Comparative analysis between analytical approximations and numerical solutions describing recession flow in unconfined hillslope aquifers

Recession flow of aquifers from a hillslope can be described by the non-linear Boussinesq equation. Under strong assumptions and for specific conceptual formulations, different authors derived analytical approximations or linearized versions to this partial differential equation. A comparative analysis between some analytical approximations of the Boussinesq equation and the numerical solution of the recession flow of an unconfined homogeneous aquifer (horizontal, inclined and concave aquifer floor) was carried out. The objective was to define the range where the analytical solutions approximate the numerical solution. The latter was considered in this study as the reference method, because it requires fewer assumptions. From the considered analytical approximations, exponential decay relationships were found to be mainly valid for fine domain materials when horizontal, mild slopes (less than 2%) and concave aquifer floors were considered, but failed to reproduce coarse aquifer numerical model outflows, in contrast to the quadratic decay relationship, which better reproduce outflows in such domains. On the basis of the comparative analysis, it has been found that recession flows obtained with the considered analytical approximations yield similar values only for certain ranges of aquifer properties and geometries.

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Résumé L’écoulement de décrue dans les aquifères de versant peut être décrit par l’équation non-linéaire de Boussinesq. En considérant d’importantes hypothèses et des formulations conceptuelles spécifiques, différents auteurs ont dérivé des approximations analytiques ou des versions linéarisées de cette équation partielle différentielle. Une analyse comparative entre des approximations analytiques de l’équation de Boussinesq et une solution numérique de la décrue d’un aquifère homogène libre (limite inférieure de l’aquifère horizontale, inclinée et concave) a été effectuée. L’objectif était de définir la plage pour laquelle les solutions analytiques approchent la solution numérique. Cette dernière a été considérée dans cette étude comme la méthode de référence car elle demande moins d’hypothèses. Parmi les approximations analytiques considérées, les relations de décroissance exponentielle se sont avérées être principalement valides pour des matériaux fins lorsque des couches aquifères horizontales, concaves et de pentes douces (moins de 2%) étaient considérées; en revanche, celles-ci n’ont pas réussi à reproduire les écoulements sortants d’un modèle numérique pour un aquifère à matériaux grossiers, contrairement à la relation de décroissance quadratique qui reproduit mieux les écoulements sortants dans de tels milieux. Sur la base de l’analyse comparative, il s’est avéré que les écoulements en décrue obtenus avec les approximations analytiques considérées présentent des valeurs similaires seulement pour certains critères géométriques et propriétés de l’aquifère.

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Resumen Puede describirse el flujo de recesión de acuíferos de una ladera mediante la ecuación no-lineal de Boussinesq. Bajo fuertes supuestos y para formulaciones conceptuales específicas, distintos autores han derivado aproximaciones analíticas o versiones lineales para esta ecuación parcial diferencial. Se realizó un análisis comparativo entre algunas aproximaciones analíticas de la ecuación de Boussinesq y la solución numérica del flujo de recesión de un acuífero homogéneo no confinado (piso de acuífero cóncavo, inclinado, y horizontal). El objetivo consistió en definir el rango donde las soluciones analíticas aproximan la solución numérica. En este estudio se consideró la solución numérica como el método de referencia debido a que requiere menores supuestos. De las aproximaciones analíticas consideradas se encontró que las relaciones de desintegración exponencial eran principalmente válidas para materiales de ámbitos finos donde se consideraron pisos de acuíferos horizontal, pendientes medianas (menores a 2%) y cóncavos pero fallaron en reproducir flujos de salida de modelos numéricos de ámbito grueso, en contraste con la relación de desintegración cuadrática la cual reproduce mejor los flujos de salida en tales ámbitos. En base al análisis comparativo se encontró que los flujos de recesión obtenidos con las aproximaciones analíticas consideradas aportaron valores similares solo para ciertos rangos de propiedades y geometrías de acuíferos.

     

Evidence for the nucleation and epitaxial growth of Zn phyllosilicate on montmorillonite

Zinc uptake in suspensions (?3.7 g L⁻¹) of MX80 montmorillonite was investigated at pH 4.0 and 7.3, a total Zn concentration ([Zn]_total) of 500 μM, and dissolved Si concentrations ([Si]_aq) of ∼70 and ∼500 μM in 0.5 M NaCl, by kinetics experiments and polarized extended X-ray absorption fine structure (P-EXAFS) spectroscopy. Differential thermogravimetric analysis verified the cis-vacant character of the montmorillonite. No Zn uptake occurred at pH 4.0, confirming that cation exchange was hampered by the high ionic strength of the suspension. At pH 7.3 and low [Si]_aq (∼70 μM), Zn uptake occurred rapidly during the first hour of reaction, and then leveled off to 50 μmol/g montmorillonite at 168 h. The uptake rate is consistent with Zn sorption on pH-dependent edge sites. At pH 7.3 and high [Si]_aq (∼500 μM), the initial sorption rate was similar, but Zn sorption continued, reaching 130 μmol/g at 168 h, and was paralleled by Si uptake with a Si/Zn uptake ratio of 1.51(10), suggesting formation of a Zn (hydrous) silicate. P-EXAFS data indicated that the first oxygen coordination shell of sorbed Zn is split into two subshells at 1.97(2) and 2.08(3)-2.12(2) Å for all EXAFS samples. These two distances are assigned to a mixture of tetrahedral (^IVZn) and octahedral (^VIZn) Zn complexes. The proportion of ^IVZn was lower in the high [Si]_aq samples and decreased with reaction time. Al low [Si]_aq and 216 h of reaction, nearest cationic shells of 0.6(4) Al in the film plane and 0.5(4) Si out of the film plane were detected at 3.00(2) and 3.21(2) Å, respectively, and were interpreted as the formation of ^IVZn and ^VIZn mononuclear complexes at the edges of montmorillonite platelets, in structural continuity to the (Al, Mg) octahedral sheets. At high [Si]_aq, in-plane Zn and Al and out-of-plane Si neighbors were detected at 4 h, indicating the formation of Zn phyllosilicate nuclei at the layer edges. At 313 h, Zn-Al pairs were no longer detected, and Zn atoms were surrounded on average by 3.4(5) in-plane Zn at 3.10(1) Å and 1.7(9) out-of-plane Si at 3.30(2) Å, supporting the precipitation of a Zn phyllosilicate. Thus, dioctahedral Al phyllosilicate may act as a nucleating surface for the heterogeneous formation of trioctahedral Zn phyllosilicate at [Si]_aq relevant to natural systems.     

Liquefied vs stratified sediment mobilization processes: Insight from the South of the Barbados accretionary prism

This paper discusses the nature and origin of subsurface sediment mobilization processes in deep marine clay-rich environments. In the studied area of the southern Barbados accretionary prism, new geophysical acquisitions have emphasized the spectacular widespread development of mud volcanoes that are well-developed along ramp anticlines and along sigmoidal rises with trends that are oblique to the axes of the main folds of the accretionary wedge. On some active mud volcanoes, heat-flow measurements show high positive anomalies related to high fluxes of mud transfer. The mobilized solid fraction expelled by the mud volcanoes does not originate from a unique source bed but from various formations pierced by the mud conduits and is driven by the water phase. The area studied also exhibits trends of structures corresponding to sub-circular massive local uplifts of deformed but well-preserved stratified sediments (turbidites and hemipelagics). No piercing shale diapirs have been encountered in this area. Some of these local uplift structures are complicated by the development of collapses, calderas, and superimposed mud volcanoes. Mud volcanism corresponds fundamentally to fluid displacement (water and gas), whereas massive sedimentary uplift corresponds to large vertical displacements of stratified solid levels but for which the deep cause could be partly the intrusion of mud plugs. Both are dynamic phenomena controlled by the development of overpressure at depth, contributing to sedimentary mobilizations.     

Erosion balance in the watersheds of the western Paris Basin by high-frequency monitoring of discharge and suspended sediment in surface water

An accurate quantification of erosion, based on high-frequency monitoring of river discharge and suspended sediment fluxes is proposed for two watersheds in the western Paris Basin, a sensitive area with respect to erosion phenomena. This continuous monitoring makes it possible to include flood events of short duration, but significant erosion potential. The obtained erosion rate (16 and 21 t?km^?2?yr^?1) is among the weakest of the planet (3.5 to 18?000 t?km^?2?yr^?1). However, this annual balance does not reflect the behaviour of these rivers which can be torrential in certain cases. To cite this article: B. Laignel et al., C. R. Geoscience 338 (2006).     

Internal architecture and mobility of tidal sand ridges in the East China Sea

On the basis of bathymetric and seismic data and data from piston cores collected by the Chinese–French marine geology and geophysics investigation of 1996, we discuss the internal architecture and mobility of tidal sand ridges in the East China Sea (ECS). We characterized the sand ridges on the middle to outer shelf of the ECS as tide-dominated sand ridges with southwest dipping beds, indicating that the regional net sediment transport is toward the southwest. As the sand ridges gradually migrate toward the southwest, new sand ridges are continually replacing old ones, and several generations of sand ridges have developed in the study area.     

The Paleoenvironment and Lithic Taphonomy of Shi’Bat Dihya 1, a Middle Paleolithic Site in Wadi Surdud,Yemen

The Shi'bat Dihya 1 site in western Yemen, dated by optically stimulated luminescence to 55 ka, provides insight into the Middle Paleolithic peopling of the Arabian Peninsula. The archaeological layer is interstratified within thick, sandy silt floodplain deposits filling a piedmont basin. Luminescence dates, lack of soil development, and gypsum precipitation indicate a high accretion rate of the floodplain during Marine Isotope Stage 3, in connection with a (semi)‐arid environment. Rapid overbank sedimentation was likely a result of the remobilization of loess material deposited on the Yemeni Great Escarpment at the periphery of the adjacent Tihama coastal sand desert or of other sources. Fabric and size analyses of the lithic artifacts, together with spatial projections, indicate site modifications by floods. Primary modifications include (1) selective accumulation of medium‐sized lithic pieces as a result of hydraulic sorting, (2) bimodal orientation of artifacts, and (3) ripple‐like arrangement of lithics and bone/tooth fragments. The overrepresentation of teeth may also be a consequence of sorting. Although floods have distorted the original site patterning, long‐distance transport of artifacts by water can be excluded, as indicated by relatively high refitting rate, close proximity of artifacts derived from the same block of raw material, and lack of abrasion of the pieces. Therefore, the site is considered “geologically” in situ because its remobilization by water occurred shortly after human abandonment. This study also stresses that the effective preservation of a site cannot be assessed without careful taphonomic study, even in a potentially favorable depositional context such as silty alluvium.     

Load Transfers During Vibratory Driving

The vibratory driving technique consists in applying a vibratory load onto a profile to reduce the ground resistance and allow penetration of the profile under its own weight. The vibratory action is produced by counter-rotating eccentric masses actuated within the exciter block. A proper definition of this mechanical action is fundamental for vibratory driving analyses. The vibratory force transferred from the vibrator onto the pile during vibratory driving is however generally neither well defined nor understood, in particular when using simplified closed form solutions for the analysis of pile driving. Few authors have pointed out the very low ratio observed between the force measured in the pile and the nominal inertial force developed by the eccentrics, but without offering a theoretical framework to explain and predict this low ratio. The objective of this paper is to develop a better understanding of the so-called ‘efficiency factor’ of the vibratory driving process. Analytical solutions are presented, along with more advanced numerical simulations. Theoretical solutions are illustrated with reference to field measurements collected at different test sites.     

Gradual diversions of the Rio Pastaza in the Ecuadorian piedmont of the Andes from 1906 to 2008: role of tectonics, alluvial fan aggradation, and ENSO events

The successive courses of the Rio Pastaza in the upper Amazonian Puyo plateau (Ecuador) during the past century have been followed using historical maps, aerial photographs, satellite imagery, topographic and river long profiles, and field studies. The abrupt change in direction of the Rio Pastaza from transverse to longitudinal was a result of two avulsions occurred between 1906 and 1976 at the braided-meandering transition of the former alluvial plain. These avulsions are related to aggradation at the toe of a braided piedmont fan prograding on to a hinterland-dipping topographic slope formed by ongoing tectonic backtilting. The main avulsion proceeded by annexation of a south-dipping depression created in front of the cordillera by backtilting of the plateau. A partial and gradual avulsion having occurred upstream of the former site between 1976 and 2008 is marked by the progressive predominance of a newly formed inner branch. Tectonic backtilting enhanced aggradation upstream of the initial site while it offered the newly avulsed channel a still more favorable way along the cordillera by creating a westward lateral slope. The correlation between ENSO events and the occurrence of the 1976–2008 avulsions strongly suggests that the triggers of the avulsions were the floods caused by the high water and sediment discharges associated with ENSO (La Ni?a) events contrasting with the regular monthly discharge and the lack of actual ‘normal’ floods during the inter-ENSO periods.