Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity

This paper presents a detailed numerical study of the retrogressive failure of landslides in sensitive clays. The dynamic modelling of the landslides is carried out using a novel continuum approach, the particle finite element method, complemented with an elastoviscoplastic constitutive model. The multiwedge failure mode in the collapse is captured successfully, and the multiple retrogressive failures that have been widely observed in landslides in sensitive clays are reproduced with the failure mechanism, the kinematics, and the deposition being discussed in detail. Special attention has been paid to the role of the clay sensitivity on each retrogressive failure as well as on the final retrogression distance and the final run‐out distance via parametric studies. Moreover, the effects of the viscosity of sensitive clays on the failure are also investigated for different clay sensitivities.     

Old Pulsators: White Dwarfs and Their Immediate Precursors

There are now fully six classes of pulsators among white dwarfsand their immediate precursors among central stars of planetarynebulae and on the extended horizontal branch.In this review, we outline those observational and theoreticalconsiderations that link them together and set them apart fromother kinds of pulsating stars.We summarize some select astrophysical puzzles to which studiesof such pulsators might speak, and we discuss current applicationsin the fields of atomic, nuclear, and neutrino physics.Finally, we suggest how future observing programs might solve somegeneral problems common not only to the white dwarf and pre-whitedwarf pulsators but to many types of variable stars.     

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.     

The transfer of polarized radiation in spectral lines: Formalism and solutions in simple cases

A general treatment of the transfer of polarized radiation in spectral lines assuming a Rayleigh phase function and a general law of frequency redistribution is derived. It is shown how nine families of coupled integral equations for the moments of the radiation field arise which are necessary to fully describe the state of polarization of the emergent radiation from a plane-parallel, semi-infinite atmosphere. The special case of angle independent redistribution functions is derived from the general formalism, and it is shown how the nine families of integral equations reduce to the six linearly independent integral equations derived by Collins (1972). To serve as a test of the formulation, solutions for isothermal atmospheres are given.     

Partitioning of polycyclic aromatic hydrocarbons between water and particles compared to bioaccumulation in mussels: a harbour case

Water and particles from three sites located in Halifax Harbour, near and further away from combined municipal sewage effluents (CMSE) were analysed for parental and alkylated polycyclic aromatic hydrocarbons (par and alkPAH). Bioavailability of PAH was compared for inter-tidal mussels collected at the same sites in April and November. The PAH fingerprint determined over 9 sampling times covering a period of 19 months differed more between phases (water and particles) and seasons, than between sites. In the spring, more alkPAH associated with diesel and gasoline were detected in the soluble phase, along with more bioaccumulation of alkPAH in inter-tidal mussels. A broader number of parPAH were detected in mussels collected in the fall. The mean sum of dissolved alkPAH concentrations was higher in water at the site closer to raw CMSE than at the other two sites and particles of that site. However, lowest bioconcentration factors (BCF) were determined in mussels of this more contaminated site. Similar biota-particle accumulation factors (BPAF) were determined for parPAH in mussels from the three sites, all lower than the BCF of alkPAH. The study indicates that sewage treatment plants will reduce the amount of parPAH especially larger than fluoranthene and pyrene from being deposited in the harbour; that alk naphthalenes and fluorenes present in water will continue to be discharged; that the disturbance of sediments can make particle-bound PAH available to mussels.     

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Géodésie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A simple hypoplastic model for normally consolidated clay

The paper presents a simple constitutive model for normally consolidated clay. A mathematical formulation, using a single tensor-valued function to define the incrementally nonlinear stress–strain relation, is proposed based on the basic concept of hypoplasticity. The structure of the tensor-valued function is determined in the light of the response envelope. Particular attention is paid towards incorporating the critical state and to the capability for capturing undrained behaviour of clayey soils. With five material parameters that can be determined easily from isotropic consolidation and triaxial compression tests, the model is shown to provide good predictions for the response of normally consolidated clay along various stress paths, including drained true triaxial tests and undrained shear tests.     

The major-ion composition of silurian seawater

One-hundred fluid inclusions in Silurian marine halite were analyzed in order to determine the major-ion composition of Silurian seawater. The samples analyzed were from three formations in the Late Silurian Michigan Basin, the A-1, A-2, and B Evaporites of the Salina Group, and one formation in the Early Silurian Canning Basin (Australia), the Mallowa Salt of the Carribuddy Group. The results indicate that the major-ion composition of Silurian seawater was not the same as present-day seawater. The Silurian ocean had lower concentrations of Mg²⁺, Na⁺, and SO₄²⁻, and much higher concentrations of Ca²⁺ relative to the ocean’s present-day composition. Furthermore, Silurian seawater had Ca²⁺ in excess of SO₄²⁻. Evaporation of Silurian seawater of the composition determined in this study produces KCl-type potash minerals that lack the MgSO₄-type late stage salts formed during the evaporation of present-day seawater. The relatively low Na⁺ concentrations in Silurian seawater support the hypothesis that oscillations in the major-ion composition of the oceans are primarily controlled by changes in the flux of mid-ocean ridge brine and riverine inputs and not global or basin-scale, seawater-driven dolomitization. The Mg²⁺/Ca²⁺ ratio of Silurian seawater was ∼1.4, and the K⁺/Ca²⁺ ratio was ∼0.3, both of which differ from the present-day counterparts of 5 and 1, respectively. Seawaters with Mg²⁺/Ca²⁺ <2 facilitate the precipitation of low-magnesian calcite (mol % Mg < 4) marine ooids and submarine carbonate cements whereas seawaters with Mg²⁺/Ca²⁺ >2 (e.g., modern seawater) facilitate the precipitation of aragonite and high-magnesian calcite. Therefore, the early Paleozoic calcite seas were likely due to the low Mg²⁺/Ca²⁺ ratio of seawater, not the pCO₂ of the Silurian atmosphere.     

Chemical denudation rates in Kärkevagge, Swedish Lapland

This study examines the spatial and temporal variability of chemical denudation rates in Kärkevagge, northern Sweden. The chemical flux rates within the valley are strongly influenced by the local geology. Chemical denudation rates determined for the study period are more than double those previously reported in the literature for this valley. Rates of greater than 46t km⁻² a⁻¹ were measured at the valley mouth over the course of the melt season. This difference is likely due to differences in measurement technique compared to that used by past researchers. This rate is also much higher than for other arctic and alpine watersheds. Chemical denudation in Kärkevagge is comparable to larger temperate rivers. The rapid chemical denudation in Kärkevagge is likely due to sulfide weathering creating acid solutions.