Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

Modelling the poroelastoplastic behaviour of soils subjected to internal erosion by suffusion

Granular soils subjected to seepage flow may suffer suffusion, ie, a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius-Duhem inequality accounting for dissipation due to suffusion, and we deduce restrictions on the constitutive laws of the soil. We suggest (a) a possible coupling between the seepage forces and the suffusion kinetics and (b) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains and the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided.     

A modified numerical model for moisture-salt transport in unsaturated sandy soil under evaporation

Soil salinization, caused by salt migration and accumulation underneath the soil surface, will corrode structures. To analyze the moisture-salt migration and salt precipitation in soil under evaporation conditions, a mathematical model consisting of a series of theoretical equations is briefly presented. The filling effect of precipitated salts on tortuosity factor and evaporation rate are taken into account in relevant equations. Besides, a transition equation to link the solute transport equation before and after salt precipitation is proposed. Meanwhile, a new relative humidity equation deduced from Pitzer ions model is used to modify the vapor transport flux equation. The results show that the calculated values are in good agreement with the published experimental data, especially for the simulation of volume water content and evaporation rate of Toyoura sand, which confirm the reliability and applicability of the proposed model.     

Muon density measurements with the KASCADE central detector

Frequency distributions of local muon densities in high-energy extensive air showers (EAS) are presented as signature of the primary cosmic ray energy spectrum in the knee region. Together with the gross shower variables like shower core position, angle of incidence, and the shower sizes, the KASCADE experiment is able to measure local muon densities for two different muon energy thresholds. The spectra have been reconstructed for various core distances, as well as for particular subsamples, classified on the basis of the shower size ratio N_μ/N_e. The measured density spectra of the total sample exhibit clear kinks reflecting the knee of the primary energy spectrum. While relatively sharp changes of the slopes are observed in the spectrum of EAS with small values of the shower size ratio, no such feature is detected at EAS of large N_μ/N_e ratio in the energy range of 1–10 PeV. Comparing the spectra for various thresholds and core distances with detailed Monte Carlo simulations the validity of EAS simulations is discussed.     

平衡剖面的制作流程及其地质意义

平衡剖面技术是地质思维和计算机技术的结晶,使对断层构造的研究提高到定量阶段,其依据是在垂直构造走向的剖面上,地层长度和面积(2D)或体积(3D)是均衡的。在此原理基础上利用数学手段对盆地的构造发育史进行正演和反演模拟,直观地再现地下构造的原始几何形态,迅速提供地震剖面的构造解释方案,并对解释结果进行检验(不平衡的剖面其解释一般有问题),为深刻认识构造发育史、分析油气运移及聚集规律提供依据,提高了工作效率。其结果也为盆地模拟、油藏模拟、定量计算构造伸缩量等地质研究打下了坚实的基础[1]。     

High energy phenomena in eta carinae

We have investigated with BeppoSAX the long term behaviour of the harder X-ray component of the supposed supermassive binary system η Car along its 5.52 year cycle. We have found that in March 1998 during egress from the last December 1997 eclipse, this component was the same as outside eclipse, but for a large (×3.5) increase of NH _h , that can be attributed to the presence or formation of opaque matter in front of the source near periastron. Unexpectedly, at that time the iron 6.7 keV emission line was 40% stronger. BeppoSAX has for the first time found ahard X-ray tail extending to at least 50 keV, that cannot be adequately fitted with an additional hotter thermal component. The 2–100 keV spectrum of η Car is instead well fitted with an absorbed powerlaw spectrum with photon index 2.53, suggesting non-thermal emission as an alternative model for the core source.     

Spatial measurements of stream baseflow,a relevant method for aquifer characterization and permeability evaluation. Application to a hard‐rock aquifer,the Oman ophiolite

The structure, functioning and hydrodynamic properties of aquifers can be determined from an analysis of the spatial variability of baseflow in the streams with which they are associated. Such analyses are based on simple low‐cost measurements. Through interpreting the hydrological profiles (Q = f(A)) it is possible to locate the aquifer(s) linked to the stream network and to determine the type of interrelated flow, i.e. whether the stream drains or feeds the aquifer. Using an analytical solution developed for situations with a positive linear relationship, i.e. where the baseflow increases linearly with increasing catchment size, it is also possible to estimate the permeability of the aquifer(s) concerned at catchment scale. Applied to the hard‐rock aquifers of the Oman ophiolite, this method shows that the ‘gabbro’ aquifer is more permeable than the ‘peridotite’ aquifer. As a consequence the streams drain the peridotites and ‘leak’ into the gabbro. The hydrological profiles within the peridotite are linear and positive, and indicate homogeneity in the hydrodynamic properties of these formations at the kilometre scale. The permeability of the peridotite is estimated at 5 · 10^?7 to 5 · 10^?8 m/s. Copyright © 2004 John Wiley & Sons, Ltd.     

黑子磁流体静力学的一个模型

本文对Ｏｓｈｅｒｏｖｉｃｈ的黑子返回磁通量模型作了适当的修改，使用黑子中心作为边界条件，用五种观测结果，导出了理论模型所需的五个主要参量，用半经验方法求得了黑子静力学模型的磁场、压力和温度等物理量．将此模型应用于一个中等大小的圆形对称黑子，可得到一个特解，结果发现我们的模型既能满足黑子的磁性质，同时又能满足合理的热力学量分布．     

Revisiting Sustainable Development of Dry Valleys in Hengduan Mountains Region

Dry valleys are a striking geographic landscape in Hengduan Mountains Region and are characterized by low rainfall, desert type of vegetation and fragile environment. Past efforts and resources have been concentrated mainly on rehabilitation of degraded ecosystem and fragile environment, particularly reforestation, while socio-economic development has been largely overlooked. Despite successes in pocket areas, the overall trend of unsustainability and environmental deterioration are continuing. It is important to understand that uplift of the Tibetan Plateau is the root cause of development of dry valleys, and development and formation of dry valleys is a natural process. Human intervention has played a secondary role in development of dry valleys and degradation of dry valleys though human intervention in many cases has speeded up environmental degradation of the dry valleys. It is important to understand that dry valleys are climatic enclaves and an integrated approach that combines rehabilitation of degraded ecosystems and socio-economic development should be adopted if the overall goal of sustainable development of dry valleys is to be achieved. Promotion of niche-based cash crops, rural energy including hydropower, solar energy, biogas and fuelwood plantation is recommended as the priority activities.