piecewise solution of large structures, is illustrated by analyzing a test problem with two interfaces.
TL;DR: In this article, a finite element formulation for a linear viscoelastic ageing material is developed, which is shown that these equations can be solved in the from of an eigenvalue expansion thus reducing the problem to the solution of a set of Volterra Integral equations.
Abstract: In this paper a finite element formulation for a linear viscoelastic ageing material is developed. It is shown that these equations can be solved in the from of an eigenvalue expansion thus reducing the problem to the solution of a set of Volterra Integral equations. An alternative method of solution based on expansion in terms of an operator related to Poisson's ratio is also developed and this solution method is found to significantly reduce the computational effort necessary in the solution of aproblem.