Notes on Geoplasticity

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