Failure of Rocks in the Laboratory and in the Earth

Although rocks, at least some of them, are nearly as old as the Earth itself, their behavior continues to play an important role in a variety of applications and phenomena of societal interest. These include natural disasters, such as landslides, volcanic eruptions and earthquakes. Rocks are widely used for building materials, foundations, tunnels and underground facilities. Most of the world’s energy now, and for the foreseeable future, comes from the shallow crust and an understanding of rock behavior is essential to e¢ cient and safe production and storage. Moreover, many of the by-products of energy production are re-injected to the shallow crust. An increasingly important application is geological sequestration of carbon dioxide, injection into the earth to mitigate harmful e¤ects on the climate [42]. Many of these problems involve not only mechanical behavior but also its coupling with ‡uid ‡ow, heat and chemistry. The vast majority of tests performed on rocks to determine constitutive behavior have been on cylindrical specimens loaded axially symmetrically. Of these, most have been in axisymmetric compression (largest magnitude principal stress is compressive). There are historical and technical reasons for the emphasis on this type of test and it does provide information on the dependence of the behavior on the mean stress (or con…ning stress). Such tests, however, provide very limited information about the response for the range of deviatoric stress states. Information about the full range of deviatoric stress states is needed for applications, in which the stress is seldom axially symmetric, and for numerical simulations. A particular issue is the role of the intermediate principal stress: In axisymmetric tests it is equal to either the most or least compressive principal stress. The Mohr-Coulomb condition (e.g., [14], [29]) posits behavior depending only only the sum and di¤erence of the largest and smallest principal stresses and, thus, is independent of the intermediate principal stress. Mogi ([20],[21],[22])