FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.     

High-resolution mean sea surface computed with altimeter data of Ers-1 (geodetic mission) and topex-poseidon

The remote-sensing satellite ERS-1, launched in 1991 to study the Earth's environment, was placed on a geodetic (168-day repeat) orbit between 1994 April and 1995 March to map, through altimetric measurements, the gravity field over the whole oceanic domain with a resolution of 8 km at the equator in both along-track and cross-track directions. We have analysed the precise altimeter data of the geodetic mission, and, by also using one year of Topex-Poseidon altimeter data, we have computed a global high-resolution mean sea surface. The various steps involved in pre-processing the ERS-1 data consisted of correcting the data for environmental factors, editing, and reducing, through crossover analyses, the radial orbit error, which directly affects sea-surface height measurements. For this purpose, we adjusted sinusoids at 1 and 2 cycle rev⁻¹ along the ERS-1 profiles in order to minimize crossover differences between ERS-1 and yearly averaged Topex-Poseidon profiles. In effect, the orbit of Topex-Poseidon is very accurately determined (within 2–3 cm for the radial component), so Topex-Poseidon altimeter profiles can serve as a reference to reduce the ERS-1 radial orbit error. The ERS-1 residual orbit error was further reduced through a second crossover analysis between all ascending and descending profiles of the geodetic mission. The along-track ERS-1 and Topex-Poseidon data were then interpolated over the whole oceanic domain on a regular grid of 1/16°× 1/16° size. The mapping of the gridded sea-surface heights reveals the very fine structure of the marine geoid, up until now unknown at a global scale. This new data set will be most useful for marine geophysical and tectonic investigations.     

Correcting the distortion of apparent resistivity pseudosection produced by 3D effect of the embankment geometry

Two-dimensional electrical resistivity tomography data acquired on the crest of the embankment are distorted by the 3D effect of the embankment geometry, reservoir water level and abutment. The distortion affects seriously the final solution of the 2D inverse problem. By comparing the apparent resistivity pseudosections from a 3D and 2D electrical resistivity model of the embankment, the distortion degrees of the apparent resistivity pseudosections along the axis on the crest were estimated for the cases of reservoir and which does not contain water. The obtained results indicate that the distortion degree acquired in the case of a reservoir that contains water was much less than that in the case of the reservoir that does not contain water. In the case of reservoir that contains water, the apparent resistivity pseudosections of the P–P and ED–ED arrays had the largest distortion degree and of D–D, W–S and P–D arrays had the smallest distortion degree. In the case of the reservoir that does not contain water, the apparent resistivity pseudosection of P–P array had the smallest distortion among all arrays. Through modeling investigation, a correction process to reduce the distortion of the apparent resistivity pseudosection was proposed. The correction process was tested in the embankment model, and two field works were carried out in the To Lich River in Hanoi and Khuan Cat embankment in Lang Son province, Vietnam. It is possible to bring the distortion of the apparent resistivity pseudosection down to 2.8–13.9%, depending on the type of electrode arrays and the type of reservoirs, containing or does not contain water. The distortion correction of the apparent resistivity pseudosection is strongly recommended before doing the 2D inverse interpretation.     

The occurrence of cyanobacteria and microcystins in the Hoan Kiem Lake and the Nui Coc reservoir (North Vietnam)

The occurrence of increasing blooms of toxic cyanobacteria in freshwaters has received much attention due to the ability of many cyanobacteria to produce potent cyanotoxins. In this paper, the occurrence of dominant cyanobacteria and the concentration of microcystins (MCs) analysis were investigated monthly from July 2008 to April 2009 in the Hoan Kiem Lake and from February to April 2009 in the Nui Coc reservoir. Concentrations of intracellular MCs from water, bloom samples, and isolated strains were quantified by using high performance liquid chromatography (HPLC). During the study period, the microscopic examination of the phytoplankton samples showed the dominance of the genus Microcystis in the water environment of the Hoan Kiem Lake and the Nui Coc reservoir. The toxin analysis by HPLC demonstrated the presence of two MC variants: MC-LR and MC-RR in water samples. Total concentrations of the toxins in filtered samples from surface water ranged from non-detected to 0.91 μg L^?1 at Nui Coc reservoir and they ranged from 2.1 to 46.0 μg L^?1 at Hoan Kiem Lake. The results of the HPLC analysis confirmed the production of MCs in bloom samples (ranged from 115.9 to 184.6 μg L^?1 in the Hoan Kiem Lake and from 726.5 to 1116 μg L^?1 in the Nui Coc reservoir) and isolated strains of Anabaena sp. and Microcystis with the concentration of MC ranging from 152 to 396.2 μg g^?1 dry mass, respectively.     

Terrestrial water dynamics in the lower Ganges—estimates from ENVISAT and GRACE

In this study, the hydrodynamics of lower Ganges basin in India has been monitored using radar altimetry data from environmental satellite (ENVISAT) mission and microgravity data from the Gravity Recovery and Climate Experiment (GRACE) mission. River stage time series have been constructed for different virtual stations on the lower Ganges. Time series for the integrated water volume changes from microgravity measurements have also been constructed to characterize the seasonal and interannual fluctuation patterns in water storage and flux. The ENVISAT dataset indicates an average seasonal river stage fluctuation of 8 m in the lower Ganges River. The GRACE dataset reveals a seasonal fluctuation ranging from 0.18 to 0.40 m in the vertically integrated total water storage in the lower Ganges basin. The two independent datasets show broad similarity in the lower Ganges basin and outline the importance of space-based techniques for monitoring continental water resources.     

Numerical experiment applicable to the latest stage of planet growth

A three-dimensional numerical model was developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (～ Moon size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion, and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of R. Greenberg et al. (1978, Icarus, 35, 1–26). In the present work, we consider 25 protoplanets with uniform mass distribution in the range 2 × 10²⁵?4 × 10²⁶ g on heliocentric orbits in the Earth zone. These bodies are initially confined to a small volume of space to permit gravitational perturbations by close approaches and collisions within a finite length of integration time. The dynamical evolution of the swarm is followed for four different sets of initial ranges in semimajor axis, eccentricity, and inclination: Δa=0.01, 0.02, 0.04, 0.08 AU; Δe= 0.005, 0.01, 0.02, 0.04; Δi=0°3, 0°6, 1°2, 2°4. Among other results, it is found that average eccentricities and inclinations evolve toward a steady state such that $\text{i}\text{?}\text{1}\text{2}\text{,}\text{e}$; it is also found that, whatever the initial conditions, the population evolves toward a quasi-equilibrium relative velocity distribution corresponding to a Safronov parameter value $\text{θ?10}$. Moreover, the growth process of the growing planet presents very similar behavior in the four cases considered, except for the time scale of evolution, which increases with the initial range of orbital elements. Earlier works of this kind have been presented by L.P. Cox and J.S. Lewis (1980, Icarus, 44, 706–721) and by G.N. Wetherill (1980b, In Geol. Soc. Canad. Spec. Publ., p. 20), although a number of differences exist between the three approaches.     

High-resolution simulations for Vietnam - methodology and evaluation of current climate

To assist the government of Vietnam in its efforts to better understand the impacts of climate change and prioritise its adaptation measures, dynamically downscaled climate change projections were produced across Vietnam. Two Regional Climate Models (RCMs) were used: CSIRO’s variable-resolution Conformal-Cubic Atmospheric Model (CCAM) and the limited-area model Regional Climate Model system version 4.2 (RegCM4.2). First, global CCAM simulations were completed using bias- and variance-corrected sea surface temperatures as well as sea ice concentrations from six Coupled Model Intercomparison Project Phase 5 (CMIP5) global climate models. This approach is different from other downscaling approaches as it does not use any atmospheric fields from the GCMs. The global CCAM simulations were then further downscaled to 10 km using CCAM and to 20 km using RegCM4.2. Evaluations of temperature and precipitation for the current climate (1980-2000) were completed using station data as well as various gridded observational datasets. The RCMs were able to reproduce reasonably well most of the important characteristics of observed spatial patterns and annual cycles of temperature. Average and minimum temperatures were well simulated (biases generally less than 1oC), while maximum temperatures had biases of around 1oC. For precipitation, although the RCMs captured the annual cycle, RegCM4.2 was too dry in Oct.-Nov. (-60% bias), while CCAM was too wet in Dec.- Mar. (130% bias). Both models were too dry in summer and too wet in winter (especially in northern Vietnam). The ability of the ensemble simulations to capture current climate increases confidence in the simulations of future climate.     

Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry,satellite altimetry and Argo

From the IPCC 4th Assessment Report published in 2007, ocean thermal expansion contributed by ～ 50% to the 3.1 mm/yr observed global mean sea level rise during the 1993–2003 decade, the remaining rate of rise being essentially explained by shrinking of land ice. Recently published results suggest that since about 2003, ocean thermal expansion change, based on the newly deployed Argo system, is showing a plateau while sea level is still rising, although at a reduced rate (～ 2.5 mm/yr). Using space gravimetry observations from GRACE, we show that recent years sea level rise can be mostly explained by an increase of the mass of the oceans. Estimating GRACE-based ice sheet mass balance and using published estimates for glaciers melting, we further show that ocean mass increase since 2003 results by about half from an enhanced contribution of the polar ice sheets – compared to the previous decade – and half from mountain glaciers melting. Taking also into account the small GRACE-based contribution from continental waters (< 0.2 mm/yr), we find a total ocean mass contribution of ～ 2 mm/yr over 2003–2008. Such a value represents ～ 80% of the altimetry-based rate of sea level rise over that period. We next estimate the steric sea level (i.e., ocean thermal expansion plus salinity effects) contribution from: (1) the difference between altimetry-based sea level and ocean mass change and (2) Argo data. Inferred steric sea level rate from (1) (～ 0.3 mm/yr over 2003–2008) agrees well with the Argo-based value also estimated here (0.37 mm/yr over 2004–2008). Furthermore, the sea level budget approach presented in this study allows us to constrain independent estimates of the Glacial Isostatic Adjustment (GIA) correction applied to GRACE-based ocean and ice sheet mass changes, as well as of glaciers melting. Values for the GIA correction and glacier contribution needed to close the sea level budget and explain GRACE-based mass estimates over the recent years agree well with totally independent determinations.