土木 地质岩土工程专业毕业英文翻译原文和译文.docx

1、土木 地质 岩土工程专业毕业英文翻译原文和译文Failure 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 p

2、oorer mechanical characteristics 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 stru

3、ctures involving jointed 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 joi

4、nt interfaces. Many design-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; Warburt

5、on 1987; Goodman 1995). 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

6、 as rigid or deformable bodies. In this context, attention is primarily focused on the formulation of realistic models for describing the joint behavior.Since the previously mentioned direct approach is becoming highly complex, and then numerically untractable, as soon as a very large number of bloc

7、ks is involved, it seems 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 intu

8、itive idea that from 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

9、properties.The objective 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

10、considered, a closed-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

11、 a computer code based 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 me

12、thod which attempts to 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

13、in terms of stresses and couple 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 p

14、ier or abutment) resting 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 expre

15、ssed by means of the cohesion and the friction angle . Note that tensile stresses will be counted positive throughout the paper.Likewise, 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 involvin

16、g the stress vector 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

17、 distribution which satises the equilibrium equations along with the stress boundary conditions,while complying with the strength requirement expressed at any point of the structure.This problem amounts to evaluating the ultimate load Q beyond which failure will occur, or equivalently within which i

18、ts stability is ensured. Due to the strong heterogeneity of the jointed rock mass, insurmountable difculties are likely to arise when trying to implement the above reasoning directly. As regards, for instance, the case where the strength properties of the joints are considerably lower than those of

19、the rock matrix, the implementation of a kinematic approach would require the use of failure mechanisms involving velocity jumps across the joints, since the latter would constitute preferential zones for the occurrence offailure. Indeed, such a direct approach which is applied in most classical des

20、ign methods, is becoming rapidly complex as the density of joints increases, that is as the typical joint spacing l is becoming small in comparison with a characteristic length of the structure such as the foundation width B.In such a situation, the use of an alternative approach based on the idea o

21、f homogenization and related concept of macroscopic equivalent continuum for the jointed rock mass, may be appropriate for dealing with such a problem. More details about this theory, applied in the context of reinforced soil and rock mechanics, will be found in (de Buhan et al. 1989; de Buhan and S

22、alenc ,on 1990; Bernaud et al. 1995).Macroscopic Failure Condition for Jointed Rock MassThe formulation of the macroscopic failure condition of a jointed rock mass may be obtained from the solution of an auxiliary yield design boundary-value problem attached to a unit representative cell of jointed

23、rock (Bekaert and Maghous 1996; Maghous et al.1998). It will now be explicitly formulated in the particular situation of two mutually orthogonal sets of joints under plane strain conditions. Referring to an orthonormal frame Owhose axes are placed along the joints directions, and introducing the fol

24、lowing change of stress variables:such a macroscopic failure condition simply becomeswhere it will be assumed that A convenient representation of the macroscopic criterion is to draw the strength envelope relating to an oriented facet of the homogenized material, whose unit normal n I is inclined by

25、 an angle a with respect to the joint direction. Denoting by and the normal and shear components of the stress vector acting upon such a facet, it is possible to determine for any value of a the set of admissible stresses ( , ) deduced from conditions (3) expressed in terms of (, , ). The correspond

26、ing domain has been drawn in Fig. 2 in the particular case where .Two comments are worth being made:1. The decrease in strength of a rock material due to the presence of joints is clearly illustrated by Fig. 2. The usual strength envelope corresponding to the rock matrix failure condition is truncat

27、ed by two orthogonal semilines as soon as condition is fullled.2. The macroscopic anisotropy is also quite apparent, since for instance the strength envelope drawn in Fig. 2 is dependent on the facet orientation a. The usual notion of intrinsic curve should therefore be discarded, but also the conce

28、pts of anisotropic cohesion and friction angle as tentatively introduced by Jaeger (1960), or Mc Lamore and Gray (1967).Nor can such an anisotropy be properly described by means of criteria based on an extension of the classical Mohr-Coulomb condition using the concept of anisotropy tensor(Boehler a

29、nd Sawczuk 1977; Nova 1980; Allirot and Bochler1981).Application to Stability of Jointed Rock ExcavationThe closed-form expression (3) obtained for the macroscopic failure condition, makes it then possible to perform the failure design of any structure built in such a material, such as the excavatio

30、n shown in Fig. 3, where h and denote the excavation height and the slope angle, respectively. Since no surcharge is applied to the structure, the specic weight of the constituent material will obviously constitute the sole loading parameter of the system.Assessing the stability of this structure wi

31、ll amount to evaluating the maximum possible height h+ beyond which failure will occur. A standard dimensional analysis of this problem shows that this critical height may be put in the formwhere =joint orientation and K+=nondimensional factor governing the stability of the excavation. Upper-bound e

32、stimates of this factor will now be determined by means of the yield design kinematic approach, using two kinds of failure mechanisms shown in Fig. 4.Rotational Failure Mechanism Fig. 4(a)The rst class of failure mechanisms considered in the analysis is a direct transposition of those usually employed for homogeneous and isotropic soil or rock slopes. In such a mechanism a volume of homogenized jointed rock mass is rotating about a point with an angular velocity . The curve separating this volume from the rest of the structure which is kept mot