The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data. 相似文献
Vicksburg loess is characterized by preferred orientation of constituent grains, which on the average dip 4° toward the west (N 80–85°W). This investigation was undertaken to study, quantitatively, the relationship between natural fabric anisotropies of Vicksburg loess and the orientation of applied stress distribution Results of the study indicate the fabric anisotropies in Vicksburg loess are reflected by definite variation in triaxial shear strength of dry and moist specimens.
In two series of triaxial tests, ultimate strength of the loess is maximum where σ1 is perpendicular to grain orientation, and it is reduced where the principal stresses are 45° to the fabric plane. In this respect, Vicksburg loess may serve as a structural model for granular earth materials in illustrating the influence of fabric on ultimate strength. Moreover, the Mohr-Coulomb fracture line consists of two line segments, with an increase in slope at higher confining pressure. This characteristic suggests that poorly-cemented sands, or sandstones, and silts, or siltstones, may undergo two failures: one at small strains where cement bonds are disrupted and the other at larger strains where internal shearing resistance of granular components is exceeded. 相似文献