Evaluation of properties of a rock mass from those of its constituent elements has been for a long time the key problem in the application of rock mechanics to the exploitation of mines and to large scale civil engineering works. During the last two decades, a number of theories have been proposed for that purposes, most of them based on certain simple rock mass models, intended to take into account both the characteristics of structural discontinuities in the mass, and the physical properties of the rock substance (Patton, 1966; Ladanyi and Archambault, 1969; Barton, 1971, Jaeger, 1971).
Among these various theories of shear strength of rock mass, the one proposed by Ladanyi and Archambault (1969) has the advantage of clearly defining the failure mechanism, in a physical sense, and of taking into account the majority of components that affect the peak shear strength of the mass. An objection which can be raised with respect to this theory is that it does not consider the statistical character of the rock strength, and of the rock mass failure, so that it should be considered essentially as a deterministic approach.
Experimental evidence shows, however, that rock mass failure is mostly a progressive phenomenon (Muller, 1963; Deere et al., 1967). The progressive failure is generally considered in rock mechanics to start in the shear zone by a gradual loss of interlock of the rock blocks formed by several intersecting joint sets. Following this loss of interlock, certain blocks in the zone start breaking. The resulting loss of strength leads to stress redistribution and stress concentration to some other blocks in the failure zone. The process continues until a general rupture of the mass occurs.
In addition, because the majority of rock strength parameters entering into the Ladanyi-Archambault model are usually considered to be random variables, it follows that the peak strength of the mass determined from that theory for various potential failure surfaces, should also be a random variable.
The present paper proposes a non-deterministic version of the Ladanyi-Archambault simulation model, which enables to predict the probability-density function of the peak shear strength of the rock mass. Moreover, the proposed version simulates the progressivity of failure in the mass.
In elaborating this version of the Ladanyi-Archambault model (called "LADAR" model in the following), a numerical approach has been selected rather than an analytical one, in order to conserve the maximum of flexibility in defining the probability density functions of the variables to be substituted in the model, as well as in defining the variables themselves.
ORIGINAL VERSION OF THE LADANYIARCHAMBAULT MODEL
In its original version (Ladanyi and Archambault, 1969), the "LADAR" model takes into account the variables contributing to the peak strength of the rock mass in shear by defining four strength components. In the case of a rock mass with intersecting discontinuities without infilling, these components are associated with:
the work carried out against the normal stress resulting from dilatancy, S 1 (Mathematic equation)(Available in full paper)