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SSP 1995 project summary:
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The Stress Distribution in Faulted Porous Rocks
Background
Pore fluids in rocks play a fundamental role in the brittle
deformation of the shallow Earth's crust and, in turn, their migration
is widely driven by the fault distribution and the
porosity-permeability structure of each fault. Until recently
however, little emphasis has been placed on the modelling of this
coupled evolution of brittle deformation and pore fluids. We are
currently working towards a numerical model that couples the evolution
of fluid flows and deformations in a range of geologically realistic
conditions. Such a model must:
- solve the diffusion equation for the pore fluid pressure,
- solve the elastic wave equation (or Laplace's equation) to
determine the stress tensor distribution,
- account for elastic to brittle deformations by adopting a
proper constitutive law, and
- couple the above equations.
Goal
Some of the difficulties raised by the construction of this model have
been solved (the pore pressure diffusion and the implementation of the
constitutive law). The most important remaining problem is the
determination of the stress distribution after any breaking has
occured. This is the goal of the present project.
Ideally, such a determination should be both accurate and fast.
Accurate because the anisotropic character of the stress plays a
determinant role in the resulting fracture patterns, fast because it
will be performed hundreds to thousands of times (i.e. at each time
step) during a single simulation. Eventually, it cannot rely on
simplifying assumptions about heterogeneities of the medium since they
are precisely arbitrary, exhibiting sharp contrasts of all parameters
in the regions of faults and fractures.
Method
At the present time, we are considering three strategies to determine
the stress distribution after each dynamic (slip) event along any
fault. One of these will be chosen before the project starts:
- the most accurate way is to solve Laplace's equation, but this
involves an inversion procedure which might take
unrealistically long computation times in the case of
anisotropic stresses, even on the Cray-T3D;
- such a solution can be approximated using coarse-graining
algorithms and/or renormalisation techniques;
- a finite-difference approximation to the elastic wave equation
with a non-linear constitutive law also provides such a
solution, while introducing attenuation would improve the
convergence towards the static state we seek.
Tasks
The student will have to implement one of the three methods outlined
above on the Cray-T3D in a Message-Passing style. We intend to provide
him with a detailed description of the method and to closely follow
the development of the code. If it is succesfully implemented before
the end of the scolarship, the student will be able to perform
simulations for comparison with analytic solutions in simple cases.
Results expected
The determination of the stress distribution in a heterogeneous medium
is a fundamental problem in itself and need not be subject to the full
development of the model described above. It is worth a publication in
itself.
Regina
Schlegel worked on this project.
Compressed PostScript of the project's final report is available here
(203747 bytes) .
Webpage maintained by
mario@epcc.ed.ac.uk