Yu Zaitsev, V & Sas, P 2008, 'Determining Properties of High Compliance Porosity by Use of an Effective Medium Model Based on Crack Description in Terms of Their Normal and Shear Compliance Parameters', in Y Potvin, J Carter, A Dyskin & R Jeffrey (eds), Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium
, Australian Centre for Geomechanics, Perth, pp. 563-574.
An effective medium model recently developed by the present authors is applied for interpretation of known experimental data on pressure dependences of elastic wave velocities in dry and saturated rocks in order to elucidate the effect of the highly compliant fraction of the porosity. Our approach allows determining essential features of the soft defects in terms of their shear and normal compliances. For the dry defects, we found that the ratio of the normal to shear compliance may be as high as 5–7, which contrasts to the range 0.8–2.2 expected for such widely used defect models as Hertz–Mindlin contacts or elliptical cracks. The high normal compliance of the real defects results in strong decrease of Poisson’s ratio of the rock down to negative values. Here, we consider the case of a dry sandstone exhibiting negative Poisson’s ratio. For saturated samples, we found that although the normal compliance of the defects becomes smaller than the shear one, the difference is only 1.2–2.5 times. From the viewpoint of the role of “global” (in the sense of Biot) and local (squirt) fluid flows, the performed examination indicates strong domination of the squirt mechanism including the cases, for which a third, unidentified dispersion mechanism was earlier supposed.
Bakulin, A., Grechka, V. and Tsvankin, I. (2000) Estimation of fracture parameters from reflection seismic data - Pts. I-III. Geophysics, 65(6), pp. 1788–1830.
Bakulin, A.V. and Molotkov, L.A. (1998) Effective models of fractured and porous media, St. Petersburg University, Press (in Russian).
Biot, M.A. (1956a) Theory of acoustic attenuation, propagation of elastic waves in a fluid-saturated porous solid: I. Low-frequency range, Journal of the Acoustic Society of America, 28, pp. 168–178.
Biot, M.A. (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid: II. Higher frequency range, Journal of the Acoustic Society of America, 28, pp. 179–191.
Bourbié, T., Coussy, O. and Zinszner, B. (1986) Acoustique des milieux poreux: publications de l’institut française du pétrole, Ėditions Technip, Paris.
Budiansky, B. and O’Connel, R.J. (1976) Elastic moduli of dry and saturated cracked solids, International Journal of Solid Structures, Vol. 12, pp. 81–97.
Coyner, K.B. (1984) Effects of stress, pore pressure, and pore fluids on bulk strain, velocity, and permeability in rocks: Ph.D. thesis, Massachusetts Institute of Technology.
Gordon, R.B. and Davis, L.A. (1968) Velocity and attenuation of seismic waves in imperfectly elastic rock: Journal of Geophysical Research, 73(12), pp. 3917–3935.
Han, D. (1986) Effects of porosity and clay content on acoustic properties of sandstones and unconsolidated sediments: Ph.D. dissertation, Stanford University.
Mavko, G. and Nur, A. (1975) Melt squirt in the asthenosphere: Journal of Geophysical Research, 80, pp. 1444–1448.
Mavko, G. and Jizba, D. (1991) Estimating grain-scale fluid effects on velocity dispersion in rocks, Geophysics, Vol. 56, pp. 1940–1949.
Mavko, G. and Jizba, D. (1994) The relation between seismic P- and S- velocity dispersion in saturated rocks, Geophysics, 59(1), pp. 87–92.
Mavko, G.M. and Nur, A. (1978) The effect of nonelliptical cracks on the compressibility of rocks, Journal of Geophysical Research, Vol. 83, pp. 4459–4468.
Murphy, W.F. (1984) Acoustic measures of partial gas saturation in tight sandstones, Journal of Geophysical Research, 89, pp. 11,549–11,559.
O’Connel, R.J. and Budiansky, B. (1974) Seismic velocities in dry and saturated cracked solids, Journal of Geophysical Research, 79(10), pp. 5412–5426.
Saenger, E.H. and Shapiro, S.A. (2002) Effective velocities in fractured media: A numerical study using the rotated staggered finite-difference grid, Geophysical Prospecting, 50(2), pp. 183–194.
Schoenberg, M. and Douma, J. (1988) Elastic wave propagation in media with parallel fractures and aligned cracks, Geophysical Prospecting, Vol. 36, pp. 571–590.
Schoenberg, M. and Sayers, C. (1995) Seismic anisotropy of fractured rock, Geophysics, 60, pp. 204–211.
Seipold, U., Mueller, H-J. and Tuisku, P. (1998) Principle differences in the pressure dependence of thermal and elastic properties of crystalline rocks, Physics and Chemistry of the Earth, 23, pp. 357–360.
Vavakin, A.S. and Salganik, R.L. (1978) Effective elastic characteristics of bodies with isolated cracks, cavities and rigid inclusions, Mechanics of the solid body [in Russian], No. 2, pp. 95–107.
Walsh, J.B. (1965a) The effect of cracks on the uniaxial elastic compression of rocks, Journal of Geophysical Research, 70, pp. 399–411.
Walsh, J.B. (1965b) The effect of cracks on Poisson’s ratio, Journal of Geophysical Research, 70, pp. 5249–5247.
Winkler, K.W. (1983) Contact stiffness in granular porous materials: comparison between theory and experiment, Geophysical Research Letters, 10(11), pp. 1073–1076.
Winkler, K.W. (1985) Dispersion analysis of velocity and attenuation in Berea sandstone, Journal of Geophysical Research, Vol. 90, pp. 6793–6800.
Winkler, K.W. (1986) Estimates of velocity dispersion between seismic and ultrasonic frequencies: Geophysics, Vol. 51, pp. 183–l 89.
Zaitsev, V. and Sas, P. (2000) Elastic moduli and dissipative properties of microinhomogeneous solids with isotropically oriented defects, Acta Acustica united with Acustica, 86, pp. 216–228.
Zaitsev, V.Yu. and Matveev, L.A. (2006) Strain-amplitude dependent dissipation in linearly dissipative and nonlinear elastic microinhomogeneous media, Russian Geology and Geophysics, 47(5), pp. 694–709.
Zaitsev, V.Yu., Saltykov, V.A. and Matveev, L.A. (2008) Relation between the Tidal Modulation of Seismic Noise and the Amplitude-Dependent Loss in Rock, Acoustical Physics, 54, pp. 538–544.