Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.     

Using time‐domain reflectometry to characterize shallow solute transport in an oak woodland hillslope in northern California,USA

The natural heterogeneity of water and solute movement in hillslope soils makes it difficult to accurately characterize the transport of surface‐applied pollutants without first gathering spatially distributed hydrological data. This study examined the application of time‐domain reflectometry (TDR) to measure solute transport in hillslopes. Three different plot designs were used to examine the transport of a conservative tracer in the first 50 cm of a moderately sloping soil. In the first plot, which was designed to examine spatial variability in vertical transport in a 1·2 m² plot, a single probe per meter was found to adequately characterize vertical solute travel times. In addition, a dye and excavation study in this plot revealed lateral preferential flow in small macropores and a transport pattern where solute is focused vertically into preferential flow pathways. The bypass flow delivers solute deeper in the soil, where lateral flow occurs. The second plot, designed to capture both vertical and lateral flow, provided additional evidence confirming the flow patterns identified in the excavation of the first plot. The third plot was designed to examine lateral flow and once again preferential flow of the tracer was observed. In one instance rapid solute transport in this plot was estimated to occur in as little as 3% of the available pore space. Finally, it was demonstrated that the soil anisotropy, although partially responsible for lateral subsurface transport, may also homogenize the transport response across the hillslope by decreasing vertical solute spreading. Copyright © 2002 John Wiley & Sons, Ltd.     

Holocene environmental reconstruction from deltaic deposits in northeast Greenland

Terraces of different age in the Zackenberg delta, located at 74°N in northeast Greenland, have provided the opportunity for an interdisciplinary approach to the investigation of Holocene glacial, periglacial, pedological, biological and archaeological conditions that existed during and after delta deposition. The raised Zackenberg delta accumulated mainly during the Holocene Climatic Optimum, starting slightly prior to 9500 cal. yr BP (30 m a.s.l.) and continued until at least 6300 cal. yr BP (0.5 m a.s.l.). Evidence of sea‐level change is based on conventional ¹⁴C dates of shells from the marine delta bottomsets, ¹⁴C AMS dating of macroscopic plant material from the foresets and of fluvial deposits. Arthropod and plant remains from 7960 cal. yr BP in the delta foresets include the oldest evidence of the arctic hare in Greenland and evidence of a rich herb flora slightly different from the modern flora. Empetrum nigrum and Salix herbacea remains indicate a summer temperature at least as high as today during delta deposition. Post‐depositional nivation activity, dated by luminescence, lichenometry and Schmidt Hammer measurements indicate mainly late Holocene activity, at least since 2900 yr BP, including Little Ice Age (LIA) avalanche activity. Pedological analyses of fossil podsols in the Zackenberg delta, including ¹⁴C AMS dating of selected organic rich B‐horizons, show continued podsol development during the Holocene Climatic Optimum and into the subsequent colder period of the late Holocene, until 3000–2400 yr BP. A Neo‐Eskimo house ruin found on the lower part of the delta, presently being eroded by the sea, is dated to AD 1800. It presumably was abandoned prior to AD 1869, and suggests that some of the last Eskimos that lived in northeast Greenland might have occupied the Zackenberg delta. Copyright © 2002 John Wiley & Sons, Ltd.     

Norwegian sea‐surface palaeoenvironments of marine oxygen‐isotope stage 3: the paradoxical response of dinoflagellate cysts

High‐resolution marine palynological data have been obtained from two very long sediment cores (MD952009 and MD952010) retrieved from the southern Norwegian Sea. The dinoflagellate cyst assemblages show pronounced fluctuations in composition, which correlate strongly with magnetic susceptibility records and also mimic the δ¹⁸O signal of the GISP2 Greenland ice‐core. If focusing on the period from 48 to 30 cal. kyr BP, this correlation suggests a paradoxical response of the sea‐surface environments to the atmospheric conditions over Greenland: when the Greenland δ¹⁸O signal reflects warm interstadial conditions, the Norwegian Sea depicts cold sea‐surface temperatures with quasi‐perennial sea‐ice cover (based on dinoflagellate cysts). In contrast, when the Greenland δ¹⁸O records cold stadial periods, the Norwegian Sea‐surface temperatures are warm (based on dinoflagellate cysts), probably linked to inflow of the North Atlantic Drift. These results, similar in both cores, are contrary to those of previous studies and shed light on a possible decoupling of Norwegian sea surface‐water conditions and atmospheric conditions over Greenland. This decoupling could be linked to an atmosphere–ocean system behaving similar to that which the Northern Hemisphere is experiencing at present, i.e. strongly variable owing to the North Atlantic Oscillation. Copyright © 2002 John Wiley & Sons, Ltd.     

Kinematic wave solutions for pollutant transport over an infiltrating plane with finite‐period mixing and mixing zone

Kinematic wave solutions are derived for transport of a conservative non‐point‐source pollutant during a rainfall‐runoff event over an infiltrating plane for two cases: (i) finite‐period mixing and (ii) soil‐mixing zone. Rainfall is assumed to be steady, uniform and finite in duration, and it is assumed to have zero concentration of pollutants. Infiltration is assumed constant in time and space. Prior to the start of rainfall, the pollutant is distributed uniformly over the plane. In the first case, when rainfall occurs, the mixing of pollutant in the runoff water occurs in a finite period of time. In the second case, the chemical concentration is assumed to be a linearly decreasing function of rainfall intensity and overland flow. The solute concentration and discharge are found to depend on the flow characteristics as well as the solute concentration parameters. The characteristics of solute concentration and discharge graphs seem to be similar to those reported in the literature and observed in laboratory experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

An extended version of the classical Generalized Backward Euler (GBE) algorithm is proposed for the numerical integration of a three‐invariant isotropic‐hardening elastoplastic model for cemented soils or weak rocks undergoing mechanical and non‐mechanical degradation processes. The restriction to isotropy allows to formulate the return mapping algorithm in the space of principal elastic strains. In this way, an efficient and robust integration scheme is developed which can be applied to relatively complex yield surface and plastic potential functions. Moreover, the proposed algorithm can be linearized in closed form, thus allowing for quadratic convergence in the global Newton iteration. A series of numerical experiments are performed to illustrate the accuracy and convergence properties of the algorithm. Selected results from a finite element analysis of a circular footing on a soft rock layer undergoing chemical weathering are then presented to illustrate the algorithm performance at the boundary value problem level. Copyright © 2002 John Wiley & Sons, Ltd.     

40Ar/39 mineral ages from the Scituate Granite, Rhode Island: implications for Late Palaeozoic tectonothermal activity in New England

The alkalic Scituate Granite was emplaced into crystalline sequences within the New England Esmond–Dedham terrane in the Late Devonian ( c. 370 Ma). Variably recrystallized amphibole (iron-rich, hastingsite–hastingsitic hornblende) from four variably deformed samples of the pluton record south-westerly younging ⁴⁰Ar/³⁹Ar plateau ages ranging between 276 and 263 Ma. These are interpreted to date diachronous cooling through temperatures appropriate for intracrystalline retention of argon following late Palaeozoic orogenic activity. Iron-rich biotite concentrates from the samples record only slightly younger ages, and therefore suggest relatively rapid post-metamorphic cooling. The ⁴⁰Ar/³⁹Ar ages indicate that the late Palaeozoic tectonothermal overprint was much more regionally pervasive than was previously considered. The apparent timing of this activity is similar to previous estimates for the chronology of high-grade metamorphism throughout the adjacent Hope Valley terrane and for phases of ductile movement on the intervening Lake Char–Honey Hill fault system.     

A relook at NEH‐4 curve number data and antecedent moisture condition criteria

This paper investigates the variation of the popular curve number (CN) values given in the National Engineering Hand Book–Section 4 (NEH‐4) of the Soil Conservation Service (SCS) with antecedent moisture condition (AMC) and soil type. Using the volumetric concept, involving soil, water, and air, a significant condensation of the NEH‐4 tables is achieved. This leads to a procedure for determination of CN for gauged as well as ungauged watersheds. The rainfall‐runoff events derived from daily data of four Indian watersheds exhibited a power relation between the potential maximum retention or CN and the 5‐day antecedent rainfall amount. Including this power relation, the SCS‐CN method was modified. This modification also eliminates the problem of sudden jumps from one AMC level to the other. The runoff values predicted using the modified method and the existing method utilizing the NEH‐4 AMC criteria yielded similar results. Copyright © 2006 John Wiley & Sons, Ltd.     

Separation of gamma and hadron initiated air showers with energies between 20 and 500 TeV

The discrimination between air showers initiated by γ rays and by hadrons is one of the fundamental problems in experimental cosmic-ray physics. The physics of this ‘γ/hadron separation’ is discussed in this paper. We restrict ourselves to the energy range from about 20 to 500 TeV, and take only the information contained in the lateral Čerenkov light distribution and the number of electrons at the detector level into consideration. An understanding of the differences between air showers generated by γ rays and those due to hadrons leads us to formulate suitable observables for the separation process. Angle integrating Čerenkov arrays (AICA) offer a promising new approach to ground-based γ-ray astronomy in the energy region from about 20 to 500 TeV. In order to establish this technique, an efficient suppression of the overwhelming hadronic background radiation is required. As an example for our general discussion, we present one method for γ/hadron separation in AICAs called ‘LES’. It is based on the simultaneous determination of the shower size and some characteristic parameters of the lateral distribution of the Čerenkov light. The potential inherent within this technique is demonstrated in quantitative detail for the existing ‘AIROBICC’ AICA. We also propose an objective measure of the intrinsic sensitivity of a detection scheme in ground-based γ-ray astronomy, the ‘reduced quality factor’. It is shown that AICAs may reach a sensitivity to γ-ray point sources in the high VHE range similar to that of the Čerenkov-telescope imaging technique in the low VHE region.     

A bimodal four‐parameter lognormal linear model of soil water repellency persistence

Soil water repellency may be characterized in terms of the delayed infiltration time of a water droplet resting on the soil surface, which is, water drop penetration time (WDPT), or repellency persistence. Such repellency persistence varies nonlinearly with soil water content (θ_g), although no models have been proposed to reproduce the variation of WDPT with θ_g in soils. Dynamic factor analysis (DFA) is used to identify two common patterns of unexplained variability in a scattered dataset of WDPT versus θ_g measurements. A four‐parameter lognormal distribution was fitted to both common patterns obtained by DFA, and these were combined additively in a weighted multiple linear bimodal model. We show how such an empirical model is capable of reproducing a large variety of WDPT versus θ_g curve shapes (N = 80) both within a wide range of measured WDPTs (0–17 000 s) and for samples with organic matter content ranging from 21·7 to 80·6 g (100 g)^?1. Copyright © 2009 John Wiley & Sons, Ltd.