Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

About Darcy's law in non-Galilean frame

This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall–Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek⁻¹ is 𝒪(1). These variations are estimated to be less than 5% if Ek⁻¹<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

从国际司法判例和国际海洋法看中日海洋区域的划界

《联合国海洋法公约》规定，海洋划界争端应在有关国际法的基础上，以和平的方式加以解决，中、日两国的海洋介应该按照国际法的规定，找到适合两国情况的比较公平的原则和方法。     

Comprehensive development of agriculture in the Loess Plateau Area

The Loess Plateau is one of China s developing areas where socio-econ-omy is backward, ecological environment deteriorated and people's life difficult.The purpose of carrying out comprehensive development of the area's agriculture is, in essence, to open up new fields of agro-production, to intensify the utilization of related resources, to raise productivity and to win bigger output. The decision is important, as by so doing, the physical landscape could be tranformed, the local economy could be flourished, and the people's standard of living could be improved, and moreover the national development strategy of "depending on the East and shifting to the West" and building Shanxi Province into an energy and chemical industrial base could be realized.Based on field investigations in recent years, the auther proposed the purpose, target, principles, steps, tactics and strategies for the comprehensive development of the are's agriculture.     

浅谈档案行政执法和档案普法的关系

本文根据《中华人民共和国档案法》及有关档案法律法规,论述了档案行政执法和档案普法的关系。     

地学“开合律”及其在造山带研究中的意义

“开合律”是地学辩证法基本规律之一。本文概述了它的内容与特点,阐明它在造山带研究中的意义及运用它指导造山带研究的步骤,并根据目前已总结的5种“开”、“合”类型相应地提出了5种造山带类型。     

Atténuation de l'intensité macrosismique pour la France métropolitaine : importance de l'intensité épicentrale

The main result of this work is to show that macroseismic intensity decay with distance strongly depends on the epicentral intensity. An attenuation law that takes this parameter into account is proposed for Metropolitan France, from the analysis of SISFRANCE macroseismic database. Such a model significantly reduces the difference between observed and theoretical intensities. A map of the attenuation variations is also set up for Metropolitan France. No major site effects are observed, but at a broad scale, young Alpine regions display a stronger attenuation than old Hercynian regions. To cite this article: P. Arroucau et al., C. R. Geoscience 338 (2006).     

Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

The computation of electromagnetic (EM) fields, for 1-D layered earth model, requires evaluation of Hankel Transform (HT) of the EM kernel function. The digital filtering is the most widely used technique to evaluate HT integrals. However, it has some obvious shortcomings. We present an alternative scheme, based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature. This expansion reduces the integral to a simple algebraic sum. The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters. The field curves for four types (A-, K-, H-and Q-type) of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson sc heme. It is concluded that the present scheme is more accurate than the Anderson scheme