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Observation and implications of nonlinear elastic wave response in rock
PROPERTIES:DYNAMICS 944144 Dynamic-stiffness matrix of unbounded soil by finite.element multi-cell cloning J.P. W o l f & Chongmin Song, Earthquake Engineering & Structural Dynamics, 23(3), 1994, pp 233-250. To calculate the dynamic-stiffness matrix of the unbounded soil, a multi-cell cloning algorithm based solely on the finite-element formulation is developed. A non-linear system of equations has to be solved iteratively once for the whole range of frequency. For a specific frequenc.y, two- and three-cell cloning lead to highly accurate results, which is demonstrated by examples of increasing complexity. -Authors 944145 A physical model of shear-wave propagation in a transversely isotropic solid Chih-Hsiung Chang, G. H. F. Gardner & I. A. McDonald, Geophysics, 59(3), 1994, pp 484-487. Presents laboratory observations of elastic wave propagation in a transversely isotropic medium by using transmission traveltime measurements and computing the elastic constants of the TIM. The observations include both P and S body waves. By fitting the calculated group velocities to the observed data, the five independent elastic constants, which are required to describe the physical properties of the TIM, and]or in processing of multicomponent seismic data, were obtained. -Authors 944146 Theoretical study of nonlinear elastic wave propagation K . R . McCall, Journal of Geophysical Research, 99(B2), 1994, pp 2591-2600. A theoretical study of the propagation of a plane wave in a material with nonlinear response is presented. Starting with the wave equation for an isotropic, homogeneous, elastic solid with cubic anharmonicity in the moduli, accounting for attenuation by introducing complex linear and nonlinear moduli, a hierarchy of equations is developed. The influence of propagation distance, source frecJuency spectrum, source displacement amplitude, attenuauon, and nonlinear coefficient in the spectrum of a propagating wave is examined. The displacement field for various source functions is calculated using parameters typical of rocks. -from Author 944147 Observation and implications of nonlinear elastic wave response in rock P. A. Johnson & K. R. McCall, Geohysical Research Letters, 21(3), 1994, pp 165-168. Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural discontinuities. The magnitude of the harmonics created by nonlinear interactions grows linearly with propagation distance in one-dimensional systems. The effect o f nonlinear elasticity on seismic wave propagation may be large, and should be considered in modeling. -from Authors 944148 Numerical simulations of monotonic and cyclic loading of g r a n u l a r soil Tang-Tat Ng & R. Dobry, Journal of Geotechnical Engineering - ASCE, 120(2), 1994, pp 388-403. The paper explores the use of discrete element simulations to model granular soil response to monotonic and cyclic loading. Two- and three-dimensional random arrays of quartz spheres of various diameters are used that crudely represent rounded uniform quartz sand. All simulated granular specimens are first isotropically consolidated, and are then subjected to monotonic drained loading or constant volume (undrained) cyclic 'simple shear' simulations. The monotonic results exhibit similar pressure-dependent shear strength and dilation behavior to that found in actual sands, but with the simulated specimens being stiffer and failing at a smaller strain. The simulated cyclic loading results closely resemble the 'pore water vressure' builduv to initi~ liquefaction, hysteresis loop forvnation and degradation, banana loop shapes, and Imes of phase transformation observed in sand experiments. -from Authors
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944149 Estimating seismic velocities at ultrasonic frequencies in partially s a t u r a t e d rocks G. Mavko & R. Nolen-Hoeksema, Geophysics, 59(2), 1994, pp 252-258. Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation hetemgoneity are nnportant: 1) saturation differences between thin compliant pores and larger stiffer pores, and 2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. The paper proposes a formalism for predicting the range of velocities in paffJally saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. -from Authors 944150 Energy dissipation in inelastic flow of s a t u r a t e d cohesionless g r a n u l a r media N. Okada & S. Nemat-Nasser, Geotechnique, 44(1), 1994, pp 1-19. The results of a study of energy dissipation in cohesionless granular media are presented. The relation between the excess p o r e water pressure, accumulated in a watersaturated granular mass, and the corresponding external work in undrained cyclic loading is studied e x ~ . rimentally, under displacement-controlled conditions. A micromechanical model of internal energy dissipation due to slip between contacting granules is introduced, and the results are compared with experimental measurements. It is shown that the internal dissipation per unit volume in cohesionless granular media can be expressed in terms of the time history of the applied effective pressure and a single scalar parameter which depends on the density and strain amplitude. The model is further validated by torsion tests with random variation in the applied strain amplitude. -from Authors 944151 Evaluation of three- and two-field finite element methods for the dynamic response of s a t u r a t e d soil A. Oajo, A. Saetta & R. Vitaliani, International Journal for Numerical Methods in Engineering, 37(7), 1994, pp 1231-1247. The three-field formulation u-p-U is presented and is applied to solve dynamic equations for saturated porous media. In order to evaluate the accuracy and the performance of this throe-field approximation, the u-U and the u-w formulations are also considered and a few one- and two-dimensional examples are solved using the three methods. Problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u-p-U approximation. Accuracy was determined by a comparison of the finite element results with the analytical solution given by Oajo and Mongiovi, for a wide range of permeability. -Authors 944152 Elastic coefficients for liquuid- and gass a t u r a t e d porous media X. Li, International Journal of Engineering Science, 32(2), 1994, pp 195-208. The isothermal elastic behavior of porous media containing both gas and liquid phases is investigated theoretically and special attention is paid to the determination of the elastic coefficients involved. It is demonstrated that a new effective stress concept should be introduced to deal, in a generalized manner, with the multicomponent fluidsaturated porous media. It is also verified theoretically that there exist two independent stress state variables for the three-phase media, in contrast to the one variable for the two-phase ones. A compressible gas model, as a special application example of the genera~ model, is used to illustrate the influence of capillary effect on the elastic constants. -from Author 944153 The elastic anisotropy of shales C . M . Sayers, Journal of Geophysical Research, 99(131), 1994, pp 767-774. Shales constitute about 75% of the elastic fill of sedimentary basins and have a decisive effect on fluid flow and seismic wave propagation because of their low permeabil-
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944149 Estimating seismic velocities at ultrasonic frequencies in partially s a t u r a t e d rocks G. Mavko & R. Nolen-Hoeksema, Geophysics, 59(2), 1994, pp 252-258. Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation hetemgoneity are nnportant: 1) saturation differences between thin compliant pores and larger stiffer pores, and 2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. The paper proposes a formalism for predicting the range of velocities in paffJally saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. -from Authors 944150 Energy dissipation in inelastic flow of s a t u r a t e d cohesionless g r a n u l a r media N. Okada & S. Nemat-Nasser, Geotechnique, 44(1), 1994, pp 1-19. The results of a study of energy dissipation in cohesionless granular media are presented. The relation between the excess p o r e water pressure, accumulated in a watersaturated granular mass, and the corresponding external work in undrained cyclic loading is studied e x ~ . rimentally, under displacement-controlled conditions. A micromechanical model of internal energy dissipation due to slip between contacting granules is introduced, and the results are compared with experimental measurements. It is shown that the internal dissipation per unit volume in cohesionless granular media can be expressed in terms of the time history of the applied effective pressure and a single scalar parameter which depends on the density and strain amplitude. The model is further validated by torsion tests with random variation in the applied strain amplitude. -from Authors 944151 Evaluation of three- and two-field finite element methods for the dynamic response of s a t u r a t e d soil A. Oajo, A. Saetta & R. Vitaliani, International Journal for Numerical Methods in Engineering, 37(7), 1994, pp 1231-1247. The three-field formulation u-p-U is presented and is applied to solve dynamic equations for saturated porous media. In order to evaluate the accuracy and the performance of this throe-field approximation, the u-U and the u-w formulations are also considered and a few one- and two-dimensional examples are solved using the three methods. Problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u-p-U approximation. Accuracy was determined by a comparison of the finite element results with the analytical solution given by Oajo and Mongiovi, for a wide range of permeability. -Authors 944152 Elastic coefficients for liquuid- and gass a t u r a t e d porous media X. Li, International Journal of Engineering Science, 32(2), 1994, pp 195-208. The isothermal elastic behavior of porous media containing both gas and liquid phases is investigated theoretically and special attention is paid to the determination of the elastic coefficients involved. It is demonstrated that a new effective stress concept should be introduced to deal, in a generalized manner, with the multicomponent fluidsaturated porous media. It is also verified theoretically that there exist two independent stress state variables for the three-phase media, in contrast to the one variable for the two-phase ones. A compressible gas model, as a special application example of the genera~ model, is used to illustrate the influence of capillary effect on the elastic constants. -from Author 944153 The elastic anisotropy of shales C . M . Sayers, Journal of Geophysical Research, 99(131), 1994, pp 767-774. Shales constitute about 75% of the elastic fill of sedimentary basins and have a decisive effect on fluid flow and seismic wave propagation because of their low permeabil-