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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 207-223 
    ISSN: 0271-2091
    Keywords: Numerical Solution ; Integrated Compartment Method ; Fluid Dynamics ; Incompressible Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. These procedures are applied to the Navier-Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one-, two-, or three-dimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity. These preliminary applications have shown promising results.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 225-235 
    ISSN: 0271-2091
    Keywords: Turbulence ; Fluid Flow ; Mathematical Models ; Reynolds Stresses ; Channels Lateral Motion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The solution for the stress transport turbulence model equations for the situation where the flow is unidirectional is now commonly applied to flows with weak secondary currents in closed ducts, open channels, and rod bundles in nuclear reactor channels. Here, perturbations to the unidirectional flow solutions are studied by solving the exact equations using an iterative procedure. Now the equations also contain the small lateral velocity gradients formerly neglected. The applicability as well as the limitation of the use of the unidirectional flow turbulence model for the description of channel flow with lateral motion are discussed. Modifications for weak lateral motion are suggested.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 273-290 
    ISSN: 0271-2091
    Keywords: Large Eddy ; Simulation ; Isotropic ; Turbulence ; Filtering ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: HOMTY, a code for Large Eddy Simulation of homogeneous isotropic turbulence is proven by successful simulation of two experiments. The role of each term in the equations of motion and the concept of filtering is examined. It is shown that ‘prefiltering’ is unnecessary, and the resulting additional term in the equations, instead of transferring energy to the subgrid scales, backscatters energy from the resolved large wavenumerbers to the small ones. The kinetic energy decay exponent is shown to depend on the low wavenumber part of the velocity spectrum. Pressure statistics are computed and found to be in agreement with previous computations.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-294 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-291 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 237-272 
    ISSN: 0271-2091
    Keywords: Diffraction ; Refraction ; Gravity Water Waves ; Wave Equation ; Homma's Island Tsunamis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A linear wave equation correct to first order in bed slope is used to calculate the wave field in the sea around an idealized island. This is of circular cylindrical shape and is situated on a paraboloidal shoal in an ocean of constant depth (Figure 1). The sides of the island are assumed fully reflecting. The incident waves are plane and periodic. Wave periods up to 30 min are investigated, and the Coriolis force is neglected. The solution of the wave equation is represented by a finite Fourier series, and a large number of very accurate numerical computations are carried through. The results appear partly in figures showing amplitude and phase angle curves (in some cases extending to the water area of constant depth outside the shoal), partly in figures showing amplitude vs wave period in fixed points. Comparison with solutions to the linearized long-wave equation is made, and the validity range of the corresponding shallow water theory is given. The influence of the shoal is studied by investigating the wave field around an island in an ocean of constant depth. New criteria are given for the applicability of a geometrical optics approach (i. e. refraction). Complete numerical refraction solutions for points at the shoreline (corresponding to many wave orthogonals ending at the point) for shallows water waves, as for the general case, demonstrate the inadequacy of this approach for long-period waves (seismic seawaves: tsunamis). All non-linear effects, including dissipation, are excluded.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 25-42 
    ISSN: 0271-2091
    Keywords: Penalty Method ; Incompressible Flow ; Reduced Quadrature ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 71-92 
    ISSN: 0271-2091
    Keywords: Boundary Elements ; Hamel Flow ; Free Surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A formulation of the boundary element method for the solution of non-zero Reynolds number incompressible flows in which the non-linear terms are lumped together to form a forcing function is presented. Solutions can be obtained at low to moderate Reynolds numbers. The method was tested using the flow of a fluid in a two-dimensional converging channel (Hamel flow) for which an exact solution is available. An axisymmetric formulation is demonstrated by examining the drag experienced by a sphere held stationary in uniform flow. Performance of the method was satisfactory. New results for an axisymmetric free jet at zero Reynolds number obtained using the boundary element method are also included. The method is ideal for this type of free-surface problem.
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  • 9
    ISSN: 0271-2091
    Keywords: Finite Element ; Quasi-three-dimensional ; Interconnected Aquifer Systmes ; Fluid Mass Balance ; Iterated Frontal Method ; Predictor-Corrector Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The quasi-three-dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor-corrector procedure which employs the Crank-Nicolson method in the corrector phase.This very stable procedure permits use of fairly long time-steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 493-506 
    ISSN: 0271-2091
    Keywords: Modified ; Dodge ; Algorithm ; Parabolized ; Navier-Stokes ; Computational Fluid Dynamics ; Low Speed Flow ; Channel Flow ; Zebra Algorithm ; Mass Balancing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (chequerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A chequerboard iteration is ued to solve the resulting implicit non-linear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 527-528 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 13
    ISSN: 0271-2091
    Keywords: Finite Elements ; Infinite Elements ; Acoustics ; Wave Propagation ; Radiation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite element models are presented for the calculation of near and far field acoustical radiation. These models are applied to the specific problem of fan noise radiation from axisymmetric turbofan inlets. In all cases conventional acoustic finite elements are used within an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with zero mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes in determining the near field values of acoustical pressure. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes an order of magnitude more sparse that would be required in conventional numerical discretizations, and may consequently be applied at modest computational cost.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 543-565 
    ISSN: 0271-2091
    Keywords: Low-aspect Ratio Wings ; Leading-edge Separation ; Vortex Shedding ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A multi-vortex model of the vortex sheets shed from the sharp leading edges of slender wings is considered. The method, which is developed within the framework of slender-body theory, is designed to deal with those situations in which more than one centre of rotation is formed on the wing, for example on a slender wing with lengthwise camber or with a strake. Numerical results are presented, firstly for situations where comparison can be made with a vortex sheet model and secondly for cases, such as those described above, where a vortex sheet model is unable to describe the flow. Where comparison is available, agreement is good and in the cases where more than one vortex system is present interesting interactions are obtained.
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  • 15
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 529-542 
    ISSN: 0271-2091
    Keywords: Strongly Rotating ; Incompressible ; Free-surface ; Finite-difference ; Coriolis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The flow of an incompressible fluid in a rapidly rotating right circular cylinder is considered. A source/sink mass distribution at the lateral wall, which is azimuthally uniform and symmetric across the midplane, causes a deviation from wheel flow. The container is only partially full and the inner free surface is allowed to deviate slightly from the vertical. A finite-difference solution of the full axisymmetric, non-linear governing equations was used to obtain the flow field. A special implicit technique for the Coriolis terms which maintains geostrophy was developed and is described. The results obtained for a low Rossby number flow compare quite favourably with the linearized solution. Results are also presented for a case wherein the non-linear terms are important.
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  • 16
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 103-119 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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  • 17
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 175-184 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 18
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 291-292 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 19
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 293-311 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Hysteretic and viscous material damping are compared in the context of soils. Popular assumptions about damping are shown to lead to different results for the rocking mode of surface foundations at low frequency.
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  • 20
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 389-389 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 21
    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
    Electronic Resource
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 57-78 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The trap-door problem with dry sand is treated in a statical analysis based upon model test kinematics. Integration of the equilibrium conditions along horizontal slices and introducing the mean value for the vertical stresses yields a differential equation for the trap-door force. Concerning the constitutive response of sand a statical model of a moving shear band is proposed as an internal boundary. Solutions for the trap-door force for the active and passive modes and for the ultimate and residual states are discussed.
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  • 23
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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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  • 24
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 333-359 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The analysis of the stability of slopes using limiting equilibrium considerations necessitates the determination of the critical slip surface which yields the minimal factor of safety. The numerous methods currently available for slope stability analysis provide a procedure for assigning a factor of safety to a given slip surface, but do not consider the problem of identifying the critical conditions.This paper presents an effective minimization procedure based on dynamic programming by which the minimal factor of safety, and the corresponding surface, are determined simultaneously. This procedure SSDP (Slope Stability by Dynamic Programming), couples the minimization scheme with Spencer's method of slope stability analysis. It may be applied to slopes of any geometry, layering, pore pressure and external load distributions. No arbitrary restrictions are placed on the shape of the slip surfaces, and the analysis satisfies all equilibrium equations.Application of the procedure to slope stability problems reported in the literature shows that for a given slip surface the procedure yields factors of safety which are almost identical to those reported, but in every case a more critical slip surface, with a lower factor of safety, may be found.
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  • 25
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 361-375 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.
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  • 26
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 27
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 139-163 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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  • 28
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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  • 29
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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  • 30
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), 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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  • 31
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 151-171 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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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  • 32
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 233-254 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A new one-dimensional model for penetration analysis of a rigid projectile into a soil target is presented. The soil medium is represented by a set of discs of constant thickness, responding in the radial direction under plain strain regime. When penetration through a typical disc occurs, the projectile displaces soil material and a radial plastic shock wave propagates in the disc. The interaction pressure between the projectile and soil material is compatible with the motion of the contact boundary, between them. The instantaneous resistive force is obtained by summation of the contributions of all the discs which are in contact with the nose surface of the projectile. Soil is considered as a ‘floating’ ideally locking material, in which the locking volumetric strain is adjusted to the physical stress-strain properties of the soil material. Friction between projectile and soil is assumed to be negligible. Comparison is made with both twodimensional computer program results and experimental data, and very good agreement is observed. Comparison with other analytical methods reveals that the present model most closely resembles existing experimental results and permits further analysis of the problem as predictions of target response and of stress distribution on the projectile nose. The calculations require very small amounts of computer time. Analysis with the present model yields an efficient and comprehensive means to analyse penetration and perform parameter analysis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 377-387 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A new and simple concept based on the idea of correcting for non-associative characteristics of (geologic) media is presented. A special form of the concept is adopted and introduced in a critical state plasticity model. An example problem of behaviour of a soil tested under triaxial conditions is included. The concept can permit a simplified treatment of non-associativeness and under certain assumptions can allow use of existing formulations of plasticity by maintaining symmetry of the associated matrices.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
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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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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 187-196 
    ISSN: 0363-9061
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 95-108 
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    Notes: The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 306-308 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 195-209 
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    Notes: During the last ten years the Calculus of variations technique has been applied to solve the problem of stability of slopes. All published methods are essentially based on the attainment of a functional and the search for its absolute minimum or maximum by vanishing its first variation.Obviously this statement of the problem is valid only if such a minimum or maximum exists and can be obtained by making the first variation of the functional equal to zero. So, these implicit hypotheses must be checked.This work analyses from this point of view the validity of the methods proposed by ‘Baker and Garber’, ‘Chen’ and ‘Castillo and Revilla’, and demonstrates that the first two methods are incorrectly stated while the third one is correct at least in the case of a frictionless soil.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 513-517 
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    Keywords: Engineering ; Engineering General
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 519-529 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 589-604 
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    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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    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) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 385-393 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. ii 
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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 6 (1982), S. 491-492 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 1-7 
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    Notes: The Finite Element Method is frequently used to analyse problems involving an ‘infinite domain’. A typical problem is an underground excavation in prestressed infinite medium in either tunnelling or mining operations or a foundation in an infinite half space.This paper examines the implications of mesh truncation on the accuracy of the accuracy of the solution.At the same time, a more economical and accurate method of analysing these problems using special ‘infinite domain’ Finite Elements is presented.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 57-74 
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    Notes: The problem of an impervious dam on a poro-elastic foundation is solved analytically. Using the known solution for the fluid pressure in the pores, the elastostatic stress field in the solid skeleton is analysed by reduction to two simpler problems whose solutions can be obtained by complex variable techniques. For welded contact, the rotation of the dam base is then found along with the stresses and strains in the ground. Modification for finite friction along the base is outlined in the appendix.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 269-272 
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    Notes: This paper corrects an impression, created by a recent contribution to the International Journal for Numerical and Analytical Methods in Geomechanics, that the mathematical equivalence of the direct and indirect boundary element methods for the diffusion equation implies that their respective computational needs with regard to the body integral terms are equal. It is shown that in a stepwise implementation of the numerical procedure for solving a finite body problem, indirect methods requirean integration over an infinite region and not merely over the body as is the case for the direct version.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 286-286 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 57-70 
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 141-155 
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    Keywords: Engineering ; Engineering General
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    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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    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 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 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 460-461 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 1-20 
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    Notes: The paper studies certain dynamic characteristics of soil deposits with wave velocities increasing with depth according to (1 + μz)m, where m = 1, 2/3, 1/2, 1/4 and 0. Analytical solutions are presented for the fundamental periods, mode shapes and amplification functions due to vertically propagating shear waves and the effects of type (m) and rate (μ) of heterogeneity are systematically investigated. The analytical-numerical techniques are used to study the attenuation with depth in a deposit of the vertical and horizontal displacements due to travelling of Rayleigh waves. Differences attributed to different heterogeneities are discussed in connection with the machine isolation problem and the steady-state vibration technique for soil exploration. Finally, the dependence on soil heterogeneity of the time-distance response curves, obtained during seismic refraction surveys, is graphically illustrated.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 1-23 
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 73-88 
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 57-72 
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 39-55 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress-strain behaviour of soil. The Cam Clay model is revised to model the stress-strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 245-268 
    ISSN: 0363-9061
    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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    Keywords: Engineering ; Engineering General
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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 7 (1983), S. ii 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 435-455 
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    Keywords: Engineering ; Engineering General
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 371-384 
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 263-283 
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    Keywords: Engineering ; Engineering General
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    Notes: Ground freezing technology is favoured in civil engineering, mainly in tunnelling. The time-dependent material characteristics in the form of creep control the bearing capacity of any frozen earth support system. The finite element method in connection with an initial strain algorithm is able to include these effects. The information about stress redistribution and deformation rate is important for an economic design. Case histories of different tunnel linings in frozen soil and two other examples of realized projects show the usefulness of such a procedure.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 369-378 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 449-454 
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    Keywords: Engineering ; Engineering General
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    Notes: Estimating subsurface pore water pressures in natural slopes along the periphery of rivers and reservoirs for future conditions, created by the operational requiremets to meet increases in energy demand from the observed data of the past and present, operations, is possible with the use of a mathematical model. An effective algorithm for calculating pore water pressure at any location in a slope stability section is to use a complete polynomial and to assure geometric invariance of the calculated results.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 429-447 
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    Keywords: Engineering ; Engineering General
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    Notes: A simple algorithm (PILLR) for obtaining by two-dimensional analysis thee essential results that would be obtained in an actual three-dimensional finite element analysis of stress about mine pillars in flat-laying stratified rock is presented. A series of comparisons between the distributions of the local factor of safety calculated from the results of three-dimensional analysis and that obtained in the PILLR two-dimensional analyses for pillars of length/width ratio ranging from 0.33 to 8.0 shows the algorithm to be quite effective. The average vertical stress over the horizontal mid-plane of the pillar in the PILLR two-dimensional analyses is always within 0.5 per cent of the exact average; the local safety factor distribution is always within 10 per cent of the three-dimensional result. The ratio of the computer core x time product for the 2D' to 3D analyses is approimately 1/150. Additional improvements ard possible, although with the current PILLR algorithm 3D analyses require less than 1 minute for execution. This fact makes technically sound 3D mine pillar design analyses economically feasible on a routine basis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 21-46 
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    Notes: An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 225-241 
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    Keywords: Engineering ; Engineering General
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    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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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-149 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. ii 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 308-309 
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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. 71-96 
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    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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    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 
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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 4 (1980), S. 185-189 
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    Keywords: Engineering ; Engineering General
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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) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 313-332 
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    Notes: A technique is developed for the analysis of multiple underream anchor systems resting in an elastic soil. This technique may be used to consider anchor systems involving arbitrary anchor inclination and depth beneath the soil surface, as well as arbitrary number, shape, size and spacing of underreams. The approach is largely analytical in nature and involves only a fraction of the computation required for a finite element analysis.Consideration is given to the effects of anchor depth and inclination to the soil surface, and the spacing and number of underreams upon the elastic response of anchor systems. On the basis of the result from this study, a simple, approximate method for estimating the response of multiple underream anchors is proposed. This approach involves the use of several interaction charts, which are presented in the paper, and can be used as a hand method for estimating the load-displacement behaviour of quite general anchor systems to sufficient accuracy for most practical purposes. The use of the approximate approach is illustrated by an example.
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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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    Keywords: Engineering ; Engineering General
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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 7 (1983), S. 395-395 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 197-199 
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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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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    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.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
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