毕业设计---外文翻译
原作题目：Failure Properties of Fractured Rock Mass as
Anisotropic Homogenized Media
美国崛起译作题目：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 Mass as Anisotropic清愁
Homogenized Media
Introduction
It is commonly acknowledged that rock mass 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,who deformation as well as failure patterns are mainly governed by tho of the joints. It follows that, from a geomechanical engineering standpoint, design methods of structures involving jointed rock mass, must absolutely account for such ‘‘weakness’’ surfaces in their analysis.
爱国名人名言The most straightforward way of dealing with this situation is to treat the jointed rock mass as an asmblage of pieces of intact rock material in mutual interaction through the parating 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 ud distinct element method, originating from the works of Cundall and coauthors (Cundall and S track 1979; Cundall 198
8), which makes u 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 focud 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 ems advisable to look for alternative methods such as tho 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 intercted 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 prent 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 ts are considered, a clod-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 homogeniz
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ation method,making u of the previously determined criterion, and tho obtained by means of a computer code bad on the distinct element method. It is shown that, while both methods lead to almost identical results for a denly fr actured rock mass, a ‘‘size’’ or ‘‘scale effect’’ is obrved in the ca of a limited number of joints. The cond 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 is
achieved by resorting to a micropolar or Cosrat continuum description of the fractured rock mass, through the derivation of a generalized macroscopic failure condition expresd in terms of stress and couple stress. 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 Approach
The problem under consideration is that of a foundation (bridge pier or abutment) resting upon a fractured bedrock (Fig. 1), who bearing
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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 expresd through
C and the the classical Mohr-Coulomb condition expresd by means of the cohesion
m
. Note that tensile stress will be counted positive throughout the paper. friction angle
m
Likewi, the joints will be modeled as plane interfaces (reprented 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 tho interfaces
According 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 expresd 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 ari when trying to implement the above reasoning directly. As regards, for instance, the ca where the strength properties of the joints are considerably lower than tho of the rock matrix, the implementation of a kinematic approach would require the u of failure mechanisms involving velocity jumps
across the joints, since the latter would constitute preferential zones for the occurrence of
failure. Indeed, such a direct approach which is applied in most classical design methods, is becoming rapidly complex as the density of joints increas, 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 u of an alternative approach bad 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 Mass
The 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 reprentative 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 ts of joints under plane strain conditions. Referring to an orthonormal frame O 21ξξwho axes are placed along the joints directions, and introducing the following change of stress variables:水池荷叶
such a macroscopic failure condition simply becomes
where it will be assumed that
A convenient reprentation of the macroscopic criterion is to draw the strength envelope relating to an oriented facet of the homogenized material, who 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 t of admissible stress (n σ , n τ) deduced from conditions (3) expresd in terms of (11σ,22σ , 12σ). The corresponding domain has been drawn in Fig. 2 in the
particular ca where m ϕα≤ .
Two comments are worth being made:
1. The decrea in strength of a rock material due to the prence of joints is clearly illustrated by Fig.
2. The usual strength envelope corresponding to the rock matrix failure condition is ‘‘truncated’’ by two orthogonal milines as soon as condition m j H H is fulfilled.
2. The macroscopic anisotropy is also quite apparent, since for instance the strength envelope draw
n 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 bad 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 Excavation
The clod-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,
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where h and β denote the excavation height and the slope angle, respectively. Since no
