219 research outputs found
Statistical mechanics of interacting fiber bundles
We consider quasistatic fiber bundle models with interactions. Classical load
sharing rules are considered, i.e. local, global or decaying as a power-law of
distance. All fibers are identically elastic, initially intact, and break at a
random threshold picked from a quenched disorder (q.d.) distribution. We are
interested in the probability distribution of configurations of broken fibers
at a given elongation, averaged over all possible realizations of the
underlying q.d.. This distribution is accessed by mapping the threshold set
space onto the configurational space, each path corresponding to the evolution
of a bundle corresponding to a realized q.d.. Using a perturbative approach
allows to obtain this distribution to leading order in the interactions. This
maps this system onto classical statistical mechanics models, i.e. percolation,
standard or generalized Ising models depending on the range of the interactions
chosen in the load sharing rule. This relates such q.d. based systems to
standard classical mechanics, which allows to derive observables of the system,
as e.g. correlation lengths. The thermodynamic parameters formally equivalent
to temperature and chemical potential, are functions of the externally imposed
deformation, depending on the load sharing rule and the choice of the q.d.
distribution
Hydrothermal coupling in a rough fracture
Heat exchange during laminar flow is studied at the fracture scale on the
basis of the Stokes equation. We used a synthetic aperture model (a self-affine
model) that has been shown to be a realistic geometrical description of the
fracture morphology. We developed a numerical modelling using a finite
difference scheme of the hydrodynamic flow and its coupling with an
advection/conduction description of the fluid heat. As a first step,
temperature within the surrounding rock is supposed to be constant. Influence
of the fracture roughness on the heat flux through the wall, is estimated and a
thermalization length is shown to emerge. Implications for the
Soultz-sous-For\^{e}ts geothermal project are discussed
Dynamics and structure of interfacial crack fronts
The propagation of an interfacial crack front through a weak plane of a
transparent Plexiglas block has been studied experimentally. A stable crack in
mode I was generated by loading the system by an imposed displacement. The
local velocities of the fracture front line have been measured by using an high
speed CCD camera. The distribution of the velocities exhibits a power law
behavior for velocities larger than the average front velocity with a
crossover to a slowly increasing function for velocities lower than . The
fluctuations in the velocities reflect an underlying irregular bursts activity
with a power law distribution of the bursts. We further found that the size of
the local bursts scales differently in the direction parallel to and
perpendicular to the fracture front
Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study
The characteristics of the hydro-thermal flow which occurs when a cold fluid
is injected into a hot fractured bedrock depend on the morphology of the
fracture. We consider a sharp triangular asperity, invariant in one direction,
perturbing an otherwise flat fracture. We investigate its influence on the
macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low
Reynolds number. In this study, numerical simulations are done with a coupled
lattice Boltzmann method that solves both the complete Navier-Stokes and
advection-diffusion equations in three dimensions. The results are compared
with those obtained under lubrication approximations which rely on many
hypotheses and neglect the three-dimensional (3D) effects. The lubrication
results are obtained by analytically solving the Stokes equation and a
two-dimensional (integrated over the thickness) advection-diffusion equation.
We use a lattice Boltzmann method with a double distribution (for mass and
energy transport) on hypercubic and cubic lattices. Beyond some critical slope
for the boundaries, the velocity profile is observed to be far from a quadratic
profile in the vicinity of the sharp asperity: the fluid within the triangular
asperity is quasi-static. We find that taking account of both the 3D effects
and the cooling of the rock, are important for the thermal exchange. Neglecting
these effects with lubrication approximations results in overestimating the
heat exchange efficiency. The evolution of the temperature over time, towards
steady state, also shows complex behavior: some sites alternately reheat and
cool down several times, making it difficult to forecast the extracted heat.Comment: In Journal of Geophysical Research B (2013) online firs
Local waiting time fluctuations along a randomly pinned crack front
The propagation of an interfacial crack along a heterogeneous weak plane of a
transparent Plexiglas block is followed using a high resolution fast camera. We
show that the fracture front dynamics is governed by local and irregular
avalanches with very large size and velocity fluctuations. We characterize the
intermittent dynamics observed, i.e. the local pinnings and depinnings of the
crack front which trigger a rich burst activity, by measuring the local waiting
time fluctuations along the crack front during its propagation. The local front
line velocity distribution deduced from the waiting time analysis exhibits a
power law behavior, with , for
velocities larger than the average front speed . The burst size
distribution is also a power law,
with . Above a characteristic
length scale of disorder , the avalanche clusters become
anisotropic, and the scaling of the anisotropy ratio provides an estimate of
the roughness exponent of the crack front line, , in close agreement
with previous independent estimates.Comment: Phys. Rev. Lett., accepte
Dynamic development of hydrofracture
Many natural examples of complex joint and vein networks in layered sedimentary rocks are hydrofractures that form by a combination of pore fluid overpressure and tectonic stresses. In this paper, a two-dimensional hybrid hydro-mechanical formulation is proposed to model the dynamic development of natural hydrofractures. The numerical scheme combines a discrete element model (DEM) framework that represents a porous solid medium with a supplementary Darcy based pore-pressure diffusion as continuum description for the fluid. This combination yields a porosity controlled coupling between an evolving fracture network and the associated hydraulic field. The model is tested on some basic cases of hydro-driven fracturing commonly found in nature, e.g., fracturing due to local fluid overpressure in rocks subjected to hydrostatic and nonhydrostatic tectonic loadings. In our models we find that seepage forces created by hydraulic pressure gradients together with poroelastic feedback upon discrete fracturing play a significant role in subsurface rock deformation. These forces manipulate the growth and geometry of hydrofractures in addition to tectonic stresses and the mechanical properties of the porous rocks. Our results show characteristic failure patterns that reflect different tectonic and lithological conditions and are qualitatively consistent with existing analogue and numerical studies as well as field observations. The applied scheme is numerically efficient, can be applied at various scales and is computational cost effective with the least involvement of sophisticated mathematical computation of hydrodynamic flow between the solid grains
Direct velocity measurement of a turbulent shear flow in a planar Couette cell
In a plane Couette cell a thin fluid layer consisting of water is sheared
between a transparent band at Reynolds numbers ranging from 300 to 1400. The
length of the cells flow channel is large compared to the film separation. To
extract the flow velocity in the experiments a correlation image velocimetry
(CIV) method is used on pictures recorded with a high speed camera. The flow is
recorded at a resolution that allows to analyze flow patterns similar in size
to the film separation. The fluid flow is then studied by calculating flow
velocity autocorrelation functions. The turbulent pattern that arise on this
scale above a critical Reynolds number of Re=360 display characteristic
patterns that are proven with the calculated velocity autocorrelation
functions. The patterns are metastable and reappear at different positions and
times throughout the experiments. Typically these patterns are turbulent rolls
which are elongated in the stream direction which is the direction the band is
moving. Although the flow states are metastable they possess similarities to
the steady Taylor vortices known to appear in circular Taylor Couette cells
Morphological analysis of stylolites for paleostress estimation in limestones surrounding the Andra Underground Research Laboratory site
We develop and test a methodology to infer paleostress from the morphology of
stylolites within borehole cores. This non-destructive method is based on the
analysis of the stylolite trace along the outer cylindrical surface of the
cores. It relies on an automatic digitization of high-resolution photographs
and on the spatial Fourier spectrum analysis of the stylolite traces. We test
and show, on both synthetic and natural examples, that the information from
this outer cylindrical surface is equivalent to the one obtained from the
destructive planar sections traditionally used. The assessment of paleostress
from the stylolite morphology analysis is made using a recent theoretical
model, which links the morphological properties to the physical processes
acting during stylolite evolution. This model shows that two scaling regimes
are to be expected for the stylolite height power spectrum, separated by a
cross-over length that depends on the magnitude of the paleostress during
formation. We develop a non linear fit method to automatically extract the
cross-over lengths from the digitized stylolite profiles. Results on cores from
boreholes drilled in the surroundings of the Andra Underground Research
Laboratory located at Bure, France, show that different groups of sedimentary
stylolites can be distinguished, and correspond to different estimated vertical
paleostress values. For the Oxfordian formation, one group of stylolites
indicate a paleostress of around 10 MPa, while another group yields 15 MPa. For
the Dogger formation, two stylolites indicate a paleostress of around 10 MPa,
while others appear to have stopped growing at paleostresses between 30 and 22
MPa, starting at an erosion phase that initiated in the late Cretaceous and
continues today. This method has a high potential for further applications on
reservoirs or other geological contexts where stylolites are present.Comment: International Journal of Rock Mechanics and Mining Sciences (2013)
online firs
Growth activity during fingering in a porous Hele Shaw cell
We present in this paper an experimental study of the invasion activity
during unstable drainage in a 2D random porous medium, when the (wetting)
displaced fluid has a high viscosity with respect to that of the (non-wetting)
displacing fluid, and for a range of almost two decades in capillary numbers
corresponding to the transition between capillary and viscous fingering. We
show that the invasion process takes place in an active zone within a
characteristic screening length from the tip of the most advanced finger. The
invasion probability density is found to only depend on the distance to the
latter tip, and to be independent of the value for the capillary number Ca. The
mass density along the flow direction is related analytically to the invasion
probability density, and the scaling with respect to the capillary number is
consistent with a power law. Other quantities characteristic of the
displacement process, such as the speed of the most advanced finger tip or the
characteristic finger width, are also consistent with power laws of the
capillary number. The link between the growth probability and the pressure
field is studied analytically and an expression for the pressure in the
defending fluid along the cluster is derived. The measured pressure are then
compared with the corresponding simulated pressure field using this expression
for the boundary condition on the cluster.Comment: 11 pages 10 figure
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