巖土工程專業(yè)翻譯英文原文和譯文(共16頁)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上畢業(yè)設(shè)計(jì)-外文翻譯原作題目：Failure Properties of Fractured Rock Masses as Anisotropic Homogenized Media譯作題目：均質(zhì)各向異性裂隙巖體的破壞特性 專 業(yè)：土木工程姓 名：吳 雄指導(dǎo)教師：吳 雄 志河北工程大學(xué)土木工程學(xué)院2012年5月21日Failure Properties of Fractured Rock Masses as AnisotropicHomogenized MediaIntroductionIt is commonly acknowledged that rock mass

2、es 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

3、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

4、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 t

5、heory, 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

6、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 deformable bodies. In this context, attention is primarily focused on the formulation of realistic models for describing the joint behavior

7、.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

8、 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 a macroscopic point of view, a rock mass intersected by a regular network of joint surfaces, may be perceived as a homogeneous cont

9、inuum. 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 medi

10、um, 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

11、 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 fractured roc

12、k 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 is achieved by resorting to a micro

13、polar 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 nally illustrated on a simple example, showing how it may actually account

14、 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 bearing capacity needs to be evaluated from the knowledge of the strength capacities o

15、f 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 cohesion and the friction angle . Note that tensile stresses will be counted positive throughout the paper.Likewise, the joints wil

16、l 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 vector of components (, ) acting at any point of those interfacesAccording to the yield design (or limit analysis) reasoning, the above str

17、ucture 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

18、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 difculties are likely to arise when trying to implemen

19、t 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 jumps across the joints, sinc

20、e 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

21、 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.

22、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 jointe

23、d 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

24、 joints under plane strain conditions. Referring to an orthonormal frame Owhose 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 that A convenient representation of the ma

25、croscopic 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 and the normal and shear components of the stress vector acting upon such a facet, it is po

26、ssible to determine for any value of a the set of admissible stresses ( , ) deduced from conditions (3) expressed in terms of (, , ). The corresponding 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 t

27、o 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 is fullled.2. The macroscopic anisotropy is also quite apparent, since for instance the strength env

28、elope 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 pr

29、operly 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

30、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 denote the excavation height and the slope angle, respectively. Since no surcharge is applied to the structure, the speci

31、c weight 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

32、critical height may be put in the formwhere =joint orientation 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.Ro

33、tational 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 an

34、gular velocity . 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 and focus the velocity discontinuity at any point of this line is inclined at angle wm with respect to the tangent at the s

35、ame 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 and =dimensionless functions, and 1 and 2=angles specifying the position of the center of rotation .Since the kinematic appr

36、oach 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 rst class of mechanism is obtained by minimization with respect to 1 and 2which may be determined numerically.Piecewise Ri

37、gid-Block Failure Mechanism Fig. 4(b)The second class of failure mechanisms involves two translating blocks of homogenized material. It is dened by ve angular parameters. In order to avoid any misinterpretation, it should be specied that the terminology of block does not refer here to the lumps of r

38、ock 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

39、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 obta

40、ined 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 specied, a series of calculations has been performed vary

41、ing the number n of regularly spaced joints, inclined at the same angle=10° with the horizontal, and intersecting the facing of the excavation, as sketched in Fig. 5. The corresponding estimates of the stability factor have been plotted against n in the same gure. It can be observed that these

42、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 included in the classicalhomogenization mo

43、del. 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 advoc

44、ated for instance by Biot (1967); Besdo(1985); Adhikary and Dyskin (1997); and Sulem and Mulhaus (1997) for stratied 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.均質(zhì)各向異性裂隙巖體的破壞特性概述 由于巖體表面的裂隙或節(jié)理大小與傾向不同

45、，人們通常把巖體看做是非連續(xù)的。盡管裂隙或節(jié)理表現(xiàn)出的力學(xué)性質(zhì)要遠(yuǎn)遠(yuǎn)低于巖體本身，但是它們在巖體結(jié)構(gòu)性質(zhì)方面起著重要的作用，巖體本身的變形和破壞模式也主要是由這些節(jié)理所決定的。從地質(zhì)力學(xué)工程角度而言，在涉及到節(jié)理巖體結(jié)構(gòu)的設(shè)計(jì)方法中，軟弱表面是一個(gè)很重要的考慮因素。 解決這種問題最簡單的方法就是把巖體看作是許多完整巖塊的集合，這些巖塊之間有很多相交的節(jié)理面。這種方法在過去的幾十年中被設(shè)計(jì)者們廣泛采用，其中比較著名的是“塊體理論”，該理論試圖從幾何學(xué)和運(yùn)動學(xué)的角度用來判別潛在的不穩(wěn)定巖塊（Goodman & 石根華 1985；Warburton 1987；Goodman 1995）；另外

46、一種廣泛使用的方法是特殊單元法，它是由Cundall及其合作者（Cundall & Strack 1979； Cundall 1988）提出來的，其目的是用來求解顯式有限差分?jǐn)?shù)值問題，計(jì)算剛性塊體或柔性塊體的位移。本文的重點(diǎn)是闡述如何利用公式來描述實(shí)際的節(jié)理模型。既然直接求解的方法很復(fù)雜，數(shù)值分析方法也很難駕馭，同時(shí)由于涉及到了數(shù)目如此之多的塊體，所以尋求利用均質(zhì)化的方法是一個(gè)明智的選擇。事實(shí)上，這個(gè)概念早在Hoek-Brown準(zhǔn)則（Hoek & Brown 1980；Hoek 1983）得出的一個(gè)經(jīng)驗(yàn)公式中就有所涉及，它來自于宏觀上的一個(gè)直覺，被一個(gè)規(guī)則的表面節(jié)理網(wǎng)絡(luò)所分割的

47、巖體，可以看做是一個(gè)均質(zhì)的連續(xù)體，由于節(jié)理傾向的不同，這樣的一個(gè)均質(zhì)材料顯示出了各向異性的性質(zhì)。本文的目的就是：從節(jié)理和巖體各自準(zhǔn)則出發(fā)，推求出一個(gè)嚴(yán)格準(zhǔn)確的公式，來描述作為均勻介質(zhì)的節(jié)理巖體的破壞準(zhǔn)則。先考查特殊情況，從兩組相互正交的節(jié)理著手，得到一個(gè)封閉的表達(dá)式，清楚的證明了強(qiáng)度的各向異性。我們進(jìn)行了一項(xiàng)試驗(yàn)：把利用均質(zhì)化方法得到的結(jié)果和以前普遍使用的準(zhǔn)則得到的結(jié)果以及基于計(jì)算機(jī)編程的特殊單元法（DEM）得到的結(jié)果進(jìn)行了對比，結(jié)果表明：對于密集裂隙的巖體，結(jié)果基本一致；對于節(jié)理數(shù)目較少的巖體，存在一個(gè)尺寸效應(yīng)（或者稱為比例效應(yīng)）。本文的第二部分就是在保證均質(zhì)化方法優(yōu)點(diǎn)的前提下，致力于提出一

48、個(gè)新的方法來解決這種尺寸效應(yīng)，基于應(yīng)力和應(yīng)力耦合的宏觀破壞條件，提出利用微極模型或者Cosserat連續(xù)模型來描述節(jié)理巖體；最后將會用一個(gè)簡單的例子來演示如何應(yīng)用這個(gè)模型來解決比例效應(yīng)的問題。問題的陳述和均質(zhì)化方法的原理 考慮這樣一個(gè)問題：一個(gè)基礎(chǔ)（橋墩或者其鄰接處）建立在一個(gè)有裂隙的巖床上（Fig.1），巖床的承載能力通過巖基和節(jié)理交界面的強(qiáng)度 估算出來。巖基的破壞條件使用傳統(tǒng)的莫爾-庫倫條件，可以用粘聚力C 1和內(nèi)摩擦角 m 來表示（本文中張應(yīng)力采用正值計(jì)算）。同樣，用接觸平面代替節(jié)理（圖示平面中用直線表示）。強(qiáng)度特性采用接觸面上任意點(diǎn)的應(yīng)力向量 (,)表示： 根據(jù)屈服設(shè)計(jì)（或極限分析）推

49、斷，如果沿著應(yīng)力邊界條件，巖體應(yīng)力分布滿足平衡方程和結(jié)構(gòu)任意點(diǎn)的強(qiáng)度要求，那么在一個(gè)給定的豎向荷載Q（沿著OZ 軸方向）作用下，上部結(jié)構(gòu)仍然安全。 這個(gè)問題可以歸結(jié)為求解破壞發(fā)生處的極限承載力Q+ ，或者是多大外力作用下結(jié)構(gòu)能確保穩(wěn)定。由于節(jié)理巖體強(qiáng)度的各向異性，若試圖使用上述直接推求的方法，難度就會增大很多。比如，由于節(jié)理強(qiáng)度特性遠(yuǎn)遠(yuǎn)低于巖基，從運(yùn)動學(xué)角度出發(fā)的方法要求考慮到破壞機(jī)理，這就牽涉到了節(jié)理上的速度突躍，而節(jié)理處將會是首先發(fā)生破壞的區(qū)域。 這種應(yīng)用在大多數(shù)傳統(tǒng)設(shè)計(jì)中的直接方法，隨著節(jié)理密度的增加越來越復(fù)雜。確切地說，這是因?yàn)橄啾容^結(jié)構(gòu)的長度（如基礎(chǔ)寬B）而言，典型節(jié)理間距L變得更小

50、，加大了問題的難度。在這種情況下，對節(jié)理巖體使用均質(zhì)化方法和宏觀等效連續(xù)的相關(guān)概念來處理可能就會比較妥當(dāng)。關(guān)于這個(gè)理論的更多細(xì)節(jié)，在有關(guān)于加固巖土力學(xué)的文章中可以查到（de Buhan等 1989；de Buhan & Salenc 1990；Bernaud等 1995）。節(jié)理巖體的宏觀破壞條件 節(jié)理巖體的宏觀破壞條件公式可以從對節(jié)理巖體典型晶胞單元的輔助屈服設(shè)計(jì)邊值問題中得到（Bekaert & Maghous 1996; Maghous等 1998）?，F(xiàn)在可以精確地表示平面應(yīng)變條件下，兩組相互正交節(jié)理的特殊情況，建立沿節(jié)理方向的正交坐標(biāo)系O ，并引入下列應(yīng)力變量： 宏觀破壞條件可簡化為： 其中，假定宏觀準(zhǔn)則的一種簡便表示方法是畫出均質(zhì)材料傾向面上的強(qiáng)度包絡(luò)線，其單位法線n的傾角 為節(jié)理的方向，分別用n 和n 表示這個(gè)面上的正應(yīng)力和切應(yīng)力，用(, , ) 表示條件（3），推求出一組許可