- Rachid ABABOU, Prof. Emeritus,Dr-Ing (INP Grenoble), PhD (MIT), Institut National Polytechnique de Toulouse, CNRS U... moreRachid ABABOU, Prof. Emeritus,Dr-Ing (INP Grenoble), PhD (MIT), Institut National Polytechnique de Toulouse, CNRS University of Toulouse, France Professional address: Institut de Mécanique des Fluides de Toulouse, 2 Allée du professeur Camille Soula, 31400, Toulouse, Franceedit
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Three-dimensional (3-D) groundwater flow is simulated numerically in a porous medium characterized by an isotropic or anisotropic stationary conductivity field. The solution is obtained by the finite element technique by discretizing the... more
Three-dimensional (3-D) groundwater flow is simulated numerically in a porous medium characterized by an isotropic or anisotropic stationary conductivity field. The solution is obtained by the finite element technique by discretizing the medium into 60 x 60 x 60 elements. Various simulations are performed for different variances of lnK and anisotropy ratios. Analytical expressions for second-order moments of the flux field, are compared with numerical results. The kinetic energy of the velocity fluctuations is also studied.
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Research Interests: Geography, Geology, Numerical Simulation, Porosity, Porous Media, and 14 moreSignals, Mathematical Model, Mecanique Des Fluides, Capacitive Pressure Sensor, Sea Water, Coupling, Three Dimensional, Coastal Process, Porous Medium, Unsaturated Flow, Boundary Condition, Water Level, Richards Equation, and Water level fluctuations
... that very complex spatial patterns can be efficiently represented based on a stochastic approach. ... In Figure 8.9 the permeability field of the multi-layered sedimentary structure of ... aquifer near Visp (Switzerland) was partially... more
... that very complex spatial patterns can be efficiently represented based on a stochastic approach. ... In Figure 8.9 the permeability field of the multi-layered sedimentary structure of ... aquifer near Visp (Switzerland) was partially reconstructed (estimated) by kriging using the ISATIS3 ...
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First, a mathematical overview of these analysis methods is given. The wavelet transform methods used here can be divided into two main parts: the continuous Morlet wavelet transform and the multiresolution orthogonal analysis. A... more
First, a mathematical overview of these analysis methods is given. The wavelet transform methods used here can be divided into two main parts: the continuous Morlet wavelet transform and the multiresolution orthogonal analysis. A statistical interpretation of the wavelet coefficients ...
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We derive the effective displacement relation for acoustic waves in a spatially random heterogeneous one-dimensional medium. This relationship is expressed in terms of parameters σR and σA which represent the standard deviations of the... more
We derive the effective displacement relation for acoustic waves in a spatially random heterogeneous one-dimensional medium. This relationship is expressed in terms of parameters σR and σA which represent the standard deviations of the randomly varying density ρ(x) and the randomly varying Young's modulus α(x), of the medium. In this way, we build the contributions into the total displacement relationship
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This paper deals with the generation of rock fractures in 3D space around a cylindrical excavation (here a horizontal gallery or “drift”), based on geometric and probabilistic concepts. This research is conducted in the framework of... more
This paper deals with the generation of rock fractures in 3D space around a cylindrical excavation (here a horizontal gallery or “drift”), based on geometric and probabilistic concepts. This research is conducted in the framework of studies on the isolation properties of a geological claystone repository for radioactive waste disposal (MeuseHaute Marne Underground Research Laboratory, France). The overall objective is to quantify equivalent “upscaled” hydro-mechanical properties of the disturbed porous rock, and to analyze the effect of fracturing on macroscale rock properties, e.g., equivalent permeability [1], mechanical stiffnesses, and hydro-mechanical couplings. The present work focuses on the mathematical and probabilistic representation of fractures, and their spatial distributions around the drift. The methodology is as follows. We use a mixed random/deterministic fracturing model, comprising: (i) a statistical set of 10 000 small planar joints with radially inhomogeneous statistics (size, aperture, and spatial density increasing near the wall), and (ii) a deterministic set of large curved “chevron” fractures, periodically spaced along the axis of the gallery according to a 3D chevron pattern (or 3D herringbone pattern). In particular, the spatial statistics of the small planar joints in 3D space were worked out using inhomogeneous Poisson process and other concepts from geometric probability. We also developed a new geometric model for the large curved chevron fractures, in terms of a deterministic parametric surface (a modified conoid). In this short paper, some of the resulting fracture patterns are shown graphically; the interested reader may refer to [1] for other mathematical and technical details.
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... are much smaller. It has been shown that the small-scale variations can have a significant effect on the transmitted wavefield and can give rise to apparent attenuation and dispersion (O'Doherty and Anstey,... more
... are much smaller. It has been shown that the small-scale variations can have a significant effect on the transmitted wavefield and can give rise to apparent attenuation and dispersion (O'Doherty and Anstey, 1971). In the context ...
Research Interests: Mathematics, Geophysics, Cross Correlation, Applied Geophysics, Mathematical Analysis, and 15 moreApplied, Geomatic Engineering, Second Order, Heterogeneous media, Seismic Wave Propagation, Probability Density Function, Infinite series, Material Properties, Random Coefficients, Physical Properties, Acoustic Waves, Mass Balance, Random Field, Integral representation, and phase velocity
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First, a mathematical overview of these analysis methods is given. The wavelet transform methods used here can be divided into two main parts: the continuous Morlet wavelet transform and the multiresolution orthogonal analysis. A... more
First, a mathematical overview of these analysis methods is given. The wavelet transform methods used here can be divided into two main parts: the continuous Morlet wavelet transform and the multiresolution orthogonal analysis. A statistical interpretation of the wavelet coefficients ...
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Research Interests: Mathematics, Standard Deviation, Taylor Expansion, Mathematical Analysis, Porous Media, and 15 moreFirst-Order Logic, PARTIAL DIFFERENTIAL EQUATION, Steady state, Functional integration, Taylor Series, First Order Logic, Groundwater flow, Power Series, Boundary Condition, Infinite series, Gaussian Markov Random Field, Heterogeneous porous media, Random Field, Taylor expansion series, and Perturbation method
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International audienceWe address Hydro-Mechanical (H-M) feed-back coupling in a fluid-filled fractured rock, whereby the hydraulic conductivity of the fractured rock is modified by its deformation. We present an upscaled description of... more
International audienceWe address Hydro-Mechanical (H-M) feed-back coupling in a fluid-filled fractured rock, whereby the hydraulic conductivity of the fractured rock is modified by its deformation. We present an upscaled description of this coupling based on previous work on tensorial macro-permeability (Kij) of fractured rock. The H-M feed-back coupling effects are expressed for the 2D case with fractures as straight line cracks, and for the 3D case with fractures as planar disc cracks. We assume at first that the deformable rock matrix remains impervious: feed-back effects are then due solely to crack deformation, while the effect of matrix deformation on Kij is neglected. The resulting tensorial H-M sensitivity coefficients, (K′ijkl) and (δ′kl), are expressed explicitly. Extensions of this work are indicated in the conclusive section, e.g.: strain of the permeable porous matrix; thermal expansion; and combining all types of H-M couplings (stress/pressure/fluid production coupling, as well as feed-back coupling)
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Research Interests: Mathematics, Geophysics, Elastic waves, Applied Geophysics, Mathematical Analysis, and 9 moreGeomatic Engineering, PARTIAL DIFFERENTIAL EQUATION, Seismic Wave Propagation, Probability Density Function, Elastic Properties, Low Velocity Zone, Random Field, Velocity Distribution, and Integral representation
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This article presents a set of statistical methods for pre-processing (or pre-conditioning) and analyzing multivariate hydro-geologic time series, such as pore pressures and atmospheric pressure (temporal structures). The pre-processing... more
This article presents a set of statistical methods for pre-processing (or pre-conditioning) and analyzing multivariate hydro-geologic time series, such as pore pressures and atmospheric pressure (temporal structures). The pre-processing methods are necessary to enhance or complete the signals due to defects in the observed time series (data gaps, spurious values, variable time steps). The statistical analyses aim, in fine, at
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ABSTRACT