毕业设计---外文翻译原作题目：Failure Properties of Fractured Rock Masses asAnisotropic Homogenized Media译作题目：均质各向异性裂隙岩体的破坏特性专业：土木工程姓名：吴雄指导教师：吴雄志河北工程大学土木工程学院2012年5月21日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 poorer 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 structures 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 joint 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; Warburton 1987; Goodman 1995). One should also quote the widely used distinct element method, originating from the works of Cundall and coauthors (Cundall and S track 1979; Cundall 1988), which makes use of an explicit finite-difference numerical scheme for computing the displacements of the blocks considered 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 blocks 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 Brown’s criterion (Hoek and Brown 1980; Hoek 1983). It stems from the intuitive 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 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 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 a computer code based on the distinct element method. It is shown that, while both methods lead to almost identical results for a densely fr actured 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 to capture such a scale effect, while still taking advantage of a homogenization technique. This isachieved 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 and couple stresses. The implementation of this model is finally 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) resting upon a fractured bedrock (Fig. 1), whose bearingcapacity 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 throughC and the the classical Mohr-Coulomb condition expressed by means of the cohesionm. Note that tensile stresses will be counted positive throughout the paper. friction anglemLikewise, the joints will be modeled as plane interfaces (represented by lines in the figure’s plane). Their strength properties are described by means of a condition involving the stress vector of components (σ, τ) 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 satisfies 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 its stability is ensured. Due to the strong heterogeneity of the jointed rock mass, insurmountable difficulties 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 the rock matrix, the implementation of a kinematic approach would require the use of failure mechanisms involving velocity jumpsacross the joints, since the latter would constitute preferential zones for the occurrence offailure. Indeed, such a direct approach which is applied in most classical design 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 of 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 Salenc ,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 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 O 21ξξwhose axes are placed along the joints directions, and introducing the following change of stress variables:such a macroscopic failure condition simply becomeswhere it will be assumed thatA 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 an angle a with respect to the joint direction. Denoting by n σ and n τthe 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 (n σ , n τ) deduced from conditions (3) expressed in terms of (11σ,22σ , 12σ). The corresponding domain has been drawn in Fig. 2 in theparticular case where m ϕα≤ .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 ‘‘truncated’’ by two orthogonal semilines as soon as condition m j H H is fulfilled.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 concepts 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 and 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 excavation shown in Fig. 3,where h and β denote the excavation height and the slope angle, respectively. Since nosurcharge is applied to the structure, the specific weight γ of the constituent material will obviously constitute the sole loading parameter of the system.Assessing the stability of this structure will 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 θ=joint orienta tion and K +=nondimensional factor governing the stability of the excavation. Upper-bound estimates 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 first 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 Ω with an angular velocity ω. The curve separating this volume from the rest of the structure which is kept motionless is a velocity jump line. Since it is an arc of the log spiral of angle m and focus Ω the v elocity discontinuity at any point of this line is inclined at angle wm with respect to the tangent at the same point.The work done by the external forces and the maximum resisting work developed in such a mechanism may be written as (see Chen and Liu 1990; Maghous et al. 1998)where e w and me w =dimensionless functions, and μ1 and μ2=angles specifying theposition of the center of rotation Ω.Since the kinematic approach of yield design states that a necessary condition for the structure to be stable writesit follows from Eqs. (5) and (6) that the best upper-bound estimate derived from this first class of mechanism is obtained by minimization with respect to μ1 and μ2which may be determined numerically.Piecewise Rigid-Block Failure Mechanism [Fig. 4(b)]The second class of failure mechanisms involves two translating blocks of homogenized material. It is defined by five angular parameters. In order to avoid any misinterpretation, it should be specified that the termino logy of block does not refer here to the lumps of rock matrix in the initial structure, but merely means that, in the framework of the yield design kinematic approach, a wedge of homogenized jointed rock mass is given a (virtual) rigid-body motion.The implementation of the upper-bound kinematic approach,making use of of this second class of failure mechanism, leads to the following results.where U represents the norm of the velocity of the lower block. Hence, the following upper-bound estimate for K+:Results and Comparison with Direct CalculationThe optimal bound has been computed numerically for the following set of parameters:The result obtained from the homogenization approach can then be compared with that derived from a direct calculation, using the UDEC computer software (Hart et al. 1988). Since the latter can handle situations where the position of each individual joint is specified, a series of calculations has been performed varying the number n of regularly spaced joints, inclined at th e same angleθ=10° with the horizontal, and intersecting the facing of the excavation, as sketched in Fig. 5. Thecorresponding estimates of the stability factor have been plotted against n in the same figure. It can be observed that these numerical estimates decrease with the number of intersecting joints down to the estimate produced by the homogenization approach. The observed discrepancy between homogenization and direct approaches, could be regarded as a ‘‘size’’ or ‘‘scale effect’’ which is not inclu ded in the classicalhomogenization model. A possible way to overcome such a limitation of the latter, while still taking advantage of the homogenization concept as a computational time-saving alternative for design purposes, could be to resort to a description of the fractured rock medium as a Cosserat or micropolar continuum, as advocated for instance by Biot (1967); Besdo(1985); Adhikary and Dyskin (1997); and Sulem and Mulhaus (1997) for stratified or block structures. The second part of this paper is devoted to applying such a model to describing the failure properties of jointed rock media.均质各向异性裂隙岩体的破坏特性概述由于岩体表面的裂隙或节理大小与倾向不同，人们通常把岩体看做是非连续的。