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.     

Strength and stability of frictional sliding of gabbro gouge at elevated temperatures

To investigate the strength of frictional sliding and stability of mafic lower crust, we conducted experiments on oven-dried gabbro gouge of 1 mm thick sandwiched between country rock pieces (with gouge inclined 35° to the sample axis) at slip rates of 1.22 × 10^− 3 mm/s and 1.22 × 10^− 4 mm/s and elevated temperatures up to 615 °C. Special attention has been paid to whether transition from velocity weakening to velocity strengthening occurs due to the elevation of temperature.Two series of experiments were conducted with normal stresses of 200 MPa and 300 MPa, respectively. For both normal stresses, the friction strengths are comparable at least up to 510 °C, with no significant weakening effect of increasing temperature. Comparison of our results with Byerlee's rule on a strike slip fault with a specific temperature profile in the Zhangbei region of North China shows that the strength given by experiments are around that given by Byerlee's rule and a little greater in the high temperature range.At 200 MPa normal stress, the steady-state rate dependence a − b shows only positive values, probably still in the “run-in” process where velocity strengthening is a common feature. With a normal stress of 300 MPa, the values of steady-state rate dependence decreases systematically with increasing temperature, and stick-slip occurred at 615 °C. Considering the limited displacement, limited normal stress applied and the effect of normal stress for the temperatures above 420 °C, it is inferred here that velocity weakening may be the typical behaviour at higher normal stress for temperature above 420 °C and at least up to 615 °C, which covers most of the temperature range in the lower crust of geologically stable continental interior. For a dry mafic lower crust in cool continental interiors where frictional sliding prevails over plastic flow, unstable slip nucleation may occur to generate earthquakes.     

Mongolian gerbils and Daurian pikas responded differently to changes in precipitation in the Inner Mongolian grasslands

Mongolian gerbils (Meriones unguiculatus) and Daurian pikas (Ochotona dauurica) are two key small mammal species in the Inner Mongolian grasslands, China. Mongolian gerbils displayed density-dependent population growth, but the time lag of density dependence was short and within season. The spring–autumn population growth rate was inversely related to population density in Mongolian gerbils of the Erdos desert grasslands. The autumn–spring population growth rate of Mongolian gerbils was inversely related to winter precipitation. Precipitation had stronger effects on the population growth of gerbils during the non-breeding season. The monthly population growth rate of Daurian pikas was positively related to the monthly precipitation and was inversely related to population density in central Inner Mongolia. Daurian pikas select habitats with tall plants. Increased precipitation enhances plant production and increases the height of plants in arid and semi-arid regions. This enhancement of plant height might increase the population growth of Daurian pikas. Mongolian gerbils live in short grasslands. Increased winter precipitation might result in higher winter mortality of Mongolia gerbils, or taller plants might supress gerbil population growth in wet years. Therefore, responses of small mammal species to changes in precipitation depend on the life history of small mammals and changes in vegetation induced by climatic changes.     

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤M_L≤4.6) recorded at a three-component digital network.By applying the pulse broadening method to the first P-wave pulse, we found an average Q_p value of ca. 140. The application of the frequency decay method provided a Q_p value of ca. 120, in the low-frequency band (3-9 Hz). Conversely, in the high frequency range (16-27 Hz) the average Q_p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2-5 Hz) the estimated average Q_s is ca. 190. As for Q_p, also Q_s, in the high frequency range (16-27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q_p and Q_s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.     

90年代世界贸易发展及空间格局变化的新特点

在世界贸易组织、日趋强烈的开放的区域主义倾向、跨国公司强劲的直接投资影响下，世界贸易正在经历着巨大变化，处在一个新的转换时期。本文从影响当今世界贸易发展的多重因素分析，揭示90年代世界贸易增长、内容结构以及空间格局发展变化的新特征，并展望世界贸易的未来发展。     

A bivariate meta-Gaussian density for use in hydrology

Convenient bivariate densities found in the literature are often unsuitable for modeling hydrologic variates. They either constrain the range of association between variates, or fix the form of the marginal distributions. The bivariate meta-Gaussian density is constructed by embedding the normal quantile transform of each variate into the Gaussian law. The density can represent a full range of association between variates and admits arbitrarily specified marginal distributions. Modeling and estimation can be decomposed into i) independent analyses of the marginal distributions, and ii) investigation of the dependence structure. Both statistical and judgmental estimation procedures are possible. Some comparisons to recent applications of bivariate densities in the hydrologic literature motivate and illustrate the model.