Re-appraisal of seismicity and seismotectonics in the north-eastern Algeria Part II: 20th century seismicity and seismotectonics analysis

The main objective of the research work isthe homogenisation of the two recentAlgerian earthquake catalogues for thecommon covered period of time, from 1900 to1990, for the region under considerationlimited by [33^°N–38^°N,4^°E-9.5^°E] and the updatingof the catalogue for the twentieth century(1900–2000). To mitigate the deficiencyof the incompleteness of catalogue, aneffort was made to establish a correlationbetween surface-wave magnitude Ms andbody-wave magnitude m_b in the form ofMs = a + b (m_b). A complete, exact andhomogeneous earthquake catalogue as much aspossible, comprising 870 seismic events,has been compiled. Seismicity analysis ofthe region shows a strong concentration ofseismicity along a band of no more than400 km width oriented mainly in theeast-west direction parallel to the coast.Moreover, earthquakes in this zone arerather associated to strike-slip mechanism.The focal mechanism show a regional stressregime that corresponds to horizontalcompression in NW-SE to N-S direction. As aresult of the review of the seismicity ofnorth-eastern Algeria from the compilationof checked and corrected data and itscorrelation with other geologic andgeophysical investigations based ondocumentary sources, it was possible toconstruct a most complete seismotectonicmap. It leads also to delineate fourseismogenic zones in the Tellian Atlas, aless important zone in the Saharan Atlas, asixth zone at the boundary of both Atlasand finally, a seventh one along thecoastal zone. The seismicity-active faultscorrelation of some of these defined zonesis examined in details with a specialattention to the Saharan Atlas zone, theHodna and Biban zone as well as Soummam andBabor zone where further research workallowed to find some neotectonic featuresconsidered as a significant sign of recenttectonic activity.     

Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Anisotropic dual-continuum representations for multiscale poroelastic materials: Development and numerical modelling

Dual-continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual-scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual-material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the DC model against fine-scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine-scale simulations show that anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show that the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine-scale representations.     

Statistical characteristics of detectable inhomogeneities in observed meteorological time series

Statistical characteristics of detectable inhomogeneities [IHs] in more than 600 observed meteorological time series have been investigated using 16 objective homogenisation methods. Forty and 100 year long series of monthly or annual characteristics of surface air temperature, precipitation total and relative air humidity from the Czech Republic and Hungary were examined. The area of the part of the Czech observing network used here is smaller, and the density of sites is larger, than in the Hungarian network, resulting in higher spatial correlations among data in the Czech dataset relative to the Hungarian dataset. Time series with low number of gaps were supplied with interpolated data. Before homogenisation relative time series were created, using weighted averages of time series from the same geographical region as reference series. For ease of comparison, the magnitudes of the detected IHs are normalised with the standard deviation of the noise in the relative time series. Results show that observed meteorological time series usually contain large number of small IHs, and that the magnitude distribution of IHs from different data segments are surprisingly similar. Effects of different spatial coherences on the results are discussed.     

Analysis of stone-column reinforced foundations

A numerical model is proposed to analyse elastic as well as elastoplastic behaviour of stone-column reinforced foundations. The stone-columns are assumed to be dispersed within the in situ soil and a homogenization technique is invoked to establish equivalent material properties for in situ soil and stone-column composite. The difficulties encountered in carrying out elastoplastic analyses of composite materials are overcome by adopting a separate yield function for each of the constituent materials and a sub-iteration procedure within an implicit backward Euler stress integration scheme. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenization procedure are satisfied for both elastic as well as elastoplastic stress states. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model circular footings resting on stone-column reinforced foundations. This prediction indicates good agreement with experimental observation. Finally, a new scheme in which the length of stone-column is variable is proposed and its behaviour is examined through a numerical example. © 1998 John Wiley & Sons, Ltd.     

鄂尔多斯盆地北部上古生界油气运聚特征及其铀成矿意义

鄂尔多斯盆地北部上古生界储层流体包裹体类型、均一温度、捕获压力及其变化的研究表明,上古生界液态烃和天然气具有长期运聚两期充注的特点,捕获压力在平面上为南高北低、北东部最低,成藏后大量天然气散失和油气向北东方向迁移,及砂岩型铀矿的地球化学特性等暗示油气可能为东胜大型铀矿的形成提供了必要条件。     

A homogenization approach for evaluating the longitudinal shear stiffness of reinforced soils: column versus cross trench configuration

The macroscopic linear elastic behaviour of inclusion‐reinforced soils, regarded as periodic composite media, is investigated by means of the homogenization theory. Special attention is given here to the determination of their longitudinal shear stiffness properties, which strongly govern the reinforced ground response under lateral loading. Combining the use of analytical, variational and numerical methods, we thoroughly examined three particular engineering‐relevant configurations: single trench, column and cross trench reinforcements. Fairly accurate closed‐form expressions are thus obtained, giving the value of the reinforced soil longitudinal shear stiffness as a function of the individual components shear moduli and reinforcement volume fraction. It is shown in particular that adopting a cross trench reinforcement layout instead of the classical column configuration results in a much higher improvement of the longitudinal shear stiffness. The results are then applied to assessing the reduction of soil liquefaction risk, which can be attributed to the presence of the reinforcing inclusions. Again, they clearly demonstrate the excellent performance of the cross trench configuration as compared with the complete inefficiency of the column reinforcement technique. Copyright © 2013 John Wiley & Sons, Ltd.     

An eddifying Stommel model: fast eddy effects in a two-box ocean

ABSTRACT

A system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the “averaged model”), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the “Gaussian model”). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models.