岩土工程专业翻译英文原文和译文

河北工程大学毕业设计 论文 1 毕业设计毕业设计 外文翻译外文翻译 原作题目原作题目 Failure Properties of Fractured Rock Masses as Anisotropic Homogenized Media 译作题目 译作题目 均质各向异性裂隙岩体的破坏特性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 河北工程大学毕业设计 论文 2 Failure Properties of Fractured Rock Masses as Anisotropic Homogenized Media Introduction It 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 Strack 1979 Cundall 1988 which makes use of an explicit fi 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 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 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 to capture such a scale effect while still taking advantage of a homogenization technique This 河北工程大学毕业设计 论文 3 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 and couple stresses The implementation of this model is fi nally 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 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 cohesion and the m C friction angle Note that tensile stresses will be counted positive throughout the paper m Likewise the joints will be modeled as plane interfaces represented by lines in the fi gure s plane Their strength properties are described by means of a condition involving the stress vector of components acting at any point of those 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 satisfi es 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 diffi culties 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 河北工程大学毕业设计 论文 4 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 of failure 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 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 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 Owhose axes are 21 placed along the joints directions and introducing the following change of stress variables such a macroscopic failure condition simply becomes where 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 an angle a with respect to the joint direction Denoting by and the normal and shear n n 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 n n terms of The corresponding domain has been drawn in Fig 2 in the particular 11 22 12 case where m 河北工程大学毕业设计 论文 5 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 is mj HH fulfi lled 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 Excavation The 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 denote the excavation height and the slope angle respectively Since no 河北工程大学毕业设计 论文 6 surcharge is applied to the structure the specifi 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 critical height may be put in the form where 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 Rotational Failure Mechanism Fig 4 a The fi 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 motionless is a velocity jump line Since it is an arc of the log spiral of angle and m focus the velocity 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 and dimensionless functions and 1 and 2 angles specifying the e w me w 河北工程大学毕业设计 论文 7 position of the center of rotation Since the kinematic approach of yield design states that a necessary condition for the structure to be stable writes it follows from Eqs 5 and 6 that the best upper bound estimate derived from this fi rst class of mechanism is obtained by minimization with respect to 1 and 2 which 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 defi ned by fi ve angular parameters In order to avoid any misinterpretation it should be specifi ed that the terminology 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 Calculation The 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 specifi ed a series of calculations has been performed varying 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 河北工程大学毕业设计 论文 8 corresponding estimates of the stability factor have been plotted against n in the same fi gure 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 included in the classical homogenization 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 stratifi ed 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 河北工程大学毕业设计 论文 9 均质各向异性裂隙岩体的破坏特性均质各向异性裂隙岩体的破坏特性 概述概述 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 尽管裂隙或节理表现出的力学性质要远远低于岩体本身 但是它们在岩体结构性质方 面起着重要的作用 岩体本身的变形和破坏模式也主要是由这些节理所决定的 从地 质力学工程角度而言 在涉及到节理岩体结构的设计方法中 软弱表面是一个很重要 的考虑因素 解决这种问题最简单的方法就是把岩体看作是许多完整岩块的集合 这些岩块之 间有很多相交的节理面 这种方法在过去的几十年中被设计者们广泛采用 其中比较 著名的是 块体理论 该理论试图从几何学和运动学的角度用来判别潜在的不稳定岩 块 Goodman Maghous 等 1998 现在可以精确地表示平 面应变条件下 两组相互正交节理的特殊情况 建立沿节理方向的正交坐标系 O 21 并引入下列应力变量 宏 观破坏条件可简化为 其 中 假定 宏观准则的一种简便表示方法是画出均质材料倾向面上的强度包络线 其单位法 线 n 的倾角 为节理的方向 分别用 n 和 n 表示这个面上的正应力和切应力 用 表示条件 3 推求出一组许可应力 n n 然后求解出倾角 当 11 22 12 m 时 相应的区域表示如图 2 所示 并对此做出两个注解如下 1 从图 2 中可以清楚的看出 节理的存在导致了岩体强度的降低 通常当 时 强度包络线和岩基破坏条件相一致 其前半部分被两个正交的半条线切 mj HH 去 2 宏观各向异性很显著 比如 图 2 中的强度包络线决定于方位角 应该抛 河北工程大学毕业设计 论文 12 弃固有曲线和各向异性粘聚力与摩擦角的概念 其中后一个概念是由 Jaeg