Smeared crack approach: back to the original track

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.     

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd     

Short-lived asteroids in the 7/3 Kirkwood gap and their relationship to the Koronis and Eos families

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼30 km)—as well as the computation of their dynamical lifetimes (3<T_D<172 Myr) shows that they cannot be on their primordial orbits, but were recently injected in the resonance. The distribution of inclinations appears to be bimodal, the two peaks being close to 2° and 10°. We argue that the resonant population is constantly being replenished by the slow leakage of asteroids from both the Koronis (I∼2°) and Eos (I∼10°) families, due to the drift of their semi-major axes, caused by the Yarkovsky effect. Assuming previously reported values for the Yarkovsky mean drift rate, we calculate the flux of family members needed to sustain the currently observed population in steady state. The number densities with respect to semi-major axis of the observed members of both families are in very good agreement with our calculations. The fact that (677) Aaltje is currently observed in the resonance is most likely an exceptional event. This asteroid should not be genetically related to any of the above families. Its size and the eccentricity of its orbit suggest that the Yarkovsky effect should have been less efficient in transporting this body to the resonance than close encounters with Ceres.     

电测深ρ＿s差值法的应用效果

用电测深研究地电断面、寻找隐伏多金属矿体时，以往采用ρ＿ｓ（或η＿ｓ）等值线断面图进行地质推断解释，因受浅源信号的干扰，效果差。本文提出了采用ρ＿ｓ（或η＿ｓ）差值法，能排除浅源干扰信号，反映出地电断面的相对变化，突出了深部微弱信息，取得了较好的地质解释效果。     

The role of heterogeneous strain in the development and preservation of a polymetamorphic record in high-P granulites, western Canadian Shield

Mafic rocks in the Chipman domain of the Athabasca granulite terrane, western Canadian Shield, provide the first well‐documented record of two distinct high‐P granulite facies events in the same domain in this region. Textural relations and the results of petrological modelling (NCFMASHT system) of mafic granulites are interpreted in terms of a three‐stage tectonometamorphic history. Stage 1 involved development of the assemblage Grt + Cpx + Qtz ± Pl (M₁) from a primary Opx‐bearing igneous precursor at conditions of 1.3 GPa, 850–900 °C. Field and microstructural observations suggest that M₁ developed synchronously with an early S₁ gneissic fabric. Stage 2 is characterized by heterogeneous deformation (D₂) and synkinematic partial retrogression of the peak assemblage to an amphibole‐bearing assemblage (M₂). Stage 3 involved a third phase of deformation and a return to granulite facies conditions marked by the prograde breakdown of amphibole (Amph₂) to produce matrix garnet (Grt_3a) and the coronitic assemblage Cpx_3b + Opx_3b + Ilm_3b + Pl_3b (M_3b) at 1.0 GPa, 800–900 °C. M₁ and M_3b are correlated with 2.55 and 1.9 Ga metamorphic generations of zircon, respectively, which were dated in a separate study. Heterogeneous strain played a crucial role in both the development and preservation of these rare examples of multiple granulite facies events within single samples. Without this fortuitous set of circumstances, the apparent reaction history could have incorrectly led to an interpretation involving a single‐cycle high‐grade event. The detailed P–T–t–D history constructed for these rocks provides the best evidence to date that much of the east Lake Athabasca region experienced long‐term lower crustal residence from 2.55 to 1.9 Ga, and thus the region represents a rare window into the reactivation and ultimate stabilization processes of cratonic lithosphere.     

Impact of land use covers upon karst processes in a typical Fengcong depression system of Nongla, Guangxi, China

The direction and intensity of karst processes can be deeply affected by soil physical and chemical variations which were resulted from land use. Taking Nongla Fengcong depression area, Mashan County, Guangxi as an example, authors discussed the impact of land use on karst processes based on the data of field limestone tablet. The results showed that the corrosional rates at varied soil depth are quite different. Corrosional rate in woodland and orchard is mostly bigger than 20 mg/a, which is much higher than that in tilled land and shrub. Generally, corrosional rate decreased from orchard, woodland, tilled land, fallow land and shrub successively, in which soil organic matter (OM) and soil pH are two major controlling factors: corrosion process is controlled remarkably by soil OM in woodland and orchard. The higher the organic matter content is and the less the pH value is, the higher the corrosional rate is. Owing to lower organic matter content, the corrosional rate is mainly affected by soil CO₂ in tilled land and shrub.     

Natural radioactivity in sediment of Wei River,China

The concentrations of natural radionuclides in sediment of Wei River of China were measured using γ-ray spectrometry with the aim of estimating the radiation hazard as establishing a database for radioactivity levels of river sediment of China. The activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K in sediment samples ranged from 10.4 to 39.9 Bq kg⁻¹, 15.3 to 54.8 Bq kg⁻¹ and 514.8 to 1,175.5 Bq kg⁻¹, respectively. The concentrations of these radionuclides were compared with the typical world values and the average activities of Chinese soil and Shaanxi soil. Radium equivalent activity (Ra_eq), external hazard index (H _ex) and representative level index (I _γr) were calculated for the samples to assess the radiation hazards arising due to the use of these sediment samples in the construction of dwellings. All the sediment samples have Ra_eq lower than the limit of 370 Bq kg⁻¹, H _ex less than unity and I _γr close to 1 Bq kg⁻¹. The overall mean outdoor terrestrial gamma dose rate is 64.8 nGy h⁻¹ and the corresponding outdoor annual effective dose is 0.079 mSv. None of the studied location is considered a radiological risk and sediment can be safely used in construction.     

Interference of Multiple Strip Footings on Sand Using Small Scale Model Tests

By using small scale model tests, the interference effect on the vertical load-deformation behavior of a number of equally spaced strip footings, placed on the surface of dry sand, was investigated. At any stage, all the footings were assumed to (i) carry exactly equal magnitude of load, and (ii) settle to the same extent. No tilt of the footing was permitted. The effect of clear spacing (s) among footings on the results was explored. A new experimental setup was proposed in which only one footing needs to be employed rather than a number of footings. The bearing capacity increases continuously with decrease in spacing among the footings. The interference effect becomes further prominent with increase in soil friction angle. In contrast to an increase in the bearing capacity, with decrease in spacing of footings, an increase in the footing settlement associated with the ultimate state of shear failure was observed. The present experimental observations were similar to those predicted by the available theory, based on the method of characteristics. As compared to the theory, the present experimental data, however, indicates much greater effect of interference especially for larger spacing among footings.