A critical analysis of some variational methods in slope stability analysis

During the last ten years the Calculus of variations technique has been applied to solve the problem of stability of slopes. All published methods are essentially based on the attainment of a functional and the search for its absolute minimum or maximum by vanishing its first variation. Obviously this statement of the problem is valid only if such a minimum or maximum exists and can be obtained by making the first variation of the functional equal to zero. So, these implicit hypotheses must be checked. This work analyses from this point of view the validity of the methods proposed by ‘Baker and Garber’, ‘Chen’ and ‘Castillo and Revilla’, and demonstrates that the first two methods are incorrectly stated while the third one is correct at least in the case of a frictionless soil.     

Seasonal metal remobilization in the sediments of Great Bay,New Hampshire

Concentrations of dissolved iron, manganese, molybdenum, copper, and organic carbon (DOC) were measured in the pore waters from surficial sediments of a temperate estuary to delineate seasonal metal remobilization from 1978 through 1980. Iron and DOC data were collected for 31 months and covaried inversely and exponentially. Iron dissolution occurred during the spring and during periods of active bioturbation with concentrations as high as 18 mg 1^?1. Iron values were low during winter due to oxidation to ferric oxides. The lack of active bioturbation during the summer of 1978 allowed for the nearly complete removal of iron as a monosulfide precipitate. However, bioturbation resumed during the summer of 1979 and 1980 and dissolved iron concentrations as high as 10 mg 1^?1 were observed at those times. The iron and DOC data were a qualitative measure of bioturbation activity. Dissolved manganese, molybdenum, and copper data were collected for 18 months during 1978 and 1979. All three metals displayed spring maxima covariate with iron, suggesting that they behaved chemically like iron and/or were associated with iron- or manganese-rich phases during this time of the year. In general, manganese and molybdenum varied temporally with iron while copper concentrations mimicked iron variations only during the spring.     

Stochastic groundwater flow analysis in the presence of trends in heterogeneous hydraulic conductivity fields

Due to changes in lithostatic pressure, differential fracturing across bedding planes and irregularities in depositional environments, hydraulic conductivity exhibits heterogeneities and trends at various spatial scales. Using spectral theory, we have examined the effect of trends in hydraulic conductivity on (1) the solution of the mean equation for hydraulic head, (2) the covariance of hydraulic head, (3) the cross-covariances of hydraulic head and log-hydraulic conductivity perturbations and their gradients, and (4) the effective hydraulic conductivity. It is shown that the field of hydraulic head is sensitive to the presence of trends in ways that cannot be predicted by the classical analysis based on stationary hydraulic conductivity fields. The controlling variables for the second moments of hydraulic head are the mean hydraulic gradient, the correlation scale of log-hydraulic conductivity and its variance, and the slope of the trend in log-hydraulic conductivity. The mean hydraulic gradient introduces complications in the analysis since it is, in general, spatially variable. In this respect, our results are approximate, yet indicative of the true role of spatially variable patterns of log-hydraulic conductivity on groundwater flow systems.     

Single multipurpose reservoir design: a modified optimal control problem by chance-constrained programming

This paper presents a chance-constrained programming model for optimal control of a multipurpose reservoir and its modification to a model for single reservoir design. An algorithm is developed for solving complex stochastic problems of multipurpose reservoir planning and design. The complexity of the problem is resolved by a two-step algorithm: (1) transformation of chance constraints on the state and control variables is performed at the first step; and (2) the choice of optimum control or optimal reservoir storage is carried out in the second step. The method of iterative convolution is chosen for the first step, while linear programming is selected for the second step. The algorithm allows the use of random inflows and random demands together with other deterministic demands. The reservoir design problem is presented as a modified optimal control problem. The procedure is illustrated with an example of a hypothetical reservoir design problem with three different types of downstream releases (hydropower production, municipal water supply, and irrigation).     

Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity

This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.     

Microstructural evolution and grain boundary structure during static recrystallization in synthetic polycrystals of Sodium Chloride containing saturated brine

The effects of brine on recrystallization in halite are well known. However, properties of brine such as morphology, connectivity, diffusivity and the resulting influences on deformation mechanisms are still a matter of debate. This paper presents a microstructural study of dense, statically recrystallizing synthetic polycrystalline halite containing small amounts of brine. We used powders of two different grain size classes: <10 µm and 200–355 µm. The aggregates were compacted to brine-filled porosities less than about 2% and annealed at room temperature, without an external stress field.Coarse-grained samples undergo recrystallization manifested by the growth of large (up to 300 µm) strain-free grains into the deformed old grains. The new grains are frequently euhedral, with mobile grain boundaries moving at rates up to 6 nm/s. Their mobility is interpreted to be high due to the presence of water. Grain surfaces are smooth and the width of the water-rich zones is usually below the resolution of the SEM (less than 50 nm).The evolution of fine-grained samples starts with primary recrystallization and a reorganization of grain boundaries. After this stage, which lasts a few hours, normal grain growth effectively stops, and no significant increase of grain size is observed even after several months. Microstructural observations indicate contact healing at the grain boundaries, with dihedral angles ranging between 20 and 110°. We interpret these boundaries to be fluid-free, with the brine residing in a network of triple junction tubes. This system of triple junctions is interconnected and associated with significant permeability.While grain growth is inhibited in the fine-grained samples, after a few hours of annealing exaggerated grain growth is commonly initiated. This is manifested by the growth of large, euhedral grains replacing the fine-grained matrix. These grains also grow with low-index facets and their boundaries are also interpreted to be mobile due to the existence of a water-rich phase.Editorial Responsibility: J. Hoefs     

A Global Inventory of Burned Areas at 1 Km Resolution for the Year 2000 Derived from Spot Vegetation Data

Biomass burning constitutes a major contribution to global emissions of carbon dioxide, carbon monoxide, methane, greenhouse gases and aerosols. Furthermore, biomass burning has an impact on health, transport, the environment and land use. Vegetation fires are certainly not recent phenomena and the impacts are not always negative. However, evidence suggests that fires are becoming more frequent and there is a large increase in the number of fires being set by humans for a variety of reasons. Knowledge of the interactions and feedbacks between biomass burning, climate and carbon cycling is needed to help the prediction of climate change scenarios. To obtain this knowledge, the scientific community requires, in the first instance, information on the spatial and temporal distribution of biomass burning at the global scale. This paper presents an inventory of burned areas at monthly time periods for the year 2000 at a resolution of 1 kilometer (km) and is available to the scientific community at no cost. The burned area products have been derived from a single source of satellite-derived images, the SPOT VEGETATION S1 1 km product, using algorithms developed and calibrated at regional scales by a network of partners. In this paper, estimates of burned area, number of burn scars and average size of the burn scar are described for each month of the year 2000. The information is reported at the country level. This paper makes a significant contribution to understanding the effect of biomass burning on atmospheric chemistry and the storage and cycling of carbon by constraining one of the main parameters used in the calculation of gas emissions.     

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale ( ):l = e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w_*), h/w_*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.     

Ecosystem metabolism and carbon fluxes of a tidally-dominated coastal lagoon

The metabolism and carbon flux in the western sector of the highly dynamic coastal lagoon Ria Formosa (south Portugal) were assessed to elucidate the relative importance of the contribution of the main communities, the treated sewage inputs from the adjacent city of Faro, and the exchange with the adjacent coastal waters to the ecosystem metabolism. The results depict the Ria Formosa as being a highly productive ecosystem dominated by the seagrassZostera noltii. The community dominated by the seagrassCymodocea nodosa had half of the gross production ofZ. noltii, followed by bare sediments and phytoplankton. The net contribution of seagrasses to community metabolism was negligible, as bothZ. noltii andC. nodosa showed a production: respiration ratio close to 1. Benthic microalgae emerge as the most important components of the net metabolism. The western sector of Ria Formosa was in metabolic balance during the summer when the study was done. Even though the total net ecosystem production was 7.22 Kmol C d⁻¹, the error associated with this estimate was 8.38 Kmol C d⁻¹, so ecosystem net production was not significantly different from zero. The Ria Formosa ecosystem is shallow and rapidly flushed by the tides, which force an important exchange of dissolved organic carbon (DOC) and particulate organic carbon (POC) with the adjacent coastal waters. The daily net export rate to the adjacent coastal waters, 0.98 Kmol d⁻¹, represented 7.6% of the net ecosystem production, suggesting that the bulk of the net ecosystem production accumulates within the ecosystem. The organic carbon retention in the western sector of the Ria Formosa is higher than net production, because the allochthonous carbon inputs from urban sewage enter the carbon mass balance with about 40% of the autochthonous processes, at about 1.6 Kmol d⁻¹ of DOC and 2.8 Kmol d⁻¹ of POC. The western sector of Ria Formosa has an organic carbon sink of about 46.4 tons per year. Most of this is harvested in the form of molluscs (clams, cuttlefish, etc.) and fish (sea bream, sea bass, etc.). The total carbon harvested every year in the form of bivalves is about 40 tons, rendering the Ria Formosa the most productive seafood area in Portugal.     

Performance of geostatistical interpolation methods for modeling sampled data with non-stationary mean

The measured ozone pollution peak in the atmosphere of Mexico City region was considered in order to study the effect of a non-stationary mean of the sampled data in geostatistics interpolation methods. With this objective the local mean value of the sampled data was estimated through a linear regression analysis of their values on the monitoring station’s coordinates. The residuals obtained by removing the data trend are considered as a set of stationary random variables. Several interpolation methods used in geostatistics, such as inverse distance weighted, kriging, and artificial neural networks techniques were considered. In an effort to optimize and evaluate its performance, we fit interpolated values to sampled data, obtaining optimal values for the parameters defining the used model, that means, the values of the parameters that give the lowest mean RMSE between the interpolated value and measured data at 20 stations at 1500 hours for a set of 21 days of December 2001, which was chosen as the training set. The training set is conformed by all the days in December 2001 excepting the days (3,6,9,12,...,27,30) which were considered as the testing set. Once the optimal model is obtained, it is used to interpolate the values at the stations at 1500 hours for the testing days. The RMSE between interpolated and measured values at monitoring stations was also evaluated for these testing values and is shown as a percentage in Table 2. These values and the defined generalization parameter G, can be used to evaluate the performance and the ability of the models to predict and reproduce the peak of ozone concentrations. Scatter plots for testing data are presented for each interpolation method. An interpretation of the ozone pollution levels obtained at 1500 hours at December 21 was given using the wind field that prevailed in the region 1 h before the same day.