Tensionless–frictionless interaction of flexible annular foundation with a transversely isotropic multi‐layered half‐space

A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.     

Intergranular diffusion rates from the analysis of garnet surfaces: Implications for metamorphic equilibration

Novel approaches to garnet analysis have been used to assess rates of intergranular diffusion between different matrix phases and garnet porphyroblasts in a regionally metamorphosed staurolite‐mica‐schist from the Barrovian‐type area in Scotland. X‐ray maps and chemical traverses of planar porphyroblast surfaces reveal chemical heterogeneity of the garnet grain boundary linked to the nature of the adjacent matrix phase. The garnet preserves evidence of low temperature retrograde exchange with matrix minerals and diffusion profiles documenting cation movement along the garnet boundaries. Garnet–quartz and garnet–plagioclase boundaries preserve evidence of sluggish Mg, Mn and Fe diffusion at comparable rates to volume diffusion in garnet, whereas diffusion along garnet–biotite interfaces is much more effective. Evidence of particularly slow Al transport, probably coupled to Fe³⁺ exchange, is locally preserved on garnet surfaces adjacent to Fe‐oxide phases. The Ca distribution on the garnet surface shows the most complex behaviour, with long‐wavelength heterogeneities apparently unrelated to the matrix grain boundaries. This implies that the Ca content of garnet is controlled by local availability and is thought likely to reflect disequilibrium established during garnet growth. Geochemical anomalies on the garnet surfaces are also linked to the location of triple junctions between the porphyroblasts and the matrix phases, and imply enhanced transport along these channels. The slow rates of intergranular diffusion and the characteristics of different boundary types may explain many features associated with the prograde growth of garnet porphyroblasts. Thus, minerals such as quartz, Fe‐oxides and plagioclase whose boundaries with garnet are characterized by slow intergranular diffusion rates appear to be preferentially trapped as inclusions within porphyroblasts. As such grain boundary diffusion rates may be a significant kinetic impediment to metamorphic equilibrium and garnet may struggle to maintain chemical and textural equilibrium during growth in pelites.     

Interpreting zirconium‐in‐rutile thermometric results

At first sight, experimental results and observations on rocks suggest that the Zr content in rutile, where equilibrated with quartz and zircon, should be a useful thermometer for metamorphic rocks. However, diffusion data for Zr in rutile imply that thermometry should not, for plausible rates of cooling, give the high temperatures commonly observed in high‐grade metamorphic rocks. It is suggested here that such observations can be accounted for by high‐T diffusive closure of Si in rutile, causing the interior of rutile grains to become insensitive to the thermometer equilibrium well above the temperature of Zr diffusive closure. Paired with comparatively slow grain boundary diffusion and problematic zircon nucleation, this allows for cases of Zr retention in rutile through temperatures where Zr is still diffusively mobile within rutile grains. Other observations that may be accounted for in this context are large inter‐grain ranges of rutile Zr contents uncorrelated with rutile grain size, and flat Zr profiles across individual rutile grains, counter to what would be expected from diffusive closure. A consequence is that it is unlikely that Zr‐in‐rutile thermometry will be useful for estimating rock cooling rates.     

Controls on metamorphic equilibration: the importance of intergranular solubilities mediated by fluid composition

A dramatic demonstration of the role of intergranular solubility in promoting chemical equilibration during metamorphism is found in the unusual zoning of garnet in pelitic schist exposed at Harpswell Neck, Maine, USA. Many garnet crystals have irregular, patchy distributions of Mn, Cr, Fe and Mg in their inclusion‐rich interiors, transitioning to smooth, concentric zoning in their inclusion‐poor outer rims; in contrast, zoning of Ca and Y is comparatively smooth and concentric throughout. We re‐assess the disputed origin of these zoning features by examining garnet growth in the context of the thermal and structural history of the rocks, and by evaluating the record of fluid–rock interaction revealed in outcrop‐scale veining and fluid‐inclusion assemblages. The transition in the character of garnet zoning correlates with the onset of a synkinematic, simple‐shear‐dominated phase of garnet growth and with a shift in the composition of the intergranular fluid from CO₂‐rich to H₂O‐rich. Compositional variations in garnet are therefore best explained by a two‐stage growth history in which intergranular diffusive fluxes reflect differences in the concentration of dissolved species in these two contrasting fluids. Interiors of garnet crystals grew in the presence of a CO₂‐rich fluid, in which limited solubility for Mn and Cr (and perhaps Fe and Mg) produced patchy disequilibrium overprint zoning, while appreciable solubility for Ca and Y permitted their rock‐wide equilibration. Rims grew in the presence of an H₂O‐rich fluid, in which high intergranular concentrations for all elements except Cr enabled diffusion over length scales sufficient for rock‐wide equilibration. This striking example of partial chemical equilibrium during reaction and porphyroblast growth implies that thermal effects may commonly be subsidiary in importance to solubilities in the intergranular medium as determinants of length scales for metamorphic equilibration.     

Oxygen isotope speedometry in granulite facies garnet recording fluid/melt–rock interaction (Sør Rondane Mountains,East Antarctica)

In situ analysis of a garnet porphyroblast from a granulite facies gneiss from Sør Rondane Mountains, East Antarctica, reveals discontinuous step‐wise zoning in phosphorus and large δ¹⁸O variations from the phosphorus‐rich core to the phosphorus‐poor rim. The gradually decreasing profile of oxygen isotope from the core (δ¹⁸O = ~15‰) to the rim (δ¹⁸O = ~11‰) suggests that the ¹⁸O/¹⁶O zoning was originally step‐wise, and modified by diffusion after the garnet rim formation at ~800°C and 0.8 GPa. Fitting of the ¹⁸O/¹⁶O data to the diffusion equation constrains a duration of the high‐T event (~800°C) to c. 0.5–40 Ma after the garnet rim formation. The low δ¹⁸O value of the garnet rim, together with the previously reported low δ¹⁸O values in metacarbonates, indicates regional infiltration, probably along a detachment fault, of low δ¹⁸O fluid/melt possibly derived from meta‐mafic to ultramafic rocks.     

Diffusive mass exchange of non‐reactive substances in dual‐porosity porous systems – column experiments under saturated conditions

Diffusive mass exchange into immobile water regions within heterogeneous porous aquifers influences the fate of solutes. The percentage of immobile water is often unidentified in natural aquifers though. Hence, the mathematical prediction of solute transport in such heterogeneous aquifers remains challenging. The objective of this study was to find a simple analytical model approach that allows quantifying properties of mobile and immobile water regions and the portion of immobile water in a porous system. Therefore, the Single Fissure Dispersion Model (SFDM), which takes into account diffusive mass exchange between mobile and immobile water zones, was applied to model transport in well‐defined saturated dual‐porosity column experiments. Direct and indirect model validation was performed by running experiments at different flow velocities and using conservative tracer with different molecular diffusion coefficients. In another column setup, immobile water regions were randomly distributed to test the model applicability and to determine the portion of immobile water. In all setups, the tracer concentration curves showed differences in normalized maximum peak concentration, tailing and mass recovery according to their diffusion coefficients. These findings were more pronounced at lower flow rates (larger flow times) indicating the dependency of diffusive mass exchange into immobile water regions on tracers' molecular diffusion coefficients. The SFDM simulated all data with high model efficiency. Successful model validation supported the physical meaning of fitted model parameters. This study showed that the SFDM, developed for fissured aquifers, is applicable in porous media and can be used to determine porosity and volume of regions with immobile water. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient DEM‐based overland flow routing using integrated recursive algorithms

Two primary concerns in performing watershed overland flow routing are the numerical instability and computational efficiency. The stability of executing an explicit scheme has to be maintained by observing the Courant–Friedrich–Lewy criterion, which is adopted to confirm that the numerical marching speed is larger than the wave celerity. Moreover, there is another criterion of time step devised in previous studies to avoid back‐and‐forth refluxing between adjacent grids. The situation of refluxing usually occurs on flat regions. In light of this, the selection of a small time increment to honor both restrictions simultaneously is believed to decrease the computational efficiency in performing overland flow routing. This study aims at creating a robust algorithm to relax both restrictions. The proposed algorithm was first implemented on a one‐dimensional overland plane to evaluate the accuracy of the numerical result by comparing it with an analytical solution. Then, the algorithm was further applied to a watershed for 2D runoff simulations. The results show that the proposed integrated algorithm can provide an accurate runoff simulation and achieve satisfactory performance in terms of computational speed.     

A discontinuous finite element suspended sediment transport model for water quality assessments in river networks

Suspended sediment plays an important role in the distribution and transport of many pollutants (such as radionuclides) in rivers. Pollutants may adsorb on fine suspended particles (e.g. clay) and spread according to the suspended sediment movement. Hence, the simulation of the suspended sediment mechanism is indispensable for realistic transport modelling. This paper presents and tests a simple mathematical model for predicting the suspended sediment transport in river networks. The model is based on the van Rijn suspended load formula and the advection–diffusion equation with a source or sink term that represents the erosion or deposition fluxes. The transport equation is solved numerically with the discontinuous finite element method. The model evaluation was performed in two steps, first by comparing model simulations with the measured suspended sediment concentrations in the Grote Nete–Molse Nete River in Belgium, and second by a model intercomparison with the sediment transport model NST MIKE 11. The simulations reflect the measurements with a Nash‐Sutcliffe model efficiency of 0.6, while the efficiency between the proposed model and the NST MIKE 11 simulations is 0.96. Both evaluations indicate that the proposed sediment transport model, that is sufficiently simple to be practical, is providing realistic results.     

Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media

Analytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of bed surface roughness on longitudinal dispersion in artificial open channels

In several empirical and modelling studies on river hydraulics, dispersion was negatively correlated to surface roughness. In this study, it was aimed to investigate the influence of surface roughness on longitudinal dispersion under controlled conditions. In artificial flow channels with a length of 104 m, tracer experiments with variations in channel bed material were performed. By use of measured tracer breakthrough curves, average flow velocity, mean longitudinal dispersion, and mean longitudinal dispersivity were calculated. Longitudinal dispersion coefficients ranged from 0·018 m² s^?1 in channels with smooth bed surface up to 0·209 m² s^?1 in channels with coarse gravel as bed material. Longitudinal dispersion was linearly related to mean flow velocity. Accordingly, longitudinal dispersivities ranged between 0·152 ± 0·017 m in channels with smooth bed surface and 0·584 ± 0·015 m in identical channels with a coarse gravel substrate. Grain size and surface roughness of the channel bed were found to correlate positively to longitudinal dispersion. This finding contradicts several existing relations between surface roughness and dispersion. Future studies should include further variation in surface roughness to derive a better‐founded empirical equation forecasting longitudinal dispersion from surface roughness. Copyright © 2011 John Wiley & Sons, Ltd.