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  • Articles  (225)
  • Engineering General  (224)
  • Chemistry
  • 1980-1984  (225)
  • 1925-1929
  • Geosciences  (225)
  • 1
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    Springer
    Pure and applied geophysics 118 (1980), S. 128-151 
    ISSN: 1420-9136
    Keywords: Galactic cosmic rays ; Solar proton events ; Particle precipitation ; Chemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract An assessment is made of the relative contribution of certain classes of energetic particle precipitation to the chemical composition of the middle atmosphere with emphasis placed on the production of odd nitrogen and odd hydrogen species and their subsequent role in the catalytic removal of ozone. Galactic cosmic radiation is an important source of odd nitrogen in the lower stratosphere but since the peak energy deposition occurs below the region where catalytic removal of O3 is most effective, it is questionable whether this mechanism is important in the overall terrestrial ozone budget. The precipitation of energetic solar protons can periodically produce dramatic enhancement in upper stratospheric NO. The long residence time of NO in this region of the atmosphere, where catalytic interaction with O3 is also most effective, mandates that this mechanism be included in future modelling of the global distribution of O3. Throughout the mesosphere the precipitation of energetic electrons from the outer radiation belt (60°≲Λ≲70°) can sporadically act as a major local source of odd hydrogen and odd nitrogen leading to observable O3 depletion. Future satellite studies should be directed at simultaneously measuring the precipitation flux and the concomitant atmosphere modification, and these results should be employed to develop more sophisticated models of this important coupling.
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  • 2
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 3
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 323-324 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 4
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-148 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 5
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 6
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 287-290 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The effectiveness of the heat balance integral approach in determining the extent of frost penetration of the ground is illustrated.
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  • 7
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 1-23 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: One major problem encountered when using the finite element method to simulate the load-deformation behaviour of an elasto-plastic soil mass is that the theoretical collapse load is generally exceeded, and in some cases the numerical solution fails to exhibit a collapse load. A mixed variational principle is used as the basis for developing the governing equations of deformation and the results from this are compared with those obtained from the use of the virtual power equation. The former is found to give improved results and is generalized to include description of finite deformation. An Eulerian frame of reference is used. The method of approximating configuration changes in the numerical solution procedure is found to determine the shape of the load-deformation curve. Finally, a simple method of accounting for anisotropy of yield is presented.
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  • 8
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 73-88 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: We continue our study of the consolidation of inhomogeneous clay soils with an analysis of the response of a soil mass, whose shear modulus increases linearly with depth, to axially symmetric pressure on its surface. This extends the work reported in Part I on the corresponding one-dimensional problem of a clay column, and generalizes researches of Gibson and coworkers on the elastic model of the soil (i.e., the initial response).Because of great mathematical complexity when Poisson's ratio is allowed to assume arbitrary values, we have confined ourselves (as did Gibson in several of his papers) to variations of the modulus from a zero surface value, this being in reasonable accord with published test results on London clay. The deflection of points within this region, the deflection relative to the central one (that is, the shape of the deformed loading area), as well as the absolute deflection of surface points exterior to the load.
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  • 9
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 57-72 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The settlement and excess pore pressure are calculated for a column of water-saturated clay in which the permeability and/or shear modulus vary with depth. Several fairly general laws of variation are investigated. In each case, the soil is assumed to have a permeable top surface and to rest on an impervious substrate.For all the variations examined, in which the shear modulus increases with depth below the surface but the permeability of the soil remains constant, the deflection at a given instant after imposition of the load decreases and the degree of settlement increases with increasing rate at which the change with depth takes place. It is found that, when the variation over the height of the column is one order of magnitude or less, the curve of degree-of-consolidation versus time is reasonably wellapproximated by the curve for a homogeneous soil whose modulus equals the depth-averaged value. When, in addition, the permeability decreases with depth, the approximation becomes less accurate.The same approximation, for moderate increase in shear modulus with depth, predicts satisfactorily the process of dissipation of excess pore pressure at a given depth, but breaks down when the variation in modulus is large.Finally, it is shown that the effect of variable modulus on the settlement is greater than of a comparable variation in permeability.
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  • 10
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 11
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. ii 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 12
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 435-455 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The consolidation problem in a plane strain porous elastic medium is treated by adopting a consistent formulation of the finite element model. To this purpose, the fluid-phase behaviour is modelled in static terms through a piecewise linear description of the pore pressure field and the behaviour of the two-phase medium is consistently modelled through rigorously equilibrated piec̰ewise linear stress distribution.Incompressibility of the pore fluid and of the skeleton grains is assumed, as is linear elastic behaviour of the solid phase.After a compact description of the model, the governing equations for the continuum problem are recalled and the solution system for the discretized problem is obtained following Galerkin's method of weighted residuals. Some examples are finally illustrated, in order to assess the reliability of the approach and to introduce possible comparisons with other methods.
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  • 13
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 209-223 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 14
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 283-285 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 15
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 286-286 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 16
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 305-320 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 17
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 321-336 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 18
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 371-384 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 19
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 20
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 419-433 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: This paper presents the complete formulation for the application of the Boundary Element Method to solve non-tension material problems. The formulation is based on including an extra term due to an initial stress field into the boundary integral statement. This is then used to iterate the solution until a state of non-tension is achieved. The resulting iteration process is very simple to apply and basically consists only of a single matrix-vector product. The applications show that accurate resultscan be obtained for boundary discretizations involving a small number of unknowns. Whenever possible, results are compared with analytical solutions or finite elements.
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  • 21
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 499-499 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 22
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 500-501 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 23
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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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  • 24
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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
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  • 25
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 217-224 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: For non-linear dynamic problems, it has been recognized that an explicit time-integration method of approach is a very efficient way of solving the dynamic equations of motion. The numerical formulation and computation for such problems fall into the two general categories of finite elements and finite differences. Over the years, there have been many arguments between schools which adopt the finite element approach and those which adopt the finite difference approach. At one extreme, arguments areconcerned with the superiority of each approach and at the other end of the spectrum the arguments are about which approach is a subset of the other. The most common of these arguments are concerned with efficiency and accuracy. This publication addresses the accuracy issue with specific reference to explicit calculations in which the analysis domain is discretized into triangular or quadrilateral plane-strain elements. It concludes that if the same basic assumptions are made in the two approaches, they, will give identical answers for problems in this category.
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  • 26
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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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  • 27
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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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  • 28
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 139-140 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 29
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 143-171 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Computational procedures for implementing some constitutive models are described and introduced in three-, and two-dimensional finite element procedures; here variable moduli, Drucker-Prager, critical state and cap models are considered. Consistent numerical schemes are presented with applications to a number of example problems. These procedures can provide successful results with advanced constitutive laws for three-dimensional analysis of a wide range of non-linear problems.
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  • 30
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 225-243 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: 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.
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  • 31
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 285-285 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 297-303 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 445-455 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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 4 (1980), S. 25-43 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A finite element model for the prediction of discrete fracture propagation in rock structures loaded in compression is presented. The model integrates any one of three theories for mixed-mode fracture initiation; it contains an energy balance algorithm for predicting crack increment length, and incorporates recent developments in finite element stress-intensity factor computation. The predictions of the model are compared with the observed fracture response of a real rock structure. Results show that the model accurately predicts both stable and unstable fracture progagations observed experimentally.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 185-189 
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    Notes: A method for determining the load-deformation response of a pile in a softening soil is presented. The results demonstrate the degree to which the flexibility of the pile can affect its ultimate capacity.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 255-276 
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    Notes: A finite element theory, suitable for describing the long-term transient thermal creep of geomechanical structures where the material obeys an arbitrary type of creep law, is presented. The method takes into account large deformation effects, is stable for the large time steps required to model geophysical phenomena and accurately simulates changing, incompressible, plastic flow fields. Applications of the theory to the prediction of long-term creep and creep rupture of simple engineering structures, are given. The theory is also applied to predict the thermal creep of layered media to study the mechanics of folding and rift formation.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 389-391 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 33-56 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical approach is presented for the ‘identification’ (or back calculation) of the earth pressure acting on embedded or retaining structures. The procedure is applicable to structures of any shape and requires a set of in situ measurements that may include displacements of points on the structure, values of concentrated forces, values of distributed loads at some locations, etc. Possible limiting values of the unknown loads, non-linear structural behaviour, varying accuracies of the input data are accounted for in the problem formulation. Depending upon the type of problem, the solution is reached by means of the unconstrained or constrained minimization of a suitably defined error function. As an example, the proposed approach is applied to the identification of the earth pressure acting on some typical geotechnical engineering structures.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 115-138 
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    Notes: The quasi-static development of the force, pore pressure and displacement is obtained in the system of a circular elastic pile partially embedded in a saturated porous elastic soil, and loaded axially on the top. The porous elastic soil is governed by Biot's theory. The problem is decomposed into two systems, namely, an extended porous elastic half-space in the absence of the pile characterized by the material constants of the medium, and a fictitious pile represented by a Young's modulus equal to the difference between the Young's moduli of the real pile and the medium. The problem is found to be governed by a Fredholm integral equation of the second kind. Laplace transforms are applied to time functions involved, and Hankel transforms to the radial coordinate of which the origin is at the centre of the pile. Numerical solutions are obtained for final and initial solutions for various practical values of the parameters involved.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 225-228 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 229-245 
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    Notes: In this paper models are given for analysis and description of non-linear properties of joints, weak intercalations and interfaces in rock masses.Models for analysis consist of four parts, i.e. shear displacement model, normal deformation model, shear strength model and a relationship between unit shear stiffness and normal stress.The method of non-linear analysis given in this paper is based on an incremental procedure.The proposed method is available for different types of shear-displacement curves, and also adapted to the complicated process of loading-unloading-reloading.The results of computer simulation of an in-situ shear test obtained by this method gave a good fit to the measured data.The method of non-linear analysis of joint elements has been used in some practical rock engineering problems, and some interesting results and conclusions have been obtained.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 47-76 
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    Notes: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al.1 is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15-noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al., 1 it is established theretically that if lower order finite elements are employed rigorously for non-trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 129-139 
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    Notes: Collapse loads are overestimated by finite-element or finite-difference procedures when the material discretization does not allow locally incompressible plastic flow: for example, constant-strain triangles or tetrahedra give unacceptable results. The use of different discretizations for the isotropic and deviatoric parts of the strain tensor is advocated for preventing this problem. The technique can be easily implemented in existing two- and three-dimensional computer programs. Its effectiveness is demonstrated by several examples.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 173-194 
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    Notes: The theory developed in Part I of this paper is extended to apply to the consolidation of horizontally layered soils under both axially symmetric and general surface loading. The method again leads to a considerable reduction in the amount of core storage necessary for computer solution and can be implimented on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 211-218 
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    Notes: The bearing capacity of deep foundations has been analysed using finite elements in conjunction with elasto-viscoplasticity. The influence of elastic parameters, mesh size and strain conditions on computed collapse loads was observed. Axisymmetric problems in particular were of interst, because it was found that good numerical solutions could be obtained through to collapse provided reduced integration was used.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 291-292 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 307-322 
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    Notes: The method of slices commonly used for estimating static stability of natural slopes and embankments is extended to include the dynamic effects due to earthquake loading. The equation of motion of a typical slice along a path different from its base is derived. The calculations of displacement of a slide mass using the Newmark procedure are discussed and illustrated with an example problem.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 353-382 
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    Keywords: Engineering ; Engineering General
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    Notes: Talbingo Dam is a well instrumented, 162m high rockfill structure with an upstream sloping silty clay core, located in the southern New South Wales, Australia. A non-linear finite element analysis of its behaviour was carried out under plane strain conditions, simulating its construction, reservoir filling and steady seepage loading stages. Material parameters are determined from triaxial tests on the rockfill, core, filter and transition materials, compacted to field dry density and moisture content. All materials show non-linear stress-strain behaviour, with rockfill exhibiting work softening at large strain. Mohr envelopes for rockfill are slightly curved but linear approximations are acceptable. When compared with stresses and deformations at maximum cross section, the analytical results show good agreement in most areas. A non-linear model for pore pressure response is used successfully to predict the high pore pressures in the lower region of the core. A stability analysis performed for the end of construction stage, based on finite element stresses, shows that the design safety factors are slightly conservative.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 101-115 
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    Notes: Two simple constitutive laws appropriate for elastic-plastic deformation up to peak load of low porosity rocks are presented. Both laws account for mean stress dependence of yield hardening between yield and peak strength and non-associative plastic straining. The two constitutive laws are based on the Mohr-Coulomb and the Mises-Schleicher yield criteria. The yield criteria are matched at axisymmetric compression and the relationships among the constitutive parameters are given. The parameters are then evaluated for two evaporite rocks anhydrite and polyhalite based on axisymmetric compression data. Comparison of predicted stress-strain laws with those measured in the laboratory show that these laws can be used for engineering analysis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 140-141 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 173-186 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 397-418 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 469-484 
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    Notes: A constitutive model is described for the prediction of dynamic crack formation in geological media. The model includes a simple tensile failure criterion for crack formation and a soil plasticity model for both deviatoric and volumetric plasticity. Numerical results are presented which show that the model reproduces the observed dependence of fracture formation on loding rate for dynamic pressure loading of boreholes. The use of the model as a numerical tool for design is demonstrated through two example parameter studies.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 500-500 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 427-444 
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    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 4 (1980), S. 103-119 
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    Notes: The spontaneous shear band formation in the biaxial test on dry sand samples with constant cell pressure is treated as a bifurcation problem. The constitutive response of sand is described in terms of mobilized friction and dilatancy. Dilatancy is looked upon as an internal constraint and the hardening rule is expressed in terms of an adequate dimensionless stress measure. Owing to fail of normality in sand, localization always occurs in the hardening regime. The theoretical solution of the shear band inclination is a geometrical mean of the classical Coulomb and Roscoe solutions and is in good agreement with the experimental data. The incipient shear modulus is proportional to the stress level and can be estimated to be also proportional to these cant modulus.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 175-184 
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 191-196 
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    Notes: Finite element solutions for steady-state flow of fluids through porous media do not include an explicit develpoment of the flow net, and many engineers find this lack frustrating. To solve for the stream function, the analyst can use essentially the same finite element routines as he used for the potential, but the matrix corresponding to the hydraulic conductivity is not the inverse of the conductivity. Contouring the potential and the stream function is done element by element; certain anomalous situations are described in an appendix.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 121-129 
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    Notes: This paper examines the problem of the eccentric loading of a rigid circular disc-shaped foundation embedded in bonded contact with an istropic elastic medium of infinite extent. The solution of this problem is achieved by using a Hankel integral transform technique which reduces the problem to two sets of dual integral equations. These systems of dual integral equations represent the equations which govern the axisymmetric and asymmetric states of deformation induced by the loaded foundation. Explicit results are derived both for the displacement and rotation of the circular foundation and for the contact stress at the interface.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 159-174 
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    Notes: An exact formulation is presented for the problem of a rigid circular body performing harmonic vibrations on an elastic half-space whose shear modulus increases linearly with depth and is interrupted at some finite depth by a frictionless horizontal plane. The static case is derived in the limit of zero frequency vibrations while the known result for the uninterrupted half-space is recovered in either extreme limit of the horizontal frictionless plane coinciding with the surface or when it is pushed down to an infinite depth.It is shown that the maximum effect of the interruption occurs when the frictionless plane is at a depth where the shear modulus is about 1·6 times the surface shear modulus. Furthermore, this maximum effect is equivalent to a reduction of about 5 per cent of the surface shear modulus or a reduction of about 2½ per cent in the natural frequency of the rigid body on an uninterrupted half-space. The important conclusion, therefore, is that irrespective of the depth at which a half-space isso interrupted, the surface shear modulus is still the dominant parameter and that both the increase in shear modulus with depth and the interruption are not only secondary but also opposing effects.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 277-284 
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 345-368 
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    Notes: A method allowing for the presence of infinitely distant boundaries in prismatic bodies is developed. The method is closely related to the consistent boundary concept used in dynamic applications but the development presented is algebraic and context free and is thus applicable to a wide variety of geotechnical problems both static and dynamic.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 455-457 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 139-163 
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    Keywords: Engineering ; Engineering General
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    Notes: A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately.The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 405-428 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A layer of fill deposited in a soft wet condition will consolidate under its own weight and will commonly undergo comparatively large strains in the process. Neither of these aspects of behaviour can be modelled by traditional consolidation theories. In this paper, a consolidation model is developed from the theory proposed by Gibson et al.5 and is applied here to soil consolidation during and after soil deposition. No restriction is made on the magnitude of strain, so that the boundaries are not taken as being fixed in space, but are allowed to move as required by the process of consolidation. However, perhaps the more important aspect is the consideration of self-weight, since in many instances, the surface loading applied to soft, soils is small, and the majority of the compression of the layer occurs while the effective stresses reach equilibrium with the weight of the soil. Although some idealizations have to be made in assuming relationships between soil parameters, it is shown that the self weight effects in consolidation can be significant, and fundamental to an understanding of soft soil behaviour.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
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    Notes: It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
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    Notes: A mapping finite element method is proposed for the solution of elastic problems in two-dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect-ratio problems of this type, accurately and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 151-171 
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    Keywords: Engineering ; Engineering General
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    Notes: A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 243-275 
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    Notes: An incremental formulation of constitutive laws is first presented and the fundamental notion of incremental non-linearity, necessary for the description of cyclic behaviour of soils, is emphasized.The incremental constitutive law for soils and its principal assumptions, which make it more general than the classical elastic-plastic models are detailed.The constitutive parameters of Hostun sand and Grundite clay are then given, as well as a comparison of theoretical results with experimental axisymmetrical and true triaxial measurements (Hostun sand tests at Grenoble and Grundite clay tests at Berkeley). Different cyclic behaviour simulations are presented, as well as an example of cyclic liquefaction of Monterey loose sand. Finally, a simple shear test is simulated.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 19-38 
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    Notes: The combined isotropic-kinematic hardening rule for clays is presented using the concept of a multisurface model discussed previously in Reference 1. The mechanical behaviour of clays after one-dimensional consolidation is next simulated for the axisymmetric stress stress state. A general three-dimensional formulation of constitutive relations is also presented.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 75-86 
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    Keywords: Engineering ; Engineering General
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    Notes: Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 135-139 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 245-268 
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    Keywords: Engineering ; Engineering General
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    Notes: Using the correspondence principle of viscoelasticity the Displacement Discontinuity Method has been extended to model the rate-dependent behaviour of a jointed rock mass. The intact rock is assumed to behave as a linear viscoelastic material while, in general, a non-linear rate-dependent behaviour of the rock joints can be accounted for. A number of numerical examples are presented which illustrate the accuracy and potential of the method for analysing complex engineering problems.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 273-281 
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    Notes: In many cases the analysis of the consolidation of axi-symmetric bodies subjected to non axi-symmetric loading may be carried out without recourse to a full three-dimensional treatment. Advantage may be taken of the axi-symmetric nature of the body and field quantities such as displacement and pore pressure can be given a Fourier representation. The problem is then reduced from one in three spatial dimensions (r, θ, z) and the time domain to one in two spatial dimensions (r, z) and the time domain.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 337-356 
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    Notes: A theory describing plastic deformation of granular (purely frictional) materials is presented. The theory is developed from postulates for energy dissipation and for the mode of plastic deformation. The postulates are based on some restrictions for the properties of granular materials and on a frictional analogy. A distinction is made between the description of plastic behaviour of a locally homogeneous and a locally non-homogeneous material. An interpretation of the deformation process is presented which implies that the theory accounts for the changes in the density of some local non-homogeneities underlying a plastic hardening effect. Based on this interpretation, an analogy between elastic-plastic behaviour of granular materials and frictional, sliding of two solid bodies is assumed. In the general case, the presented constitutive equations describe two hardening (softening) effects and are capable of describing both initial and advanced plastic deformations. A special, simplest form of the constitutive equations is examined in detail and a yield condition and a stress-strain relationship are derived. An example of elastic-plastic stress-strain-strength behaviour is presented for the cuboidal loading conditions.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 395-395 
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 199-213 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A numerical technique called Summary Representation was used to solve the problem of seepage through a leaky sheetpile; this particular method was selected owing to its accuracy and computational speed. Seepage parameters were evaluated quantitatively and the influence of the leakiness of sheetpiles in a porous medium underlain by an impervious horizontal stratum was determined. The case of a single sheetpile was first considered, and the effect of the depth of penetration and coefficient of leakiness on the total rate of flow and on the values of the exit gradient was analysed. Next, the flow under an impervious dam was considered to assess the accuracy of the method. Finally, the case of seepage under a dam with leaky sheetpiles at both ends was studied, including the effect of the leaky sheetpiles on the uplift pressure acting along the foundation of the dam. Patterns of seepage through the flow line deformation that is caused by the leakiness of the sheetpiles.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 285-289 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 485-492 
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    Notes: This paper deals with the plane plastic equilibrium of a cohesive frictional material in the case of a jump non-homogeneity. Three types of interface separating rigid-plastic bodies with different material parameters are distinguished: (i) a perfect adhesion contact, (ii) a thin layer of a material different from the adjacent bodies, (iii) a combined frictional-adhesive contact. A sliding along the interface may occur if certain conditions are satisfied. For the first two types of joint, the direction and propagation of the velocity jump vector along the interface follow from the classical theory of plane plastic flow. In the third case, the potential sliding rule relating the velocity jump vector to the limit condition of the joint, or to the potential different from the limit condition, may be adopted. The direction of the velocity jump vector results from such a rule.The problem of stability of a slope, being continuously non-homogeneous in one region, and homogeneous in another, is shown in an example. The two regions of the slope are separated by the interface, a thin layer of a different material, (type ii). The associated flow law for both regions of the slope and for the material of the interface is assumed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 399-407 
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    Keywords: Engineering ; Engineering General
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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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    Keywords: Engineering ; Engineering General
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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 6 (1982), S. 392-392 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 117-127 
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    Notes: A coupled finite element-rigid block model for the transient analysis of caverns in jointed media is presented. This coupling permits the modelling of lined openings in a jointed rock mass as well as the propagation of stress waves to the cavern. Both the finite element and the rigid block algorithms employ explicit time integration; an efficient, stable scheme is developed for coupling the two algorithms. Two numerical examples are given: one is a simple validation, the second is a representation of a lined cavern in a sparsely jointed medium.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 457-468 
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    Notes: 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.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 493-498 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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