Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

“BASS 300 PARACOM”: a “model” underwaterparametric communication system

Parametric transduction offers valuable advantages for underwater acoustic communications. Perhaps the most significant benefit is the fact that high directivity is achieved by means of a physically small transmit transducer. This feature may, ultimately, be employed to permit long-range, low-frequency communication using a compact source. The high directivity is desirable to combat multipath propagation and to achieve data communications in water which is shallow by comparison with range. A real-time, high data-rate “model” differential phase shift keying (DPSK) communication system has been constructed and demonstrated. This system uses parametric transduction, with a 300-kHz primary frequency and a 50-kHz secondary frequency. Experimental results show that the system can be employed to combat multipath propagation in shallow water and can achieve high data-rate text and color image transmission at 10 and 20 kb s^-1 for 2-DPSK and 4-DPSK, respectively, through a transmission bandwidth of 10 kHz. The “model” system was developed to confirm performance predictions for a future, operational long-range link employing a 50-kHz primary frequency and a 5-kHz secondary frequency     

Geochemistry of metabauxites in the Bergsträsser Odenwald (Mid German Crystalline Rise) and palaeoenvironmental implications

Summary Pre- to early Variscan metamorphosed volcano-sedimentary series of the western (Bergstr?sser) Odenwald have been intruded by Variscan calc-alkaline magmatites with plate margin affinities. Within the NE-SW trending metabasic and metapelitic series, intercalations of anomalously aluminous- and iron-rich compositions representing former bauxites are distinguishable. Geochemical data indicate that the Al-, Fe-rich rocks are the metamorphic equivalents of a former bauxitic-ferralitic weathering profile, now comprising spinel fels (top) with relics of pisolitic structures, corundum-chlorite fels, corundum-cordierite-plagioclase gneiss, sillimanite-cordierite-plagioclase gneiss, cordierite-plagioclase gneiss and kinzigite (base) displaying a decrease of weathering in the order as listed. The evolution of such terrestrial sediments is related to specific climatic, environmental, and physico-chemical conditions similar to those of the present-day tropical to subtropical humid regions with high seasonal rains and intensive drainage. Comparison with palaeomagnetic and palaeoclimatic data indicate that the Odenwald metabauxites originally formed during the Lower to Mid-Devonian. Our results imply that, during this geological time span, parts of the precursors of the Mid-German Crystalline Rise not only transversed low latitudes but also were exposed to terrestrial weathering.

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Zusammenfassung Die Geochemie der Metabauxite im Bergstr?sser Odenwald (Mitteldeutsche Kristallinschwelle) und ihre Bedeutung für das Pal?omilieu Im westlichen (Bergstr?sser) Odenwald intrudierten variszische Plattenrand-Kalkalkali-Magmatite in pr?- bis früh-variszische, ehemalige vulkano-sediment?re Serien. Innerhalb der heute NE-SW streichenden Metabasit- und Metapelitzüge treten lokal Al-Fe-reiche Einschaltungen auf, die strukturell und geochemisch als metamorphe ?quivalente eines ehemaligen bauxitisch-ferralitischen Verwitterungsprofils klassifiziert werden k?nnen. Sie umfassen Spinellfelse mit erhaltenen, ehemaligen zonierten Pisolithen, Korund-Chloritfelse, Korund-Cordierit-Plagioklasgneise, Sillimanit-Cordierit-Plagioklasgneise, Cordierit-Plagioklasgneise und Kinzigite. Bauxite k?nnen als terrestrische Bildungen nur unter speziellen klimatischen und physiko-chemischen Bedingungen entstehen. Pal?omagnetische und pal?oklimatische Daten legen die Bildung der ehemaligen Bauxite im unteren bis mittleren Devon nahe. Daraus folgt, da? w?hrend dieser geologischen Zeitspanne die Vorl?ufer der mitteldeutschen Kristallinschwelle bei der Norddrift nicht nur ?quatorn?he passierten, sondern auch partiell ungest?rte, terrestrische, tropisch-subtropische Verwitterungsprozesse abliefen.

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Received June 10, 1999; revised version accepted October 30, 2000     

Application of micropolar plasticity to post failure analysis in geomechanics

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy–Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Isotope hydrological study of mean transit time in the granitic Strengbach catchment (Vosges massif,France): application of the FlowPC model with modified input function

Measurements of ¹⁸O concentrations in precipitation, soil solution, spring and runoff are used to determine water transit time in the small granitic Strengbach catchment (0·8 km²; 883–1146 m above sea level) located in the Vosges Mountains of northeastern France. Water transit times were calculated by applying the exponential, exponential piston and dispersion models of the FlowPC program to isotopic input (rainfall) and output (spring and stream water) data sets during the period 1989–95. The input function of the model was modified compared with the former version of the model and estimated by a deterministic approach based on a simplified hydrological balance. The fit between observed and calculated output data showed marked improvements compared with results obtained using the initial version of the model. An exponential piston version of the model applied to spring water indicates a 38·5 month mean transit time, which suggests that the volume in the aquifer, expressed in water depth, is 2·4 m. A considerable thickness (>45 m) of fractured bedrock may be involved for such a volume of water to be stored in the aquifer. Copyright © 2005 John Wiley & Sons, Ltd.     

A critical state model for sands dependent on stress and density

An elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

Porphyroblast inclusion-trail orientation data: eppure non son girate*!

Extensive examination of large numbers of spatially orientated thin sections of orientated samples from orogens of all ages around the world has demonstrated that porphyroblasts do not rotate relative to geographical coordinates during highly non-coaxial ductile deformation of the matrix subsequent to their growth. This has been demonstrated for all tectonic environments so far investigated. The work also has provided new insights and data on metamorphic, structural and tectonic processes including: (1) the intimate control of deformation partitioning on metamorphic reactions; (2) solutions to the lack of correlation between lineations that indicate the direction of movement within thrusts and shear zones, and relative plate motion; and (3) a possible technique for determining the direction of relative plate motion that caused orogenesis in ancient orogens.     

Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.