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Notes on Geoplasticity (Hardcover)
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Notes on Geoplasticity (Hardcover)
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This book is about geoplasticity, solid mechanics of rock, jointed
rock and soil beyond the domain of a purely elastic deformation.
Plastic deformation is irreversible and begins at the limit to
elasticity with any attempt at further loading. Stress at the limit
to elasticity is "strength" which is described by a functional
relationship amongst stresses, that is, by a yield function or
failure criterion. Mohr-Coulomb, Drucker-Prager and Hoek-Brown
criteria are well-known examples in geomechanics. Beyond the
elastic limit, but still within the realm of small strain
increments, a total strain increment is the sum of an elastic
increment and a plastic increment. The elastic increment is
computed through an incremental form of Hooke's law, isotropic or
anisotropic as the case may be. Computation of the plastic part is
at the core of any plasticity theory and is approached through the
concept of a plastic potential. The plastic potential is a function
of stresses and perhaps other material parameters such as plastic
strain and temperature. Derivatives of the plastic potential with
respect to stress lead to the plastic part of the total strain
increment. If the yield criterion and plastic potential are the
same, then the plastic stress-strain relationships are "associated
rules of flow" and follow a "normality" principle. Normality is in
reference to a graphical portrayal in principal stress space where
the plastic strain increment is perpendicular to the yield surface.
If the plastic potential and yield criterion are different, as is
often the case in geoplasticity, then the rules of flow are
"non-associated". Drucker's famous stability postulate implies
normality at a smooth point on the yield surface, convexity of the
yield function and other important features of plasticity theory in
geomechanics. However, there is no point to proceeding to
theoretical analyses without physical justification. Hence, the
physical foundations for application of plasticity theory to rock,
jointed rock and soil are examined in Chapter 2 of this book. A
brief review of continuum mechanics principles is given in Chapter
3. Chapter 4 focuses on plane plastic strain and "sliplines". The
technical literature is replete with numerous diagrams of
sliplines, especially in discussions of foundations on soils, but
the relevant mathematics is often lacking and with it genuine
understanding. Examples illustrate application of theory to
traditional geomechanics problems such as computation of retaining
wall forces in soils, foundation bearing capacity of soil and rock,
wedge penetration of rock under confining pressure and others.
Brief discussions of anisotropy, visco-plasticity and
poro-plasticity are presented in Chapters 6, 7 and 8. This book
will be of interest to civil, geological and mining engineers,
particularly those involved in reliable design of excavations and
foundations beyond elasticity, especially in jointed rock.
General
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