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1、1Failure Properties of Fractured Rock Masses as AnisotropicHomogenized MediaIntroductionIt is commonly acknowledged that rock masses always display discontinuous surfaces of various sizes and orientations, usually referred to as fractures or joints. Since the latter have much poorer mechanical chara
2、cteristics than the rock material, they play a decisive role in the overall behavior of rock structures,whose deformation as well as failure patterns are mainly governed by those of the joints. It follows that, from a geomechanical engineering standpoint, design methods of structures involving joint
3、ed rock masses, must absolutely account for such weakness surfaces in their analysis.The most straightforward way of dealing with this situation is to treat the jointed rock mass as an assemblage of pieces of intact rock material in mutual interaction through the separating joint interfaces. Many de
4、sign-oriented methods relating to this kind of approach have been developed in the past decades, among them,the well-known block theory, which attempts to identify poten-tially unstable lumps of rock from geometrical and kinematical considerations (Goodman and Shi 1985; Warburton 1987; Goodman 1995)
5、. One should also quote the widely used distinct element method, originating from the works of Cundall and coauthors (Cundall and Strack 1979; Cundall 1988), which makes use of an explicit nite-difference numerical scheme for computing the displacements of the blocks considered as rigid or deformabl
6、e bodies. In this context, attention is primarily focused on the formulation of realistic models for describing the joint behavior.2Since the previously mentioned direct approach is becoming highly complex, and then numerically untractable, as soon as a very large number of blocks is involved, it se
7、ems advisable to look for alternative methods such as those derived from the concept of homogenization. Actually, such a concept is already partially conveyed in an empirical fashion by the famous Hoek and Browns criterion (Hoek and Brown 1980; Hoek 1983). It stems from the intuitive idea that from
8、a macroscopic point of view, a rock mass intersected by a regular network of joint surfaces, may be perceived as a homogeneous continuum. Furthermore, owing to the existence of joint preferential orientations, one should expect such a homogenized material to exhibit anisotropic properties.The object
9、ive of the present paper is to derive a rigorous formulation for the failure criterion of a jointed rock mass as a homogenized medium, from the knowledge of the joints and rock material respective criteria. In the particular situation where twomutually orthogonal joint sets are considered, a closed-
10、form expression is obtained, giving clear evidence of the related strength anisotropy. A comparison is performed on an illustrative example between the results produced by the homogenization method,making use of the previously determined criterion, and those obtained by means of a computer code base
11、d on the distinct element method. It is shown that, while both methods lead to almost identical results for a densely fractured rock mass, a size or scale effect is observed in the case of a limited number of joints. The second part of the paper is then devoted to proposing a method which attempts t
12、o capture such a scale effect, while still taking advantage of a homogenization technique. This is achieved by resorting to a micropolar or Cosserat continuum description of the fractured rock mass, through the derivation of a generalized macroscopic failure condition expressed in terms of stresses
13、and 3couple stresses. The implementation of this model is nally illustrated on a simple example, showing how it may actually account for such a scale effect.Problem Statement and Principle of Homogenization ApproachThe problem under consideration is that of a foundation (bridge pier or abutment) res
14、ting upon a fractured bedrock (Fig. 1), whose bearing capacity needs to be evaluated from the knowledge of the strength capacities of the rock matrix and the joint interfaces. The failure condition of the former will be expressed through the classical Mohr-Coulomb condition expressed by means of the
15、 cohesion and the friction angle mC. Note that tensile stresses will be counted positive throughout the paper.mLikewise, the joints will be modeled as plane interfaces (represented by lines in the gures plane). Their strength properties are described by means of a condition involving the stress vect
16、or of components (, ) acting at any point of those interfacesAccording to the yield design (or limit analysis) reasoning, the above structure will remain safe under a given vertical load Q(force per unit length along the Oz axis), if one can exhibit throughout the rock mass a stress distribution which satises the equilibrium equations along with the stress boundary conditions,while complying with the strength requirement expressed at any point of the structur
