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.     

Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

Extensional tectonic origin of gneissosity and related structures of the Feiran–Solaf metamorphic belt, Sinai, Egypt

The Feiran–Solaf metamorphic belt consists of low-P high-T amphibolite facies, partly migmatized gneisses, schists, amphibolites and minor calc-silicate rocks of metasedimentary origin. There are also thick concordant synkinematic sheets of diorite, tonalite and granodiorite orthogneiss and foliated granite and pegmatite dykelets. The gneissosity (or schistosity) is referred to as S₁, and is almost everywhere parallel to lithological layering, S₀. This parallelism is not due to transposition. The gneissosity formed during an extensional tectonic event (termed D1), before folding of S₀. S₁ formed by coaxial pure shear flattening strain (Z normal to S₀, i.e. vertical; with X and Y both extensional and lying in S₁). This strain also produced chocolate tablet boudinage of some layers and S₁-concordant sills and veins. S₁ has a strong stretching lineation L₁ with rodding characteristics. Within-plane plastic anisotropy (lower ductility along Y compared to along X) resulted in L₁-parallel extensional ductile shears and melt filled cracks. Continued shortening of these veins, and back-rotation of foliations on the shears produced intrafolial F₁ folds with hinges parallel to the stretching lineation. F₁ fold asymmetry variations do not support previous models involving macroscopic F₁ folds or syn-gneissosity compressional tectonics. The sedimentary protoliths of the Feiran–Solaf gneisses were probably deposited in a pre-800 Ma actively extending intracratonic rift characterizing an early stage of the break-up of Rodinia.     

Applications of particle-tracking techniques to bank infiltration: a case study from El Paso,Texas, USA

This paper presents results of a small scale study that utilized particle-tracking techniques to evaluate transport of river water through an alluvial aquifer in a bank infiltration testing site in El Paso, Texas, USA. The particle-tracking survey was used to better define filtration parameters. Several simulations were generated to allow visualization of the effects of well placement and pumping rate on flow paths, travel time, the size of the pumping influence zone, and proportion of river-derived water and groundwater mixing in the pumping well. Simulations indicate that migration of river water into the aquifer is generally slow. Most water does not arrive at the well by the end of an 18-day pumping period at 0.54 m³/min pumping rate for a well located 18 m from the river. Forty-four percent of the water pumped from the well was river water. The models provided important information needed to design appropriate sampling schedules for bank filtration practices and ensured meeting adequate soil-retention times. The pumping rate has more effect on river water travel time than the location of the pumping well from the river. The examples presented in this paper indicate that operating the pumping well at a doubled distance from the river increased the time required for the water to travel to the well, but did not greatly change the capture zone.     

An operational multiscale system for hazards prediction, mapping, and response

By definition, a crisis is a situation that requires assistance to be managed. Hence, response to a crisis involves the merging of local and non-local emergency response personnel. In this situation, it is critical that each participant: (1) know the roles and responsibilities of each of the other participants; (2) know the capabilities of each of the participants; and (3) have a common basis for action. For many types of natural disasters, this entails having a common operational picture of the unfolding events, including detailed information on the weather, both current and forecasted, that may impact on either the emergency itself or on response activities. The Consequences Assessment Tool Set (CATS) is a comprehensive package of hazard prediction models and casualty and damage assessment tools that provides a linkage between a modeled or observed effect and the attendant consequences for populations, infrastructure, and resources, and, hence, provides the common operational picture for emergency response. The Operational Multiscale Environment model with Grid Adaptivity (OMEGA) is an atmospheric simulation system that links the latest methods in computational fluid dynamics and high-resolution gridding technologies with numerical weather prediction to provide specific weather analysis and forecast capability that can be merged into the geographic information system framework of CATS. This paper documents the problem of emergency response as an end-to-end system and presents the integrated CATS–OMEGA system as a prototype of such a system that has been used successfully in a number of different situations.     

Integration and magnitude homogenization of the Egyptian earthquake catalogue

The aim of the present work is to compile and update a catalogue of the instrumentally recorded earthquakes in Egypt, with uniform and homogeneous source parameters as required for the analysis of seismicity and seismic hazard assessment. This in turn requires a detailed analysis and comparison of the properties of different available sources, including the distribution of events with time, the magnitude completeness, and the scaling relations between different kinds of magnitude reported by different agencies. The observational data cover the time interval 1900–2004 and an area between 22°–33.5° N and 25°–36° E. The linear regressions between various magnitude types have been evaluated for different magnitude ranges. Using the best linear relationship determined for each available pair of magnitudes, as well as those identified between the magnitudes and the seismic moment, we convert the different magnitude types into moment magnitudes M _W, through a multi-step conversion process. Analysis of the catalogue completeness, based on the M _W thus estimated, allows us to identify two different time intervals with homogeneous properties. The first one (1900–1984) appears to be complete for M _W ≥ 4.5, while the second one (1985–2004) can be considered complete for magnitudes M _W ≥ 3.     

Distribution of Boron in Some Egyptian Aquatic Environments

Concentrations of boron in seawater (from four regions along the Alexandria coastline, subjected to land disposal), brackish water (Lake Edku) and drains water (e.g. El-Umum Drain) were determined during the period from February to August 2000. Boron was determined spectrophotometrically by a modified curcumin method. For Lake Edku, boron concentration fluctuated between 0.023 and 0.105 mmol/l. There are several factors that affect the concentration of B in the Lake water: (a) effect of the drainage water via El-Khairy and Barsiek Drains, (b) utilization of boron by hydrophytes, and (c) water exchange through the sea-lake connection. It may be concluded that the level of boron in the Lake water cannot be considered a substantial hazard to the Lake organisms. Boron concentration varied from 0.392 to 0.522 mmol/l in seawater samples and from 0.141 to 0.458 mmol/l in the sites where the water from the drains (El-Umum Drain and El-Noubaria Canal) mixed with the seawater. The broader variation of boron (mmol/l)/salinity ratios for seawater samples (0.0106–0.0138) may be due to that the samples were collected from the upper seawater layers, where contributions from land run-off, atmospheric precipitation and differences in the biota affect the concentration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Full-range equation for wave boundary layer thickness

Full-range equation covering all the flow regimes in a wave boundary layer is proposed for the boundary layer thickness. The results are compared with the available experimental data and good agreement has been found. In case of wave boundary layers, there are three definitions of boundary layer thickness in use. Therefore, the full-range equation is derived for three of the definitions. The findings of this study may be useful in calculating suspended sediment transport in coastal environments and studying wave–current combined motion.     

Stability of waterfront retaining wall subjected to pseudo-static earthquake forces

Waterfront retaining walls supporting dry backfill are subjected to hydrostatic pressure on upstream face and earth pressure on the downstream face. Under seismic conditions, if such a wall retains a submerged backfill, additional hydrodynamic pressures are generated. This paper pertains to a study in which the effect of earthquakes along with the hydrodynamic pressure including inertial forces on such a retaining wall is observed. The hydrodynamic pressure is calculated using Westergaard's approach, while the earth pressure is calculated using Mononobe-Okabe's pseudo-static analysis. It is observed that when the horizontal seismic acceleration coefficient is increased from 0 to 0.2, there is a 57% decrease in the factor of safety of the retaining wall in sliding mode. For investigating the effect of different parameters, a parametric study is also done. It is observed that if φ is increased from 30° to 35°, there is an increase in the factor of safety in the sliding mode by 20.4%. Similar observations were made for other parameters as well. Comparison of results obtained from the present approach with [Ebeling, R.M., Morrison Jr, E.E., 1992. The seismic design of waterfront retaining structures. US Army Technical Report ITL-92-11. Washington DC] reveal that the factor of safety for static condition (k_h=0), calculated by both the approaches, is 1.60 while for an earthquake with k_h=0.2, they differ by 22.5% due to the consideration of wall inertia in the present study.