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  • 1
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 319-319 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 2
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 320-320 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 3
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 343-375 
    ISSN: 0363-9061
    Keywords: Bearing capacity ; Deformation ; Earth pressure ; Finite elements ; Friction plastic properties ; Retaining walls ; Soil mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Three constitutive models of soil are used in finite element analyses of lateral earth pressure and bearing capacity. The three models are an elasto-plastic formulation derived from the Mohr-Coulomb law, a similar model with the plastic dilatancy removed, and a strain hardening model with a capped yield criterion. Stiffness formulations are described; the non-dilatant model has a non-symmetric stiffness. The results for the retaining walls are in close agreement with classical soil mechanics, but the bearing capacity analyses greatly overestimate the bearing capacity. The patterns of motion are, however, reasonable. Reasons for the discripancies in the bearing capacity case include: (a) the elements are too stiff and do not permit sliding on discrete failure planes; (b) the bearing capacity problem is itself not well settled theoretically; (c) very fine element divisions are necessary in areas of strong stress gradients and (d) rotation of principal stresses is significant.
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  • 4
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 5
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 387-396 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 6
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 397-405 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 7
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 8
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 187-196 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 9
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 306-308 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 10
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 513-517 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A method is devised for measuring soil thermal diffusivity in situ. It is based on direct experimental simulation of the finite difference approximation to the one-dimensional heat conduction equation.The method does not require the soil to be homogeneous except between the three thermometers that are used, at depths z + d, z and z - d. Nor need the energy input curve be sinusoidal. However, it must be fairly smooth for the finite difference approximation to be accurate.Experimental results for London Clay are presented, obtained using thermometers at depths of 1, 6 and 11 cm to give a mean thermal diffusivity of 0.0074 cm2/s at a depth of 6 cm. This value is consistent with other estimates of diffusivity for clay soils.The method is capable of automation, and should be suitable for use on engineering sites, at low cost.The method is capable of generalization to other linear diffusion equations containing one independent parameter. The same limitation also applies to its application to constitutive or geometrical non-linear one dimensional diffusion equations, and each equation requires individual study to assess feasibility of use of the method.The method in effect uses the usual finite difference approximation, not to prepare a numerical solution, but to design an experiment carried out essentially within the finite difference ‘molecule’. The measured parameter of the diffusion equation is the usable product of the method.
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  • 11
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 519-529 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 12
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 589-604 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The analysis of mechanisms which could control the growth of fractures in non-homogeneous regions is of paramount importance. One such mechanism is the behavior of the fracture as it reaches a frictional interface; coupled with this is the question of re-initiation, e.g. whether a fracture can be contained within the region of initiation. Though the problems of slippage have been dealt with by other investigators, the present paper gives a more comprehensive picture and detailed treatment: effects of various frictional models at an interface are considered for a crack which intersects it at any angle; specialization then allows comparison with existing results in the literature.The problem of re-initiation, after slippage has occurred at a frictional interface, is also considered, using two different models. First, by introducing microcracks in the adjacent stratum and looking at the effects on propagation criteria and, secondly, by examining the actual distribution of the stress tangential to the slip surface; detailed computations are performed and a simple criterion for re-initiation is given, relating the re-initiation stress dominantly to the confining stress on the interface.
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  • 13
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 25-43 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 14
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 15
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 151-176 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 16
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 249-269 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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's 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 analytical 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.
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  • 17
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 323-341 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 18
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 407-407 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 19
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 57-70 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The paper deals with the propagation of shock waves at the surface of soils. Heterogeneity and damping are introduced into analytical half-space solutions. The suggested model explains two phenomena, often observed with shock propagation in actual soils, that differ from the behaviour of the homogeneous half-space: the pronounced decay of the disturbances with distance and the elongation of the disturbance into a train of waves. The effects of heterogeneity and damping are discussed quantitatively.The response of footings on heterogeneous soils has been investigated by several authors. Awojobi4 considered the Gibson soil in which the shear modulus increases linearly with depth. Luco5 and Gazetas and Roesset6 investigated a multi-layered soil, the shear modulus being constant within each layer. Gazetas7, using a technique suggested by Gupta8 extended this method to layers with linearly varying shear modulus. Little work is available on the propagation of waves in heterogeneous bodies. Some results concerning the modes and the mode shapes in heterogeneous soils were reported by Ewing, Jardetzky and Press9 and Bath.10 The modes have to be superposed in an appropriate way to obtain the displacement field at the surface. This has been approximately achieved by the finite element formulations of Lysmer, 11, Lysmer and Waas12 and Waas.13 Auersch14 applied this method to a homogeneous layer on a rigid base. He found some dispersion of the Rayleigh wave within a narrow frequency range. Finite elements combined with discrete Laplace transforms, however, consume much computer time. Rao and Goda15 and Rao16 calculated surface vibrations of a half-space with exponentially varying shear modulus and density. Their method is similar to Lamb'S1 procedure for the homogeneous half-space. Only one mode-the Rayleigh wave-occurs in their heterogeneous half-space. The examples show the considerable effect of heterogeneity on wave propagation. In the present paper, more general variations of the shear modulus are considered.
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  • 20
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 141-155 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The stress and deformation resulting from rapidly applied axial traction on the face of a cylindrical cavity in a saturated soil are analysed. A simple rate-type constitutive model is used for the effective stress response.
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  • 21
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 1-4 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 22
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 57-74 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 23
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 139-150 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 24
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 25
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 26
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 45-55 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 27
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 107-138 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 28
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 271-281 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 29
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 225-241 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A set of coupled field equations is developed for transport of liquid brine in natural rock salt. The natural rock salt consists of individual crystals brought together so that only a portion of the crystal faces or grain boundaries contribute to the hydraulically connected pore space. Transport of brine inclusions within individual crystals is considered to be thermally driven; whereas transport along crystal interfaces or grain boundaries is considered to be pressure driven. The field equations for both transport mechanisms are developed and incorporated in a finite element program. An analytical solution to a one-dimensional boundary value problem is derived and compared to the finite element solution. An application of the finite element code to radioactive waste emplacement is briefly discussed.
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  • 30
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 308-309 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 31
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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  • 32
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 71-96 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 33
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 567-588 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A computational procedure for simulating heat conduction in fractured rock masses is proposed and illustrated within the context of the finite element method. The procedure makes use of simple local models for conduction in the vicinity of a single open fracture. The local models allow effective thermal properties for fractured rock to be expressed in terms of fracture characteristics such as spacing, orientation and aperture. The distributions of fractures and fracture properties within the finiteelement model are derived from a statistical representation of geological field data. The procedure is demonstrated to satisfactorily reproduce heat transfer results across single fractures and provide an efficient means of representing conduction in formations with multiple fractures.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 197-199 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 167-185 
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    Notes: The restrictions imposed by the form-invariance principle on the structure of the elasto-plastic constitutive law for small strains are examined. It is shown that the yield and plastic potential functions may depend on the joint invariants of the stress and plastic strain tensors in addition to their dependence on the direct invariants of these tensors and additional scalar hardening parameters such as the plastic work; inclusion of the joint invariants as parameters in the constitutive functions allows for induced anisotropy during plastic deformation. It is demonstrated that the physical meaning of the joint invariants is related to the deviation of the principal directions of the stress tensor from those of the plastic strain tensor. It is also shown that only three cases of anisotropy (orthorhombic, transverse and isotropy) are possible in the types of material models discussed herein. The model proposed in this paper does not imply coaxiality between the principal directions of the stress and, plastic strain increment tensors; however, implications of the assumption of coaxiality on the structure of the constitutive equations is investigated. It is shown that coaxiality does not necessarily imply isotropy, but no deviations from coaxiality can be expected in isotropic materials.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 201-224 
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    Notes: The erosion model computes the rill and inter-rill flow over a surface with random roughness, and the erosion caused by this flow. The measured roughness of a surface is analysed and used to generate random surfaces for the simulation process. Computations are carried out over a number of time intervals; the steady state condition is assumed for each interval. Changes in the surface geometry due to erosion during an interval are used to revise the surface for the subsequent interval. The model includes simplified mechanisms to simulate ponding, deposition and failure of side slopes of rills.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 305-306 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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  • 40
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 195-216 
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    Notes: 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 yield 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 strain-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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 319-319 
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  • 42
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 283-297 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 377-386 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 5-23 
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 75-103 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 177-194 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 219-247 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 399-407 
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    Notes: A simple and effective extension to the boundary element method for solving Laplace'S equation (∇2u = 0) for boundary value problems is presented to solve steady confined and (or) steady unconfined seepage problems in zoned anisotropic mediums. Sample problems indicating the accuracy of results are given.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 411-426 
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    Notes: Circular ring footings on an elastic stratum are considered. The static and dynamic stiffnesses are calculated using an efficient numerical technique. The results indicate that the static torsional and rocking stiffnesses of a ring footing do not deviate significantly from the corresponding stiffness of the circular footing for values of the inner-radius-to-outer-radius ratio up to about 0.75. The static horizontal and vertical stiffnesses change considerably only for values of this ratio greater than about 0.60. The change in the stiffness and damping coefficients is small for values of the ratio between 0 and 0.5.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 101-123 
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    Notes: We employ a finite element method to consider the numerical solution of Aifantis' equations of double porosity.1-5 The physical and mathematical foundations of the theory of double porosity were considered in two previous papers, 6,7 where analytical solutions of the relevant equations are also given. For practical purposes and for the completeness of the presentation, we re-derive the basic equations without resorting to the more rigorous scheme of multiporosity theory.1-6 Instead, we follow the more familiar approach of Biot8,9 which we now extend from the case of single porosity to the case of double porosity. Then a general finite element formulation of the relevant eqations is thoroughly discussed and explicitly described for the two-dimensional case where four-node rectangular non-conforming isoparametric elements are employed. Three numerical examples are presented in detail to illustrate the method and assess the differences between single and double porosity models in consolidation.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 359-379 
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    Notes: The most flexible and generally applicable methods for elasto-plastic analysis are those based on an incremental-iterative form of the initial stress approach, but such methods often exhibit slow convergence. The acceleration procedure known as the alpha-constant stiffness method is reconsidered and some modifications are proposed. The principal difference in the present approach lies in the use of a single acceleration parameter, rather than a diagonal matrix of acceleration coefficients. The new scheme shows a significant improvement in numerical stability and converges three times faster than the standard initial stress method. Some practical aspects associated with the method are discussed and a number of applications are presented.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 381-398 
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    Notes: The general forms for the field equations governing the transient response of poroelastic media given by Biot and by Zienkiewicz are compared and relations between the material constants are obtained. A one-dimensional analytical solution is presented for the situation where the solid and fluid materials satisfy Biot'S dynamic compatibility relation. The transient response of porous media is illustrated for varying degrees of solid and fluid compressibility when subjected to step, cyclic and short duration spike surface tractions. The results obtained (for the special situation where the materials are dynamically compatible) exhibit the overall characteristics of wave propagation in porous media and will provide representative test problems which allow a quantitative evaluation of the accuracy of various numerical solution methods (e.g. finite element models).
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 457-471 
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    Notes: A rheological model which is able to explain the delayed failure phenomenon has been proposed and applied to the analysis of the time dependent behaviour of deep tunnels. The model is the three element Voigt type before yielding and becomes the five element Voigt type after yielding. This means that the stiffness of the model is decreased by yielding. It is assumed that the yielding takes place when the stored elastic energy density of distortion reaches a certain maximum value. Some experiments to determine material constants are proposed. The numerical results clearly exhibited a delayed failure state of the rock masses around the tunnel surface. It was found that the extension of the yielding zone due to tunnel excavation depends on the opening method.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 503-509 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 125-140 
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    Notes: An analytical solution for rapid (undrained) expansion of a long cylindrical cavity from initially zero radius is presented. A simple rate-type soil model possessing the salient features of the modified Cambridge critical state model is used. Application of the solution to determination of the stress field surrounding a pile immediately after driving is discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 259-286 
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    Notes: A large proportion of the constitutive models currently employed in Geomechanics are based on the theory of plasticity. Owing to the limitations of the data obtained from conventional testing equipment, arbitrary assumptions are often made about the behaviour of the material in generalized stress space.In this paper it is shown that the Lode angle of the stress state at failure in plane strain deformation is dependent on the shape adopted for the plastic potential. The influence of the shape of the plastic potential in the deviatoric plane on the predicted behaviour of two boundary value problems both prior to and at failure is then considered. In both cases a form of the Modified Cam Clay model is employed to describe the soil behaviour, and numerical predictions are obtained using a finite element computer code. For drained situations it is shown that the Lode angle of the stress state at failure has a dominating influence on the predicted behaviour. However, for undrained cases the effects are not so important as long as the correct undrained strength at failure is enforced.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 297-303 
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    Notes: A variational principle and the corresponding finite element equations for determination of the stream function for soil seepage problems is given using the standard finite element potential solution as data. The procedure is very simple and independent of the element type employed. Generalization of the method to multiply connected domains is included.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 325-342 
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    Notes: An analytical solution is presented for the time-dependent stresses and displacements in plane strain around a circular hole when it is loaded by an axisymmetric internal and far-field pressure. The material is assumed to be elasto-viscoplastic with dilatant plastic deformations according to a non-associated flow rule. Strain softening is considered by a modified St. Venant slider which is characterized by Mohr-Coulomb yield conditions for both the peak and the residual strengths.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 409-409 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 445-455 
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    Notes: An analytical solution to the problem of a load applied to a portion of the wall of a circular tunnel installed deep in a homogeneous isotropic material has been found. The solution is obtained by taking a Fourier transform, in the axial direction, of the field quantities and then representing these as a Fourier series in the polar angle. The integration which is necessary for the inversion of Fourier transforms has to be performed numerically using Gaussian quadrature.The solution has been used to analyse the problem of uniform normal loading applied over rectangular patches of the tunnel wall. An indication of how the solution can be applied to the tunnel jacking problem is given.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 19-43 
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    Notes: The idea of using a thin solid element, called a thin-layer element, in soil-structure interaction and rock joints is proposed. A special constitutive model is used and various deformation modes such as no slip, slip, debonding and rebonding are incorporated. The shear stiffness is found from special laboratory tests and the normal stiffness is assumed to be composed of participation of the thin-layer element and the adjoining solid elements. A parametric study shows that the thickness of the thin-layer element can be such that the ratio of thickness to (mean) dimension of the adjacent element is in the range of 0.01 to 0.1. A number of simple and practical problems are solved to illustrate the success of the thin-layer element for soil-structure interaction problems.
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    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 299-318 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 1-17 
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    Notes: Most deposited sands exhibit anisotropic behaviour. A plasticity model has been proposed with the capacity for simulating such anisotropic behaviour. The proposed model contains a number of coefficients of anisotropy. Methodology for determination of the coefficients of anisotropy has been discussed. Using experimental data, the coefficients of anisotropy have been determined for a number of well-known sands. Stress-dilatancy has been modelled by using the ‘normalized work’ and it has been shown that the normalized work is independent of inherent anisotropy. Finally, some reasonably close comparisons between experimental results and model simulations have been reported.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 157-166 
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    Notes: This paper examines the problem of the flexure of a strip of finite width which is embedded in bonded contact with an isotropic elastic medium of infinite extent. The analysis of the problem is applicable to flexible beams of narrow width which experience flexure only in the longitudinal direction. Numerical results are developed for the maximum flexural moment induced in the embedded beam due to the action of a concentrated force.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 243-257 
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    Notes: A smoothing technique is developed to remove the oscillatory errors in initial nodal pore pressures, associated with the use of quadratic isoparametric elements to model soil consolidation. Numerical results using this technique are compared with the performance of other types of element in problems of one-and two-dimensional consolidation.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 287-296 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The dispersion of torsional surface waves in two types of inhomogeneous elastic media is discussed (1) in a half-space with shear modulus varying linearly with depth and with constant density (Gibson'S half-space) and (2) in a half-space with shear modulus varying with the square-root of the depth co-ordinate and with constant density. Inhomogeneous media with constant shear wave velocity are also reviewed and the obtained solutions are discussed in relation to appropriate boundary conditions.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 311-323 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Constitutive models for description of the non-linear stress-strain behaviour of engineering materials are often developed and presented in forms which cannot be employed directly in non-linear matrix computer analysis codes. Presented herein is a procedure for developing the incremental stiffness matrix for an elasto-plastic material model with multiple, intersecting yield surfaces. Associated or non-associated flow may occur on the individual yield surfaces. The material stiffness matrix is non-symmetric if non-associated flow occurs on any one of the yield surfaces. In order to illustrate the matrix forms which are generated, the case of a recently developed model with two yield surfaces is presented in detail. This model involves associated flow on one and non-associated flow on the other yield surface.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 45-55 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The work presents an exact expression for the Hankel transform of the surface displacement of a rigid circular body performing harmonic vertical vibrations on a homogeneous elastic half-space of arbitrary Poissn'S ratio interrupted at some depth by a frictionless horizontal plane. The limiting case of the uninterrupted half-space is recovered in each of the extreme cases when the frictionless plane coincides with the surface or sinks to an infinite depth. Furthermore, the static case is derived in the limiting case of zero frequency and it is shown that the result agrees with the limiting case of zero gradient shear modulus variation for the static case of the incompressible non-homogeneous half-space.It is also established that Poisson'S ratio effect is linear, and the important proposition is again sustained that only surface shear modulus dominates vibrations on elastic media whereas any other factor such as the interruption of the frictionless plane as in the present case, merely constitutes a negligible secondary parameter.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 97-100 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 473-492 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A simple rigid block model has been developed for analysing the stability of caverns and tunnels in jointed rock. Rigid block interactions are idealized as linear edge-to-edge contacts with a zero joint tension constraint and a Mohr-Coulomb friction law. In the method, the minimum friction angle for stability is determined by sequentially eliminating tension and then minimizing the shear. It is demonstrated through examples that the minimum joint friction angle which results in a stable configuration is independent of the stiffness of the joint, and depends only upon the loading and geometry of the jointing and cavern. This insensitivity of stability to the normal and tangential joint stiffnesses, which can be difficult to obtain, is very useful for design purposes.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 511-511 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 605-605 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 606-606 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 343-357 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 409-409 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 427-444 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Numerical solutions have been obtained for stresses and displacements in a linear elastic half space due to distributed loads of circular, rectangular and elliptical shapes. The technique primarily involves use of a multi-dimensional numerical integration technique to integrate point load solutions over the distributed loading after discretizing the area into a finite number of elements. Both uniform vertical and shear loads have been considered as well as vertical conical loads and inward shear loads. The technique evolved facilitates the determination of stresses and displacements by the use of mini-computers and is neither as tedious and cumbersome as the use of tables and charts nor as costly as FEM solutions.A detailed comparison has been presented between the results obtained by the numerical solutions and those of the existing analytical solutions wherever they are available. It is found that the agreement between the two is within one per cent for displacements at all depths for the different cases studied. The matching is also good in the case of stresses, except at shallow depths.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 493-502 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A differential slice technique is applied in order to obtain the solution for the pressure distribution on rigid retaining walls. The technique is based on a statical analysis of a plane differential slice, for which only the global equilibrium is required. An analytical solution to the problem is found for a non-cohesive material and a linear slip surface. For more complicated cases the numerical solution is required.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 531-548 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 549-566 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: An approximate step-by-step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non-approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint.
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