This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations. 相似文献
Numerical models of groundwater flow require the assignment of hydraulic conductivities to large grid blocks discretizing the flow domain; however, conductivity data is usually available only at the much smaller scale of core samples. This paper describes a geostatistical model for hydraulic conductivity at both the core or point scale and that of grid blocks. Conductivity at the block scale is obtained empirically as a spatial power-average of point scale values. Assuming a multivariate Gaussian model for point log-conductivity, expressions are derived for the ensemble mean and variance of block conductivity. The expression for the ensemble mean of block scale conductivity is found to be similar to an expression for the ensemble effective conductivity of an infinite field derived analytically by earlier authors. Here, block conductivities obtained by power averaging are compared with effective conductivities obtained from a numerical flow model and are found to be in excellent agreement for a suitably chosen averaging exponent. This agreement deteriorates gradually as the log variance of conductivity increases beyond 2. For arbitrary flow field geometry and anisotropic conductivity covariances, the averaging exponent can be calibrated by recourse to numerical flow experiments. For cubic fields and an isotropic spatial covariance, the averaging exponent is found to be 1/3. In this particular case, it was found that flow field discretization at the block scale through local averaging of point conductivities gave similar results to those obtained directly using a point scale discretization of the flow field. 相似文献
We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126). 相似文献
This study investigated the adsorption and precipitation of phosphate by blast furnace slag (BFS) separately.
In order to evaluate the adsorption capacity of BFS, BFS was treated before its use by acid. The authors aim to develop a new porous carrier to adsorb simultaneously ammonium and phosphate from seawater under eutrophic conditions. The current paper deals with a promising new approach to improve the utilization of some industrial solid wastes such as BFS and zeolite synthesized from fly ash [ZFA(Fe)] by their solidification to cylindrical porous carriers using a hydrothermal hot-pressing (HHP) method.
Attempts to produce porous carriers using an arranged HHP method with different porosities (24%, 40% and 52% (v/v)) were carried out. Physical properties of carriers such as porosity, compressive strength and height have been investigated. Laboratory studies showed strong evidence that the porous carrier was very selective towards phosphate and ammonium. The results demonstrated the role of porosity in enhancing phosphate and ammonium adsorption by the increase of the surface area per weight. The estimates of the parameters and the correlation coefficients according to the Freundlich equations revealed that adsorption was related to the porosity of carriers and phosphate and ammonium were adsorbed well on the carriers having large porosity.
The results suggested that developing carrier with high porosity was a promising way to enhance nutrients adsorption. 相似文献