Explicit stress integration with error control for the Barcelona Basic Model: Part I: Algorithms formulations

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

EPR and magnetism of the nanostructured natural carbonaceous material shungite

The X-band EPR and magnetic susceptibility in the temperature range 4.2–300 K study of the shungite-I, natural nanostructured material from the deposit of Shunga are reported. Obtained results allow us to assign the EPR signal to conduction electrons, estimate their number, N _P, and evaluate the Pauli paramagnetism contribution to shungite susceptibility. A small occupation (~5%) of the localized nonbonding π states in the zigzag edges of the open-ended graphene-like layers and/or on σ (sp ^2+x ) orbitals in the curved parts of the shungite globules has been also revealed. The observed temperature dependence of the EPR linewidth can be explained by the earlier considered interaction of conduction π electrons with local phonon modes associated with the vibration of peripheral carbon atoms of the open zigzag-type edges and with peripheral carbon atoms cross-linking different nanostructures. The relaxation time T ₂ and diffusion time T _D are found to have comparable values (2.84 × 10⁻⁸ and 1.73 × 10⁻⁸ s at 5.2 K, respectively), and similar dependence on temperature. The magnetic measurements have revealed the suppression of orbital diamagnetism due to small amount of large enough fragments of the graphene layers.     

2.5-D seismic tomographic modelling of the crustal structure of north-western Spitsbergen based on deep seismic soundings

Deep seismic sounding measurements were performed in the continent-ocean transition zone of the northern Svalbard continental margin in 1985 and 1999. Data from seismic profile AWI-99200 and from additional crossing profiles were used to model the seismic crustal structure of the study area. Seismic energy (airgun and TNT shots) was recorded by land (onshore) seismic stations, ocean bottom seismometers (OBS), and hydrophone systems (OBH). 3-D tomographic inversion methods were applied to test the previous 2-D modelling results. The results are similar to the earlier 2-D modelling, supplemented by new off-line information. The continental crust thins to the west and north. A minimum depth of about 6 km to the Moho discontinuity was found east of the Molloy Deep. The continent-ocean transition zone to the east is characterized by a complex seismic velocity structure according to the 2-D model and consists of several different crustal blocks. The zone is covered by deep sedimentary basins. Sediment thicknesses reach a maximum of 5 km. The Moho interface deepens to 28 km depth beneath the continental crust of Svalbard.     

Flow in open channels under the influence of ice cover

During winters in Poland, lakes, ponds, rivers, channels, run-of-reservoirs, ditches and streams are covered with ice, which changes significantly the flow and thermal conditions in water bodies. The paper presents a very complicated process of ice formation on stagnant and flowing waters. Various kinds of ice are described together with their consequences for flow and thermal conditions. The possibility to define flow conditions in open channels with ice cover is described. In 1982, a significant flood on Włocławek Reservoir (Lower Vistula River) appeared, which was caused by the coincidence of unfavourable, extreme hydrological and meteorological conditions. These conditions, as well as the run and consequences of the flood, are described. Detailed field measurements of ice cover and flow were carried out. One-dimensional model for steady nonuniform flow was developed and applied to the conditions existing in 1982 on the Włocławek Reservoir.     

On the influence of microphysics parametrization on the rainfall rates in numerical models of clouds

Accuracy of formulas for growth by accretion and evaporation of rain in bulk parametrization of these processes for the case of light and moderate precipitation is investigated. It is done by comparison of results from two simple models: with bulk approach and with exact calculations of growth or evaporation of drops in each size bin separately. Growth by accretion is accurately represented in bulk parametrization but rain evaporation is overpredicted. Corrected formula for rain evaporation is suggested.     

On the bulk parameterization of snow and its application to the quantitative studies of precipitation growth

Appropriate formulation of bulk parameterization of snow growth and evaporation based on observational characteristics of snow particles is presented. The parameterization is compared to that of S. A. Rutledge and P. V. Hobbs and to detailed treatment in which snow particles are assumed to grow or evaporate in each size bin separately. On the contrary to bulk parameterization of rain, snow diffusional growth or evaporation is accurately represented in the suggested bulk formulation, but growth by riming is overpredicted. Integrations of water budget equations in a one-dimensional updraft have shown that quantitative results, e.g., precipitation intensity, cloudwater content, supersaturation with respect to ice, depend on the parameterization scheme employed, which suggests that comparisons of field measurements with parameterized model outputs is usually not straightforward.     

Holocene climate and glacial history of the northeastern Antarctic Peninsula: the marine sedimentary record from a long SHALDRIL core

A high-resolution record of Holocene deglacial and climate history was obtained from a 77 m sediment core from the Firth of Tay, Antarctic Peninsula, as part of the SHALDRIL initiative. This study provides a detailed sedimentological record of Holocene paleoclimate and glacial advance and retreat from the eastern side of the peninsula. A robust chronostratigraphy was derived from thirty-three radiocarbon dates on carbonate material. This chronostratigraphic framework was used to establish the timing of glacial and climate events derived from multiple proxies including: magnetic susceptibility, electric resistivity, porosity, ice-rafted debris content, organic carbon content, nitrogen content, biogenic silica content, and diatom and foraminiferal assemblages. The core bottomed-out in a stiff diamicton interpreted as till. Gravelly and sandy mud above the till is interpreted as proximal glaciomarine sediment that represents decoupling of the glacier from the seafloor circa 9400 cal. yr BP and its subsequent landward retreat. This was approximately 5000 yr later than in the Bransfield Basin and South Shetland Islands, on the western side of the peninsula. The Firth of Tay core site remained in a proximal glaciomarine setting until 8300 cal. yr BP, at which time significant glacial retreat took place. Deposition of diatomaceous glaciomarine sediments after 8300 cal. yr BP indicates that an ice shelf has not existed in the area since this time.The onset of seasonally open marine conditions between 7800 and 6000 cal. yr BP followed the deglacial period and is interpreted as the mid-Holocene Climatic Optimum. Open marine conditions lasted until present, with a minor cooling having occurred between 6000 and 4500 cal. yr BP and a period of minor glacial retreat and/or decreased sea ice coverage between 4500 and 3500 cal. yr BP. Finally, climatic cooling and variable sea ice cover occurred from 3500 cal. yr BP to near present and it is interpreted as being part of the Neoglacial. The onset of the Neoglacial appears to have occurred earlier in the Firth of Tay than on the western side of the Antarctic Peninsula. The Medieval Warm Period and Little Ice Age were not pronounced in the Firth of Tay. The breadth and synchroneity of the rapid regional warming and glacial retreat observed in the Antarctic Peninsula during the last century appear to be unprecedented during the Holocene epoch.     

Tectonic, eustatic and environmental controls on mid-Cretaceous carbonate platform deposition, south-central Pyrenees, Spain

Cenomanian–Turonian strata of the south‐central Pyrenees in northern Spain contain three prograding carbonate sequences that record interactions among tectonics, sea level, environment and sediment fabric in controlling sequence development. Sequence UK‐1 (Lower to Upper Cenomanian) contains distinct lagoonal, back‐margin, margin, slope and basin facies, and was deposited on a broad, flat shelf adjacent to a deep basin. The lack of reef‐constructing organisms resulted in a gently dipping ramp morphology for the margin and slope. Sequence UK‐2 (Upper Cenomanian) contains similar shallow‐water facies belts, but syndepositional tectonic modification of the margin resulted in a steep slope and deposition of carbonate megabreccias. Sequence UK‐3 (Lower to Middle Turonian) records a shift from benthic to pelagic deposition, as the shallow platform was drowned in response to a eustatic sea‐level rise, coupled with increased organic productivity. Sequences UK‐1 to UK‐3 are subdivided into lowstand, transgressive and highstand systems tracts based on stratal geometries and facies distribution patterns. The same lithologies (e.g. megabreccias) commonly occur in more than one systems tract, indicating that: (1) the depositional system responded to more than just sea‐level fluctuations; and (2) similar processes occurred during different times throughout sequence development. These sequences illustrate the complexity of carbonate platform dynamics that influence sequence architecture. Rift tectonics and flexural subsidence played a major role in controlling the location of the platform margin, maintaining a steep slope gradient through syndepositional faulting, enhancing slope instability and erosion, and influencing depositional processes, stratal relationships and lithofacies distribution on the slope. Sea‐level variations (eustatic and relative) strongly influenced the timing of sequence and parasequence boundary formation, controlled changes in accommodation and promoted platform drowning (in conjunction with other factors). Physico‐chemical and climatic conditions were responsible for reducing carbonate production rates and inducing platform drowning. Finally, a mud‐rich sediment fabric affected platform morphology, growth geometries (aggradation vs. progradation) and facies distribution patterns.     

Sediment lithology and stable isotope composition of organic matter in a core from a cirque in the Krkonoše Mountains,Czech Republic

This study presents detailed lithostratigraphy and stable carbon and nitrogen isotopic variations in a 520-cm-long sediment core from a cirque basin in the Labsky důl Valley, Krkonoše Mountains, Czech Republic. Detailed study of the core reveals five major periods of sedimentation during the last 7600 years: silt and sand deposition during ~7.6–5.1 ka cal BP, Sphagnum peat accumulation during ~5.1–4.0 ka cal BP, sandy silt and sand during ~4.0–2.8 ka cal BP, raised peat bog during ~2.8–2.0 ka cal BP (Sphagnum peat), and sedimentation of sandy silt since ~2.0 ka cal BP. The δ¹³C values of the organic matter in the core vary in the range typical for C3 plants, from −24.35 to −27.68‰, whereas the δ¹⁵N values vary from −2.65 to +4.35‰. Core sections having ash contents ≥70% have δ¹⁵N > 1‰ and δ¹³C < −26‰, whereas those having ≤70% ash content have δ¹⁵N < 1‰ and δ¹³C > −26‰. Strong linear correlations are observed between δ¹³C and δ¹⁵N values as well as between C:N ratios and δ¹⁵N values in the horizons with ash content >10%, primarily for sand and silt horizons. On the other hand, poor correlations between δ¹³C and C:N ratio, as well as δ¹⁵N and C:N ratio, were observed in Sphagnum peat layers (45–125 and 185–265 cm). We conclude that the primary stable isotope variations are not preserved in the layers where significant correlation between δ¹⁵N and C:N ratio is observed. The relatively small δ¹³C variation in the uppermost Sphagnum peat layer suggests stable temperature during ~2.8–2.0 ka cal BP.