岩石物理学-03岩石中波的传播与衰减.ppt

The Voigt and Reuss averages are interpreted as the ratio of average stress and average strain within the composite. The stress and strain are generally unknown in the composite and are expected to be nonuniform. The upper bound (Voigt) is found assuming that the strain is everywhere uniform. The lower bound (Reuss) is found assuming that the stress is everywhere uniform. Geometric interpretations: Voigt iso-strain model Reuss iso-stress model Since the Reuss average describes an isostress situation, it applies perfectly to suspensions and fluid mixtures. Hill提出将这两种模型的结果取算术平均，并称为VRH值 ： 3.4 岩石模型 Kumazawa（1969）仿照Hill的做法，取几何平均值： 两种矿物组成的岩石模型，其平均岩性参数用不同方法计算时得到的K随第2种矿物体积百分比V2的变化曲线 1. Voigt模型； 2. Ruess模型； 3. Hill模型； 4. 几何平均模型 大量的实验测试表明，在高压状态下，计算值和与测试值符合得较好。 3.4 岩石模型 岩石种类 实际测量的K值 计算的 值 误差 花岗岩 49.1 49.0 1% 花岗岩 54.6 52.3 4% 花岗二长岩 60.4 57.3 5% 辉长岩 81.5 84.3 4% 辉 岩 84.8 84.2 1% Velocity-porosity relationship in clastic sediments compared with the Voigt and Reuss bounds. Virtually all of the points indeed fall between the bounds. Furthermore, the suspensions, which are isostress materials (points with porosity 40%) fall very close to the Reuss bound. Data from Hamilton (1956), Yin et al. (1988), Han et al. (1986). Compiled by Marion, D., 1990, Ph.D. dissertation, Stanford Univ. G.1 Hashin-Shtrikman Bounds Interpretation of bulk modulus: where subscript 1 = shell, 2 = sphere. f1 and f2 are volume fractions. These give upper bounds when stiff material is K1, ?1 (shell) and lower bounds when soft material is K1, ?1. The narrowest possible bounds on moduli that we can estimate for an isotropic material, knowing only the volume fractions of the constituents, are the Hashin-Shtrikman bounds. (The Voigt-Reuss bounds are wider.) For a mixture of 2 materials: Distance between bounds depends on similarity/difference of end-member constituents. Here we see that a mixture of calcite and water gives widely spaced bounds, but a mixture of calcite and dolomite gives