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.     

Effect of spatial variation characteristics on contouring of design storm depth

The ordinary kriging method, a geostatistical interpolation technique, was applied for developing contour maps of design storm depth in northern Taiwan using intensity–duration–frequency (IDF) data. Results of variogram modelling on design storm depths indicate that the design storms can be categorized into two distinct storm types: (i) storms of short duration and high spatial variation and (ii) storms of long duration and less spatial variation. For storms of the first category, the influence range of rainfall depth decreases when the recurrence interval increases, owing to the increasing degree of their spatial independence. However, for storms of the second category, the influence range of rainfall depth does not change significantly and has an average of approximately 72 km. For very extreme events, such as events of short duration and long recurrence interval, we do not recommend usage of the established design storm contours, because most of the interstation distances exceed the influence ranges. Our study concludes that the influence range of the design storm depth is dependent on the design duration and recurrence interval and is a key factor in developing design storm contours. Copyright © 2003 John Wiley & Sons, Ltd.     

A note on turbulent perturbations of salinity in a partially mixed estuary

Measurements of salinity perturbations in a partially mixed estuary have been used to evaluate the usefulness of an inductive salinometer and to determine some of the characteristics of the salinity perturbations. The salinometer performed satisfactorily under most conditions. Although internal wave like effects were present, the turbulence fluctuations were dominant. The salinity fluctuations and the turbulent fluxes $\text{sw}$ and $\text{su}$ were found to behave in a manner similar to the density fluctuations in a thermally stratified atmospheric boundary layer and a laboratory open channel flow. A quadrant analysis suggested that the contribution of each quadrant to the turbulent flux changed with Ri. The turbulence parameters ν and c_γ were found to decrease and increase respectively as Ri increases.     

Fluid infiltration during contact metamorphism of interbedded marble and calc-silicate hornfels, Twin Lakes area, central Sierra Nevada, California

Abstract In the Twin Lakes area, central Sierra Nevada, California, most contact metamorphosed marbles contain calcite + dolomite + forsterite ± diopside ± phlogopite ± tremolite, and most calc-silicate hornfelses contain calcite + diopside + wollastonite + quartz ± anorthite ± K-feldspar ± grossular ± titanite. Mineral-fluid equilibria involving calcite + dolomite + tremolite + diopside + forsterite in two marble samples and wollastonite + anorthite + quartz + grossular in three hornfels samples record P± 3 kbar and T± 630° C. Various isobaric univariant assemblages record CO₂-H₂O fluid compositions of χCO₂= 0.61–0.74 in the marbles and χCO₂= 0.11 in the hornfelses. Assuming a siliceous dolomitic limestone protolith consisting of dolomite + quartz ° Calcite ± K-feldspar ± muscovite ± rutile, all plausible prograde reaction pathways were deduced for marble and hornfels on isobaric T-XCO₂ diagrams in the model system K₂O-CaO-MgO-Al₂O₃-SiO₂-H₂O-CO₂. Progress of the prograde reactions was estimated from measured modes and mass-balance calculations. Time-integrated fluxes of reactive fluid which infiltrated samples were computed for a temperature gradient of 150 °C/km along the fluid flow path, calculated fluid compositions, and estimated reaction progress using the mass-continuity equation. Marbles and hornfelses record values in the range 0.1–3.6 × 10⁴ cm³/cm² and 4.8–12.9 × 10⁴ cm³/cm², respectively. For an estimated duration of metamorphism of 10⁵ years, average in situ metamorphic rock permeabilities, calculated from Darcy's Law, are 0.1–8 × 10^?6 D in the marbles and 10–27 × 10^?6 D in the hornfelses. Reactive metamorphic fluids flowed up-temperature, and were preferentially channellized in hornfelses relative to the marbles. These results appear to give a general characterization of hydrothermal activity during contact metamorphism of small pendants and screens (dimensions ± 1 km or less) associated with emplacement of the Sierra Nevada batholith.     

The second order characteristic condition for plastic flow

In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd.     

An approach to quantitative analysis of regional economic links

Aimed at promoting regional coalitions and expanding the approach to economic links, this paper puts forward some new concepts such as link intensity and receiving coefficient, expounds the indexes of quantitative analysis of economic links and establishes the quantitative-analysis model of economic links. With help of the model, this paper calculates the values of the link intensities between Su-Xi-Chang (Suzhou-Wuxi-Changzhou) region and Shanghai, and analyzes the regional difference of the economic links.     

Hysteresis‐based analysis of overland metal transport

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.     

Analytical solutions of one‐dimensional infiltration before and after ponding

This paper is a continuation of previous research, which obtained a convenient solution for arbitrary surface fluxes before ponding. By means of Fourier Transformation this has been extended to derive analytical solutions of a linearized Richards' equation for arbitrary input fluxes after surface saturation. Copyright © 2003 John Wiley & Sons, Ltd.     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of macrophyte growth,typical of eutrophic conditions,on river flow velocities and turbulence production

The influence of emergent and submerged macrophytes on flow velocity and turbulence production is demonstrated in a 140 m reach of the River Blackwater in Farnborough, Hampshire, UK. Macrophyte growth occurs in patches and is dominated by Sparganium erectum and Sparganium emersum. In May 2001, patches of S. erectum were already established and occupied 18% of the channel area. The flow adjusted to these (predominantly lateral) patches by being channelled through a narrower cross‐section. The measured velocity profiles showed a logarithmic form, with deviations attributable to topographic control. The channel bed was the main source of turbulence. In September 2001, in‐stream macrophytes occupied 27% of the channel, and overhanging bank vegetation affected 32% of the area. Overall flow resistance, described by Manning's n, showed a threefold increase that could be attributed to the growth of S. emersum in the middle of the channel. Velocity profiles showed different characteristic forms depending on their position relative to plant stems and leaves. The overall velocity field had a three‐dimensional structure. Turbulence intensities were generally higher and turbulence profiles tended to mirror the velocity profiles. Evidence for the generation of coherent eddies was provided by ratios of the root mean square velocities. Spectral analysis identified deviations from the Kolmogorov ?5/3 power law and provided statistical evidence for a spectral short‐cut, indicative of additional turbulence production. This was most marked for the submerged vegetation and, in some instances, the overhanging bank vegetation. The long strap‐like leaves of S. emersum being aligned approximately parallel to the flow and the highly variable velocity field created by the patch arrangement of macrophytes suggest that the dominant mechanism for turbulence production is vortex shedding along shear zones. Wake production around individual stems of S. emersum close to the bed may also be important locally. Copyright © 2006 John Wiley & Sons, Ltd.