A synthesis of the numerical analysis of the ultimate bearing capacity and pullout strength force of shallow and deep foundations, using the Hoek and Brown failure criteria, is presented. The effect of the weight of the rock mass and a case of anisotropy are briefly included. Some results of a particular case of parabolic type failure criterion are also incorporated.


This paper should be titled "Foundations in a rock mass as a continuous medium", since one of the first and foremost assumptions behind it is that rock behaves as a whole entity, being in most cases homogeneous and isotropic. Many types of foundations and their most relevant features are considered (shallow, deep, anchors, etc.). The Hoek and Brown failure criteria addresses most of the problems posed, although this methodology could also be applied to any other non-linear failure criteria, provided the Mohr's envelope exists. Close solutions are offered after having considerably simplifying the working hypotheses. They are meant to be used with charts and simple formulae to identify the main parameters involved offering the possibility of doing parametric analyses that provide orders of magnitude simply and quickly.

2.1 Hypotheses

The most important hypotheses, most of which have been adopted in this Keynote Lecture, are related to the theory of plasticity as follows:

  1. The rock mass behaves in a perfectly plastic manner.

  2. Plasticity is coaxial.

  3. The failure criterion may be non-linear.

  4. Plane strain is assumed, when needed.

  5. The rock mass is generally assumed to be weightless. (The bearing capacity of shallow foundations has also been studied and its main results are listed for rock masses that do have their own weight).

  6. No inertial forces are acting

2.2 Failure criteria

  • Hoek and Brown's original failure criterion (1980) It is also well known that rock mass at failure does not behave according to a linear criterion. The Hoek and Brown criterion has been selected from the many non-linear failure criteria that appear in the technical literature.

2.3 Applicability of the method

There are, among many others, two factors which differentiate the soil and rock behavior:

  • The brittleness of many types of rocks, depending on its intrinsic characteristics.

  • The discontinuities of rock masses. This calculation methodology can be very appropriate depending on the spacing of discontinuities, in a manner similar to the one suggested by Hoek (1983) for solving the stability problems on rock and the elastic-plastic behavior in tunnel opening operations. Figure 2 shows how the criterion is extended to be used in the design of shallow foundations (Serrano and Olalla, 1996a). Following Hoek and Brown recommendations, their non-linear failure criteria is only valid for the "intact rock", "single discontinuity" and "jointed rock mass" situations, respectively.

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