Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling and observation of hedgerow transpiration effect on water balance components at the hillslope scale in Brittany

Vegetation has a major influence on the water and energy balance of the earth's surface. In the last century, human activities have modified land use, inducing a consequent change in albedo and potential evapotranspiration. Linear vegetation structures (hedgerows, shelterbelts, open woodland, etc) were particularly abundant but have declined considerably over the past several decades. In this context, it is important to quantify their effect on water and energy balance both on a global scale (climate change and weather prediction) and on a local scale (soil column, hillslope and watershed). The main objective of this study was to quantify the effect of hedgerows on the water cycle by evaluating spatial and temporal variations of water balance components of a hillslope crossed by a hedgerow. Water flow simulation was performed using Hydrus‐2D to emphasize the importance of transpiration in the water balance and to evaluate water extraction from groundwater. Model validation was performed by comparing simulated and observed soil matrix potentials and groundwater levels. Hedgerow transpiration was calculated from sap flow measurements of four trees. Water balance components calculated with a one‐dimensional water balance equation were compared with simulations. Simulation runs with and without tree root uptake underlined the effect of hedgerow transpiration, increasing capillary rise and decreasing drainage. Results demonstrated that the spatial and temporal variability of water balance components was related to the hedgerow presence as well as to the meteorological context. The relations between transpiration, groundwater proximity and soil‐water availability determined the way in which water balance components were affected. Increased capillary rise and decreased drainage near hedges were related to the high transpiration of trees identified in this study. Transpiration reached twice the potential evapotranspiration when groundwater level and precipitation amounts were high. Water balance analysis showed that transpiration was a substantial component, representing 40% of total water output. These results may offer support for improving hydrological models by including the effect of land use and land cover on hydrological processes. Copyright © 2012 John Wiley & Sons, Ltd.     

Nb–Ta fractionation induced by fluid‐rock interaction in subduction‐zones: constraints from UHP eclogite‐ and vein‐hosted rutile from the Dabie orogen,Central‐Eastern China

Niobium and Ta concentrations in ultrahigh‐pressure (UHP) eclogites and rutile from these eclogites and associated high pressure (HP) veins were used to study the behaviour of Nb–Ta during dehydration and fluid‐rock interaction. Samples were collected through a ～2 km profile at the Bixiling complex in the Dabie orogenic belt, Central‐Eastern China. All but one eclogite away from veins (EAVs) display nearly constant Nb/Ta ratios ranging from 16.1 to 19.2, with an average of 16.9 ± 0.8 (2 SE), similar to that of their gabbroic protolith from the Yangtze Block. Nb/Ta ratios of rutile from the EAVs range from 12.7 to 25.3 among different individual grains, with the average values close to those of the corresponding bulk rocks. These observations show that Nb and Ta were not significantly fractionated by prograde metamorphism up to eclogite facies when no significant fluid‐rock interaction occurs. In contrast, Nb/Ta ratios of rutile from eclogites close to veins (ECVs) are highly variable from 17.8 to 49.8, which are systematically higher (by up to 17) than those of rutile from the veins. These observations demonstrate that Nb and Ta were mobilized and fractionated during localized fluid flow and intensive fluid‐rock interaction. This is strongly supported by Nb/Ta zoning patterns in single rutile grains revealed by in situ LA‐ICP‐MS analysis. Ratios of Nb/Ta in the ECV‐hosted rutile decrease gradually from cores towards rims, whereas those in the EAV‐hosted rutile are nearly invariable. Furthermore, the vein rutile shows Nb/Ta zoning patterns that are complementary to those in rutile from their immediate hosts (ECVs), suggesting an internal origin for the vein‐forming fluids. The Nb/Ta ratios of such fluids evolved from low values at the early stage of subduction to higher values at later supercritical conditions with increased temperature and pressure. Quantitative modelling was conducted to constrain the compositional evolution of metamorphic fluids during dehydration and fluid‐rock interaction focusing on Nb–Ta distribution. The modelling results based on our proposed multistage fluid phase evolution path can essentially reproduce the natural observations reported in the present study.     

Modélisation des écoulements de l'oued Miliane par le modèle CEQUEAU

Résumé

Cette étude présente l'application du modèle déterministe de simulations hydrologiques CEQUEAU pour la reconstitution des débits moyens journaliers et mensuels de quatre stations hydrométriques du bassin versant de l'oued Miliane (Tunisie) ainsi que les niveaux moyens journaliers dans le barrage Bir Mcherga. Le modèle a été calibré avec les données de trois années d'observation (de 1972/73 à 1974/75). Durant cette période, les débits moyens journaliers sont reconstitués avec des coefficients de Nash variant de 0.88 à 0,97 et des écarts relatifs qui varient entre ?2.3% et ?4.7%. Pour les débits de pointe les biais sont plus élevés. L'analyse des séries résiduelles a montré que les résidus sont homogènes et temporellement dépendants mais les résidus des différents stations sont indépendants. Durant la période de validation (de 1975/76 à 1976/77), les coefficients de corrélation et de Nash se sont dégradés pour les deux stations restées en fonctionnement (0.71 et 0.89). Les biais obtenus varient entre ?3.7% et +5.5%.     

Metamorphism of ultrahigh‐pressure eclogites from the Kebuerte Valley,South Tianshan,NW China: phase equilibria and P–T path

Eclogites from the Kebuerte Valley, Chinese South Tianshan, consist of garnet, omphacite, phengite, paragonite, glaucophane, hornblendic amphibole, epidote, quartz and accessory rutile, titanite, apatite and carbonate minerals with occasional presence of coesite or quartz pseudomorphs after coesite. The eclogites are grouped into two: type I contains porphyroblastic garnet, epidote, paragonite and glaucophane in a matrix dominated by omphacite where the proportion of omphacite and garnet is >50 vol.%; and type II contains porphyroblastic epidote in a matrix consisting mainly of fine‐grained garnet, omphacite and glaucophane where the proportion of omphacite and garnet is <50 vol.%. Garnet in both types of eclogites mostly exhibits core–rim zoning with increasing grossular (X_gr) and pyrope (X_py) contents, but a few porphyroblastic garnet grains in type I eclogite shows core–mantle zoning with increasing X_py and a slight decrease in X_gr, and mantle–rim zoning with increases in both X_gr and X_py. Garnet rims in type I eclogite have higher X_py than in type II. Petrographic observations and phase equilibria modelling with pseudosections calculated using thermocalc in the NCKMnFMASHO system for three representative samples suggest that the eclogites have experienced four stages of metamorphism: stage I is the pre‐peak temperature prograde heating to the pressure peak (P_max) which was recognized by the garnet core–mantle zoning with increasing X_py and decreasing X_gr. The P–T conditions at P_max constrained from garnet mantle or core compositions with minimum X_gr content are 29–30 kbar at 526–540 °C for type I and 28.2 kbar at 518 °C for type II, suggesting an apparent thermal gradient of ～5.5 °C km^?1. Stage II is the post‐P_max decompression and heating to the temperature peak (T_max), which was modelled from the garnet zoning with increasing X_gr and X_py contents. The P–T conditions at T_max, defined using the garnet rim compositions with maximum X_py content and the Si content in phengite, are 24–27 kbar at 590 °C for type I and 22 kbar at 540 °C for type II. Stage III is the post‐T_max isothermal decompression characterized by the decomposition of lawsonite, which may have resulted in the release of a large amount of fluid bound in the rocks, leading to the formation of epidote, paragonite and glaucophane porphyroblasts. Stage IV is the late retrograde evolution characterized by the overprint of hornblendic amphibole in eclogite and the occurrence of epidote–amphibole facies mineral assemblages in the margins or in the strongly foliated domains of eclogite blocks due to fluid infiltration. The P–T estimates obtained from conventional garnet–clinopyroxene–phengite thermobarometry for the Tianshan eclogites are roughly consistent with the P–T conditions of stage II at T_max, but with large uncertainties in temperature. On the basis of these metamorphic stages or P–T paths, we reinterpreted that the recently reported zircon U–Pb ages for eclogite may date the T_max stage or the later decompression stage, and the widely distributed (rutile‐bearing) quartz veins in the eclogite terrane may have originated from the lawsonite decomposition during the decompression stage rather than from the transition from blueschist to eclogite as previously proposed.     

Statistically downscaled probabilistic multi‐model ensemble projections of precipitation change in a watershed

This paper presents the development of a probabilistic multi‐model ensemble of statistically downscaled future projections of precipitation of a watershed in New Zealand. Climate change research based on the point estimates of a single model is considered less reliable for decision making, and multiple realizations of a single model or outputs from multiple models are often preferred for such purposes. Similarly, a probabilistic approach is preferable over deterministic point estimates. In the area of statistical downscaling, no single technique is considered a universal solution. This is due to the fact that each of these techniques has some weaknesses, owing to its basic working principles. Moreover, watershed scale precipitation downscaling is quite challenging and is more prone to uncertainty issues than downscaling of other climatological variables. So, multi‐model statistical downscaling studies based on a probabilistic approach are required. In the current paper, results from the three well‐reputed statistical downscaling methods are used to develop a Bayesian weighted multi‐model ensemble. The three members of the downscaling ensemble of this study belong to the following three broad categories of statistical downscaling methods: (1) multiple linear regression, (2) multiple non‐linear regression, and (3) stochastic weather generator. The results obtained in this study show that the new strategy adopted here is promising because of many advantages it offers, e.g. it combines the outputs of multiple statistical downscaling methods, provides probabilistic downscaled climate change projections and enables the quantification of uncertainty in these projections. This will encourage any future attempts for combining the results of multiple statistical downscaling methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterizing the hydraulic properties of unsaturated sand considering various porosities and drying‐wetting paths of the retention curve

Previous studies have shown that water retention curve (WRC) and the hydraulic conductivity vary because of changes of the void ratio or porosity of soil. However, limited documents pointed out the change of hydraulic properties of soil when compacted to different porosities while considering both of the drying and wetting processes of the WRC. This information is sometimes necessary for research like finger flow analysis or the occurrence of wetting and drying cycles as what would be seen in the field. Therefore, this study aims to examine the change of WRC characteristics with varied porosity considering both of the drying and wetting path in WRC by conducting a sand box experiment. Results show that the same type of sand compacted to various porosities have different hydraulic parameters. Hydraulic conductivities generally decrease with reduced porosities; shape parameter α of the van Genuchten equation (1980) linearly decreases with declining porosity and shape parameter n in a reversal manner for the sands of interest whether in the drying process or wetting process. The unsaturated properties of sand are further characterized by inspecting the variations of moisture content, matric suction and vertical displacement of soil body subject to periodic changes of the water level by another sand box experiment. The outcomes suggest that the saturated water content and residual water content are changing during the wetting–drying process, which can be an implication of the changed properties of WRC. The characteristics of volumetric deformation might be varied as well because of the observation of the dissimilar patterns of the changing vertical displacements among each wetting–drying process. Infiltration patterns of the sands also are identified through numerical modelling by introducing a constant infiltration flux from the surface followed by a no‐influx condition. Results indicate that less water accumulates in the sand near the surface for the sand compacted to higher porosity, but water can move deeper. Hydraulic conductivity is found as the prime factor dominating the evolvement of wetting fronts. However, shape parameters of water retention curves also affect the infiltration pattern to some extent. In addition, different sands with similar porosities can have quite different infiltrating characteristics. Copyright © 2012 John Wiley & Sons, Ltd.     

Element mobility during continental collision: insights from polymineralic metamorphic vein within UHP eclogite in the Dabie orogen

Metamorphic dehydration and partial melting are two important processes during continental collision. They have significant bearing on element transport at the slab interface under subduction‐zone P–T conditions. Petrological and geochemical insights into the two processes are provided by a comprehensive study of leucocratic veins in ultrahigh‐pressure (UHP) metamorphic rocks. This is exemplified by this study of a polymineralic vein within phengite‐bearing UHP eclogite in the Dabie orogen. The vein is primarily composed of quartz, kyanite, epidote and phengite, with minor accessory minerals such as garnet, rutile and zircon. Primary multiphase solid inclusions occur in garnet and epidote from the both vein and host eclogite. They are composed of quartz ± K‐feldspar ± plagioclase ± K‐bearing glass and exhibit irregular to negative crystal shapes that are surrounded by weak radial cracks. This suggests their precipitation from solute‐rich metamorphic fluid/melt that involved the reaction of phengite breakdown. Zircon U–Pb dating for the vein gave two groups of concordant ages at 217 ± 2 and 210 ± 2 Ma, indicating two episodes of zircon growth in the Late Triassic. The same minerals from the two rocks give consistent δ¹⁸O and δD values, suggesting that the vein‐forming fluid was directly derived from the host UHP eclogite. The vein is much richer in phengite and epidote than the host eclogite, suggesting that the fluid is associated with remarkable concentration of such water‐soluble elements as LILE and LREE migration. Garnet and rutile in the vein exhibit much higher contents of HREE (2.2–5.7 times) and Nb–Ta (1.8–2.0 times) than those in the eclogite, indicating that these normally water‐insoluble elements became mobile and then were sunken in the vein minerals. Thus, the vein‐forming agent would be primarily composed of the UHP aqueous fluid with minor amounts of the hydrous melt, which may even become a supercritical fluid to have a capacity to transport not only LILE and LREE but also HREE and HFSE at subduction‐zone metamorphic conditions. Taken together, significant amounts of trace elements were transported by the vein‐forming fluid due to the phengite breakdown inside the UHP eclogite during exhumation of the deeply subducted continental crust.