09 Rock_Mass[1]
Strength of Rock and Rock Mass
Strength of Rock and Rock MassDesigning with rocks and rock masses bears many similarities to techniques that have been developed for soils. There is however a number of major differences:(1)The scale effect is overwhelming in rocks. Rock strength varies widely with sample size. Atone end, we have the intact rock (homogenous, isotropic, solid, continuous with no obvious structural defects) which really exists only at the hand-specimen scale. At the other end is the rock mass that is heterogeneous and anisotropic carrying all the defects that is characteristic of the rock mass at the field scale. In the design of engineering structures in rock, the size of interest is determined by the size of the rock mass that carries the stresses that are imposed on it.(2)Rock has tensile strength. It may have substantial tensile strength at the intact rock scale, butmuch smaller at the scale of the rock mass. Even then only in exceptional circumstances can the rock mass be considered as a “tensionless” material. Intact ro ck fails in tension along planes that are perpendicular to maximum tension (or minimum compression) and not along shear planes as suggested by the Coulomb theory).(3)The effect of water on the rock mass is more complex.(a)Pore space in most intact rocks is very small and so is the permeability. The watercontained in the pore space is not necessarily free water. The truly free water existsonly in the rock mass, in fractures, where water may flow at high rates.(b)In contrast to soils, water is more compressible (by about one order of magnitude)than intact rock. The difference would be smaller when compared with thecompressibility of the rock mass (especially close to the free surface where loose rockcommonly found).Note that in the derivation of the effectivesmall. This is not so for rocksincreasing the grain-to grain contactsignificant degree. The assumption ofwater controls the way anstress (total stress) is distributedconditions, the effective stressconcept passes the whole externalin rock, because water is more include its effect separately as a “water force” rather than mix its effect with the rock response (as in the effective stress theory).(4)In compression, intact rock does not fail according to the Coulomb theory. It is true, that itsstrength increases with confining pressure, but at failure there is no evidence for theappearance of a shear fracture as predicted by the Coulomb theory. Furthermore the “envelope “ is usually nonlinear following a y 2=x type of parabolic law. Interestingly, shear fractures do form, but not at peak stress; they form as part of the collapse mechanism, usually quite late in the post-failure history.Strength of Intact RockIntact rock has both tensile and compressive strength, but the compressive to tensile strength ratio is quite high, about 20. In uniaxial tension, failure follows the maximum principal stress theory:σ3=T owhich would suggest that the other two principal stresses have no influence. At failure a fractureplane forms that is oriented perpendicular to the σ3(Figure 28) Note that the Coulomb theory would predict shear failure in uniaxial tension at 45-φ/2with σ3. There was a suggestion to combine theCoulomb theory with the maximum stress theory (the tension cutoff) which would predict the properorientation of the failure plane for both tension andcompression. Others would rather replace both witha y 2=x type of parabola (Figure 29). As discussedearlier, the shear fracture does not appear at point of failure, so that this aspect of the Coulomb theory is meaningless. In fact, there is little point in using theMohr’s diagram. In rock mechanics, failure conditions are more meaningfully presented in theσ3-σ1 space using a nonlinear function for strength. Although there are many variations of this function, the most popular one is due to Hoek and Brown (1980) which has the general form of σσσσσ1332f c c m s =++This is shown in Figure 30. H ere σc is the uniaxial compressive strength of the intact rock, m is aconstant (characteristic of the rock type) and s is arock mass parameter. s =1 for intact rock. Typicalvalues of the m parameter can be found in the first row of Table 1. The s parameter is significant only in extending the strength function to the strength ofthe rock mass. The same diagram is often used to define the safety factor for an existing state of stress (σ3,σ1):τσSafety Factor f =σσ11where both σ1 and σ1f are measured at the value of σ3Strength of the Rock MassThe strength of the rock mass is only a fraction of the strength of the intact strength. The reason for this is that failure in the rock mass is a combination of both intact rock strength and separation or sliding along discontinuities. The latter process usually dominate. Sliding ondiscontinuities occurs against the cohesional and/or frictional resistance along the discontinuity. The cohesional component is only a very small fraction of the cohesion of the intact rock.Table 1. Finding the parameters m and s from classification parameters.In designing with the rock mass, two different procedures are used. When a rock block is well defi ned, its stability is best evaluated through a standard “rigid -body” analysis technique. All the forces on the block are vector-summed and the resultant is resolved into tangential and normal components with respect to the sliding plane. The safety factor becomes the ratio of the available resistance to sliding to the tangential (driving) force. This is the technique used in slope stabilityanalysis. The second technique is stress rather than force-based. Here the stresses are evaluated (usually modeled through numerical procedures) and compared with available strength. The latter is expressed in terms of the Hoek and Brown rock mass strength function. This is where the s parameter becomes useful. s=1 for intact rock and s<1 for the rock mass. Essentially, what we are doing is simply to discount the intact rock strength. The difficult question is what value to assign to s? There is no test that will define this value. In theory, its is possible to do field tests of the rock mass, but it is expensive and not necessarily very reliable. Hoek and Brown however have compiled a list of s values depending on the rock type and the rock classification ratings.A simplified version of this is presented in Table 1. To make use of this Table, one needs only the rock type and one of the ratings from either the CSIR or the NGI classification. Ratings that are not listed will have to be interpolated. User’s of this Table are however warned that this approach is given here as a guide and its reliability is open to question. Nevertheless, the given s values are so small that they would tend to under rather than overestimate thestrength of the rock mass. Problems however could arise when failure occurs along a single weak discontinuity (slope stability), in which case the stress-based approach is obviously invalid.We are going to show how design engineering structures in rocks through two examples. One will use the rock mass design using the Hoek and Brown approximation for strength and the other the technique of applying the block theory to designing rock slopes.In earlier discussions, we have worked an examplewith rock mass classification. Now let us assumethat we are going to build a twin-tunnel roadsystem at some depth in the worked rock mass.The plan is two make two inverted-U shapedtunnels, each tunnel to be 3 m high and 4 m wide.The tunnels are to be separated by a pillar (rockleft in place), preferably no more than 4 m wide.The safety factor for the pillar should be 1.5 orbetter. The depth of siting for the roadway has notbeen established yet, but it could range anywherebetween 100 and 300 m, the deeper the better.Your job is to find the appropriate depth withinthis range. This is an example for pillar design.The loading condition is determined by assuming that the weight of the overlying rock mass, as shown in Figure 31, is distributed evenly across the width of the pillar at AA (this is not quite true, the stresses are usually higher at the tunnel perimeter than at the center, but the high safety factor should take care of this). You follow this procedure now:(1)Find the rock mass strength using your classification and the strength table give above.(2)Find the volume and the weight of the overlying rock using 100 m for depth (check if youhave a unit weight for the rock in the report).(3)Distribute the total weigh over the cross sectional area AA. This is the average vertical stresson the cross section(4)Formulate the safety factor asSfStrength Vertical Sress(5) Check the safety factor at 300 m(6) See if you can get an algebraic expression for the safety factor using h as a variable.(7) What is the story you are going to tell the boss?In the second example, we are going to examine the stability of a block of rock found on a slope. Although this is going to be a simple problem, it will still illustrate the procedure involved in analyzing rock slope stability. Pay particular attention how the effect of ground water is incorporated into the stability analysis. We use block analysis when we expect the block to slide on a single or a combination of discontinuities and we have pretty good control over the geometry. This means that we have good knowledge of the size and through this the weight of the block and the geometry of the slope. In the simple two-dimensional case, which we are to discuss, the geometry is simply the slope angle. The biggest problem is how to get a decent estimate of the resistance to slide. In this regard, conditions are similar to rock mass analysis, where we had to come up with an estimate of the rock mass strength. Again, we will have to use a lot of judgement. There are two ways to proceed. One is to accept the definition of shear resistance as in the Coulomb theory. This means that the discontinuity shear strength is made up of two components, a cohesion and a frictional resistance. The cohesion supposed to represent the strength of "solid rock bridges" that may exist at the base and will have to be sheared off to let the block move. This is the hardest part to estimate, because it may vary between zero and the strength of the solid rock (no bread at the base). Usually, it is a very small fraction of the solid strength. The frictional part is simply the normal force times the tangent of the friction angle. We use forces rather than stresses here and the resistance force according to the Coulomb specification becomes:Discontinuity shear strength Cohesive force N =+tan φThe Coulomb type of specification is useful only in the "back analysis" of slope failures. In theconsulting business, a common chore is toredesign slopes that have either failed orshowed signs of instability (tension crack at the back of the slope). In cases like this, thea good estimate of the frictionand find the value of theshear strength. Having this,force is practically impossible. discontinuity strengthby the same author who wasinvolved in constructing the NGIw a t e r w a t e r t h r u s tclassification (reference). The Coulomb theory proposes a linear law for discontinuity strength, the Barton specification advances a non-linear law:τσσφ=⎛⎝⎫⎭⎪+⎛⎝⎫⎭⎪nnbJRCJCStan log10Here stress rather than force units are used. σn and τ would refer to the average normal stress and the unit shear strength respectively. For comparison with the Coulomb specification, τ and σn are obtained by dividing the shear resistance force and the normal force by the area of contact. The Barton strength uses three material parameters: JRC (joint roughness coefficient), JCS (joint compressive strength) and φb (basic friction angle). JRC varies between 0 (very smooth, planar joint) and 20 (rough undulating surface). JCS is a fraction of the compressive strength of the rock. The compressive strength should be discounted depending on the condition of the rock walls on the two sides of the joint. Usually the surface is weathered and altered and may carry soft filling. In the latter case, the strength would be very small indeed. The basic friction angle is what we would normally call the friction angle determined on a flat surface rubbing against another flat surface of the same rock.Besides needing three parameters as opposed to Coulomb's two, the nonlinear strength is different from the Coulomb law that it has no strength at zero normal stress. Essentially, the Barton specification is defined in terms of a friction angle that is adjusted for joint roughness and the strength of rock.Being armed with some knowledge of discontinuity strength, we can now attempt to find the safety factor for the problem shown in Figure 32. We are looking at the stability of the dark-shaded mass of rock. There is the possibility of sliding down along joint plane sloping at angle α. First, we should establish the forces that act on this block of rock. Weight is an obvious one. The water forces are based on the assumption that water flows along the slide plane and perhaps along other joints or as in this case in a tension crack as well. If there was no tension crack, we would have an uplift force alone arising from the fact that water would normally flow in at the high-elevation end and flow out at the low elevation. The head of water at the intake and discharge points is zero. It would normally maximize between. Here we assume a triangular distribution, assuming that the maximum head occurs at midpoint and its value is one half of the elevation difference between intake and the discharge points. The uplift force itself is equal to the area of the pressure distribution diagram (light-shaded area) and acts perpendicular to the slide surface. With a tension crack, there could be a slope-parallel water thrust due to water accumulating in the tension crack. Its value would be calculated from the upper (small) light-shaded triangle. For this the maximum head would occur at the base, with the maximum head being equal to the elevation difference between the top and the bottom of the tension crack.With the loads now defined, we can go and get an estimate to the shear resistance that could develop along the sliding surface. Let us use the Coulomb specification. Furthermore, let us put in an extra little story here. Imagine that you are a consulting engineer who was called to this site, because the people below that rock block claim that the block almost came down on them during the last big rainfall. This story would justify the assumption that the safety factor is close to unity. So do this:(1)Assume that the elevation difference between the intake and discharge points is 20 m and theslope angle is 30︒. Find the weight of the block of rock (hint: turn it into a triangle to ease thepain of calculation) using a width of 1 m in the third direction. Assume 25 kN/m3 for the unit weight.(2)Compute the uplift force and the water thrust(3)Resolve all the forces into components, normal and parallel with the slide plane(4)Sum the parallel (tangential) forces to get the Driving Force(5)Sum the normal forces and get the total frictional resistance by multiplying it with tan φ (use30︒)(6)Define the cohesive force as unit cohesion times the total area of contact; the unit cohesionwill stay as a variable now(7)Add the cohesive force to the total frictional force(8)Formulate the safety factor, equate it with 1 and compute the friction angle.After this operation, you have all the strength parameters defined and are ready to redesign the slope. In practice, you would get rid of the water by drilling drainage holes to intersect and drain the slide plane. Assuming that the drainage works, do the last thing:(9) Find now the safety factor for the slope with the water effect gone! If it is greater than about 1.25, tell the people that the slope is safe as long as they have the drainage holes clean. Otherwise you would have to install and anchor system to increase the safety factor (changing the weight of the block by shaving it would result in a minor improvement only, you can try this analysis too.)。
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岩体质量分级在金属矿山深部巷道支护方案设计中的应用
文章编号 ：１００２－５０６５（２０２３）１２－００５７－３
Application of rock mass classification in deep roadway support scheme design of metal mine
SUN Xian-teng
（Ｓｈａｎｄｏｎｇ Ｇｏｌｄ Ｇｒｏｕｐ Ｃｏ．， ＬＴＤ．， Ｊｉ’ｎａｎ ２５０１００， Ｃｈｉｎａ）
3 岩体质量（Q）分类法 巴顿岩体质量（Q）分类法综合考虑岩体的完整性、结
构面的形态、填充物的特征以及地下水等其他因素对岩体质 量的影响，考虑因素全面，软、硬岩石均适用 。 [1-2]
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2023年 6月下 世界有色金属 57
M 采矿工程 ining engineering
树脂锚杆长度经验公式如下 ： L=N(1.3+B/10) 式 中 ：L—— 锚 杆 长 度，m ；N—— 岩 层 稳 定 性 系 数 ； B——巷道跨度，m。 该巷道跨度 B 为 4.0m ；围岩稳定性较差，稳定性系数 取 1.1，求得 L 的取值为 1.87m。按照锚杆长度适当取大原 则，树脂锚杆长度确定为 2.0m。 4.2 锚杆直径、锚杆间排距 查阅《锚杆基本支护形式与支护参数》、《锚杆支护方案 与参数详表》，围岩质量等级为Ⅲ类时，锚杆直径的取值为 18~22mm，锚杆间排距为 0.6~1m。根据工程实践经验，选 取锚杆直径为 20mm，锚杆间排距为 0.8×0.8m。 4.3 喷射混凝土参数 该 巷 道 围 岩 质 量 等 级 为 Ⅲ 类，喷 射 混 凝 土 主 要 作 为 辅 助 支 护，使 围 岩、金 属 支 护 材 料 与 空 气、水 汽 隔 绝，防 止 岩 体、金 属 支 护 材 料 被 腐 蚀 氧 化，喷 射 混 凝 土 厚 度 确 定 为 50mm。 综 上 所 述，该 巷 道 围 岩 支 护 采 用 Φ20×2000mm 的 树脂锚杆，其间排距为 0.8×0.8m。锚杆安装完毕后，从巷 道最高处往巷道两帮挂装金属网，沿巷道走向的方向安装
On the negative effective mass density in acoustic metamaterials
On the negative effective mass density in acoustic metamaterials
H.H. Huang a, C.T. Sun a,*,G.L. Huang b
a School of Aeronautics and Astronautics, Purdue University, W. Lafayette, IN 47907, USA b Department of Systems Engineering, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA
* Corresponding author. Tel.: +1 765 494 5130; fax: +1 765 494 0307. E-mail address: sun@ (C.T. Sun).
2017年十大动感人心歌曲_世界十大摇滚歌曲
2017年十大动感人心歌曲_世界十大摇滚歌曲想知道有哪些是十大动感人心歌曲吗?唱到您感动流泪的歌曲。
以下是小编为您收集整理提供到的范文，欢迎阅读参考，希望对你有所帮助!2017年十大动感人心歌曲_世界十大摇滚歌曲十大动感人心歌曲1、the dawn《the dawn》这是一首网上广为流传的关于魔兽争霸3的亡灵族的MV，其中动画部分由WarCraft3里面的过场CG剪辑而成，背景音乐为芬兰Dreamtale乐队的曲子The Dawn，改编自美国大片《The Rock勇闯夺命岛》中的经典插曲，所以听起来有相似之处。
2、Hero's Theme《Heros Theme》这首乐曲出自次世代新主机XBOX360上面的一款作品：《Kameo卡美奥》，是由著名的英国RARE工作室开发的。
其配乐是由捷克的一个很出名的乐团做的。
3、the mass《the mass》主打曲目The Mass[弥撒曲]是十七世纪欧洲教会音乐，起源于德国，节奏强劲紧凑，用声音营造出了一种人所不能触及的壮大与压力，中间不失去优美圣洁的曲调搭配，但是后来似乎被纳粹选作精神洗礼的一种工具，不过从音乐角度来说，这样旋律实在不应该被战争的结果左右。
之后像Michael Jackson等众多艺术家把它改编成为气势磅礴的进行曲、开场乐。
4、She is my sin《she is my sin》对Cser们来说，《NightWish夜愿》的歌曲早已深入人心，众所皆知，世界不少顶级战队的宣传片都采用的是他们的歌曲，NightWish的歌曲大都是金属音乐，而这首She is My Sin 就是1.6版CS的主题曲，很多翻译版本的1.6进入界面就会响起这首歌，当你在游戏前更改各种按键设置的时候，这首歌仿佛预示着大战马上爆发。
在she is my sin出名后，因为其震撼的歌声，成为许多视频或集锦的音乐。
5、Rock House Jail《rock house jail》电影《勇闯夺命岛》中的音乐，承担本片配乐的是好莱坞三大配乐大师之一—汉斯季莫，本片的配乐非常优美，以至于在全球各媒体都借用，仅CCTV就在1、2、5、10等频道都出现过。
工程岩体分级标准GB502182 术语、符号
2术语、符号2.1 术语2.1.1 岩石工程rock engineeting以岩体为工程建筑物地基或环境，并对岩体进行开挖或加固的工程，包括地下工程和地面工程。
2.1.2 工程岩体engineering rock mass岩石工程影响范围内的岩体，包括地下工程岩体、工业与民用建筑地基、大坝基岩、边坡岩体等。
2.1.3 岩体基本质量rock mass basic quality岩体所固有的、影响工程岩体稳定性的最基本属性，岩体基本质量由岩石坚硬程度和岩体完整程度所决定。
2.1.4 结构面sructural plane(discontinuity)岩体内开裂的和易开裂的面，如层面、节理、断层、片理等，又称不连续面。
2.1.5 岩体完整性指数(Kv)(岩体速度指数)intactess index of rock mass(velocity index of rock mass)岩体弹性纵波速度与岩石弹性纵波速度之比的平方。
2.1.6 岩体体积节理数(Jv)volumetric joint count of rock mass单体岩体体积内的节理(结构面)数目。
2.1.7 点荷载强度指数(Is(50))pointloadstrengthindex直径50mm圆柱形试件径向加压时的点荷载强度。
2.1.8 地下工程岩体自稳能力(stand－up time of rock mass for underground excavation)在不支护条件下，地下工程岩体不产生任何形式破坏的能力。
2.1.9 初始应力场initial stress field在自然条件下，由于受自重和构造运动作用，在岩体中形成的应力场，也称天然应力场。
2.2 符号。
0625_w02_qp_3
FOR EXAMINER’S USE
1 2 3 4 5 6 7 8 9 10 TOTAL
This question paper consists of 14 printed pages and 2 blank pages.
SP (NF/KS) S23400/3 © CIE 2002
[Turn over
density of rock = .............................. [2]
0625/3/O/N/02
5 3 A thermocouple is used to measure the temperature of the inner wall of a pottery kiln. (a) In the space below, draw a labelled diagram of a thermocouple that could be used for this purpose. [2]
Centre Number Candidate Name
w w w
Candidate Number
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m
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International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS
(b) Describe how the volume of the rock could be found. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) The mass of the rock is 88 g and its volume is 24 cm3. Calculate the density of the rock.
Practical estimates of rock mass strength
The criterion is purely empirical and hence there are no ‘correct’ ways to interpret the various relationships which can be derived. Under the circumstances, it is not surprising that there have been a few less than useful mutations and that some users have been confused by the alternative interpretations which have been published.
shear stresses. However, these relationships are
cumbersome and the original approach used by Hoek
and Brown [1] is more practical. In this approach,
equation (1) is used to generate a series of triaxial test
Dr Evert Hoek Evert Hoek Consulting Engineer Inc. 3034 Edgemont Boulevard P.O. Box 75516 North Vancouver, B.C. Canada V7R 4X1 Email: ehoek@
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Page ii
MassLynx NT Users Guide
Contents
MassLynx NT User’s Guide............................................................................
Rock mass classification
Rock mass classification3.1 IntroductionDuring the feasibility and preliminary design stages of a project, when very little detailedinformation on the rock mass and its stress and hydrologic characteristics is available, theuse of a rock mass classification scheme can be of considerable benefit.At its simplest,this may involve using the classification scheme as a check-list to ensure that all relevantinformation has been considered. At the other end of the spectrum, one or more rockmass classification schemes can be used to build up a picture of the composition andcharacteristics of a rock mass to provide initial estimates of support requirements, and toprovide estimates of the strength and deformation properties of the rock mass.It is important to understand that the use of a rock mass classification scheme does not(and cannot) replace some of the more elaborate design procedures. However, the use ofthese design procedures requires access to relatively detailed information on in situstresses, rock mass properties and planned excavation sequence, none of which may beavailable at an early stage in the project. As this information becomes available, the useof the rock mass classification schemes should be updated and used in conjunction withsite specific analyses.3.2 Engineering rock mass classificationRock mass classification schemes have been developing for over 100 years since Ritter(1879) attempted to formalise an empirical approach to tunnel design, in particular fordetermining support requirements. While the classification schemes are appropriate fortheir original application, especially if used within the bounds of the case histories fromwhich they were developed, considerable caution must be exercised in applying rockmass classifications to other rock engineering problems.Summaries of some important classification systems are presented in this chapter, andalthough every attempt has been made to present all of the pertinent data from theoriginal texts, there are numerous notes and comments which cannot be included. Theinterested reader should make every effort to read the cited references for a fullappreciation of the use, applicability and limitations of each system.Most of the multi-parameter classification schemes (Wickham et al (1972) Bieniawski(1973, 1989) and Barton et al (1974)) were developed from civil engineering casehistories in which all of the components of the engineering geological character of therock mass were included. In underground hard rock mining, however, especially at deeplevels, rock mass weathering and the influence of water usually are not significant andmay be ignored. Different classification systems place different emphases on the variousparameters, and it is recommended that at least two methods be used at any site duringthe early stages of a project.3.2.1 Terzaghi's rock mass classificationThe earliest reference to the use of rock mass classification for the design of tunnelsupport is in a paper by Terzaghi (1946) in which the rock loads, carried by steel sets, areestimated on the basis of a descriptive classification. While no useful purpose would beserved by including details of Terzaghi's classification in this discussion on the design ofsupport, it is interesting to examine the rock mass descriptions included in his originalpaper, because he draws attention to those characteristics that dominate rock massbehaviour, particularly in situations where gravity constitutes the dominant driving force.The clear and concise definitions and the practical comments included in thesedescriptions aregood examples of the type of engineering geology information, which ismost useful for engineering design.Terzaghi's descriptions (quoted directly from his paper) are:•Intact rock contains neither joints nor hair cracks. Hence, if it breaks, it breaks acrosssound rock. On account of the injury to the rock due to blasting, spalls may drop offthe roof several hours or days after blasting. This is known as a spalling condition.Hard, intact rock may also be encountered in the popping condition involving thespontaneous and violent detachment of rock slabs from the sides or roof.•Stratified rock consists of individual strata with little or no resistance againstseparation along the boundaries between the strata. The strata may or may not beweakened by transverse joints. In such rock the spalling condition is quite common.•Moderately jointed rock contains joints and hair cracks, but the blocks between jointsare locally grown together or so intimately interlocked that vertical walls do notrequire lateral support. In rocks of this type, both spalling and popping conditionsmay be encountered.•Blocky and seamy rock consists of chemically intact or almost intact rock fragmentswhich are entirely separated from each other and imperfectly interlocked. In suchrock, vertical walls may require lateral support.•Crushed but chemically intact rock has the character of crusher run. If most or all ofthe fragments are as small as fine sand grains and no recementation has taken place,crushed rock below the water table exhibits the properties of a water-bearing sand.•Squeezing rock slowly advances into the tunnel without perceptible volume increase.A prerequisite for squeeze is a high percentage of microscopic and sub-microscopicparticles of micaceous minerals or clay minerals with a low swelling capacity.•Swelling rock advances into the tunnel chiefly on account of expansion. The capacityto swell seems to be limited to those rocks that contain clay minerals such asmontmorillonite, with a high swelling capacity.3.2.2 Classifications involving stand-up timeLauffer (1958) proposed that the stand-up time for an unsupported span is related to thequality of the rock mass in which the span is excavated. In a tunnel, the unsupported spanis defined as the span of the tunnel or the distance between the face and the nearestsupport, if this is greater than the tunnel span. Lauffer's original classification has sincebeen modified by a number of authors, notably Pacher et al (1974), and now forms part ofthe general tunnelling approach known as the New Austrian Tunnelling Method.The significance of the stand-up time concept is that an increase in the span of thetunnel leads to a significant reduction in the time available for the installation of support.For example, a small pilot tunnel may be successfully constructed with minimal support,while a larger span tunnel in the same rock mass may not be stable without the immediateinstallation of substantial support. The New Austrian Tunnelling Method includes a number of techniques for safetunnelling in rock conditions in which the stand-up time is limited before failure occurs.These techniques include the use of smaller headings and benching or the use of multipledrifts to form a reinforced ring inside which the bulk of the tunnel can be excavated.These techniques are applicable in soft rocks such as shales, phyllites and mudstones inwhich the squeezing and swelling problems, described by Terzaghi (see previoussection), are likely to occur. The techniques are also applicablewhen tunnelling inexcessively broken rock, but great care should be taken in attempting to apply thesetechniques to excavations in hard rocks in which different failure mechanisms occur.In designing support for hard rock excavations it is prudent to assume that the stabilityof the rock mass surrounding the excavation is not time-dependent. Hence, if astructurally defined wedge is exposed in the roof of an excavation, it will fall as soon asthe rock supporting it is removed. This can occur at the time of the blast or during thesubsequent scaling operation. If it is required to keep such a wedge in place, or toenhance the margin of safety, it is essential that the support be installed as early aspossible, preferably before the rock supporting the full wedge is removed. On the otherhand, in a highly stressed rock, failure will generally be induced by some change in thestress field surrounding the excavation. The failure may occur gradually and manifestitself as spalling or slabbing or it may occur suddenly in the form of a rock burst. Ineither case, the support design must take into account the change in the stress field ratherthan the ‘stand-up’ time of the excavation.3.2.3 Rock quality designation index (RQD)The Rock Quality Designation index (RQD) was developed by Deere (Deere et al 1967)to provide a quantitative estimate of rock mass quality from drill core logs. RQD isdefined as the percentage of intact core pieces longer than 100 mm (4 inches) in the totallength of core. The core should be at least NW size (54.7 mm or 2.15 inches in diameter)and should be drilled with a double-tube core barrel. The correct procedures formeasurement of the length of core pieces and the calculation of RQD are summarised inFigure 5.1.Figure 5.1: Procedure for measurement and calculation of RQD (After Deere, 1989).Palmström (1982) suggested that, when no core is available but discontinuity tracesare visible in surface exposures or exploration adits, the RQD may be estimated from thenumber of discontinuities per unit volume. The suggested relationship for clay-free rockmasses is:RQD = 115 - 3.3 Jv (5.1)Where Jvis the sum of the number of joints per unit length for all joint (discontinuity)sets known as the volumetric joint count.RQD is a directionally dependent parameter and its value may change significantly,depending upon the borehole orientation. The use of the volumetric joint count can bequite useful in reducing this directional dependence.RQD is intended to represent the rock mass quality in situ. When using diamond drillcore, care must be taken to ensure that fractures, which have been caused by handling orthe drilling process, are identified and ignored when determining the value of RQD.When using Palmström's relationship for exposure mapping, blast induced fracturesshould not be included when estimating Jv.Deere's RQD has been widely used, particularly in North America, for the past 25years. Cording and Deere (1972), Merritt (1972) and Deere and Deere (1988) haveattempted to relate RQD to Terzaghi's rock load factors and to rockbolt requirements inL = 38 cmL = 17 cmL = 0no pieces > 10 cmL = 20 cmL = 35 cmDrilling breakL = 0no recoveryTotal length of core run = 200 cmsΣ Length of core pieces > 10 cm lengthx 100 = 55 %RQD =Total length of core runX 10038 + 17 + 20 + 35200RQD =44 Chapter 3: Rock mass classificationtunnels. In the context of this discussion, the most important use of RQD is as acomponent of the RMR and Q rock mass classifications covered later in this chapter.3.2.4 Rock Structure Rating (RSR)Wickham et al (1972) described a quantitative method for describing the quality of a rockmass and for selecting appropriate support on the basis of their Rock Structure Rating(RSR) classification. Most of the case histories, used in the development of this system,were for relatively small tunnels supported by means of steel sets, although historicallythis system was the first to make reference to shotcrete support. In spite of this limitation,it is worth examining the RSR system in some detail since it demonstrates the logicinvolved in developing a quasi-quantitative rock mass classification system.The significance of the RSR system, in the context of this discussion, is that itintroduced the concept of rating each of the components listed below to arrive at anumerical value of RSR = A + B + C .1. Parameter A, Geology: General appraisal of geological structure on the basis of:a. Rock type origin (igneous, metamorphic, sedimentary).b. Rock hardness (hard, medium, soft, decomposed).c. Geologic structure (massive, slightly faulted/folded, moderately faulted/folded,intensely faulted/folded).2. Parameter B, Geometry : Effect of discontinuity pattern with respect to the directionof the tunnel drive on the basis of:a. Joint spacing.b. Joint orientation (strike and dip).c. Direction of tunnel drive.3. Parameter C: Effect of groundwater inflow and joint condition on the basis of:a. Overall rock mass quality on the basis of A and B combined.b. Joint condition (good, fair, poor).c. Amount of water inflow (in gallons per minute per 1000 feet of tunnel).Note that the RSR classification used Imperial units andthat these units have been retained in this discussion.Three tables from Wickham et al's 1972 paper arereproduced in Tables 4.1, 4.2 and 4.3. Thesetables can beused to evaluate the rating of each of these parameters toarrive at the RSR value (maximum RSR = 100).For example, a hard metamorphic rock which is slightlyfolded or faulted has a rating of A = 22 (from Table 4.1). Therock mass is moderately jointed, with joints strikingperpendicular to the tunnel axis which is being driven east-west, and dipping at between 20° and 50°. Table 4.2 gives the rating for B = 24 for driving with dip (defined in themargin sketch).Drive with dipDrive against dipThe value of A + B = 46 and this means that, for joints of fair condition (slightlyweathered and altered) and a moderate water inflow of between 200 and 1,000 gallonsper minute, Table 4.3 gives the rating for C = 16. Hence, the final value of the rockstructure rating RSR = A + B + C = 62.A typical set of prediction curves for a 24 foot diameter tunnel are given in Figure 4.2which shows that, for the RSR value of 62 derived above, the predicted support would be2 inches of shotcrete and 1 inch diameter rockbolts spaced at 5 foot centres. As indicatedin the figure, steel sets would be spaced at more than 7 feet apart and would not beconsidered a practical solution for the support of this tunnel.For the same size tunnel in a rock mass with RSR = 30, the support could be providedby 8 WF 31 steel sets (8 inch deep wide flange I section weighing 31 lb per foot) spaced3 feet apart, or by 5 inches of shotcrete and 1 inch diameter rockbolts spaced at 2.5 feetcentres. In this case it is probable that the steel set solution would be cheaper and moreeffective than the use of rockbolts and shotcrete.Although the RSR classification system is not widely used today, Wickham et al'swork played a significant role in the development of the classification schemes discussedin the remaining sections of this chapter.Figure 4.2: RSR support estimates for a 24 ft. (7.3 m) diameter circular tunnel. Note that rockboltsand shotcrete are generally used together. (After Wickham et al 1972).。
rock mech chap1-zhuzhu
Rock Mechanics School of Petroleum EngineeringWang Jing-yinZhu Li-hongPersonal Informationu Office: Room 318,Engineering Building Bu E-mail: zhulihongjd_2005@About the course •Nine weeks from 1 to 9•32 lessons in total •Credits and Roll call(30%)•Final test (70%)About the courseContentsn1. Introduction to Rock Mechanicsn2. Composition and character of the rockn3. The Fundamental of Elastic Mechanicsn4. Rock mechanical property and influencing factors n5. Rock strength and laboratory measurementØ1.1 Basic concept of rock mechanicsChapter 1Introduction to Rock Mechanics Ø1.2 Rock mechanics historyØ1.5 Prime application of rock mechanicsØ1.4 Intrinsic complexity of rock mechanics Ø1.3 Research content and methodØ1.6 Rock mechanics study features in petroleum engineeringChapter 1Introduction to Rock Mechanics1.1 Basic concept of rock mechanicsRock mechanics is a subject to study the mechanical behavior of rock or mass of rock which acts under the function of outside force, including stress state, strain state and failure criterion.It is a basic theory to resolve technical matters of engineering of rock.1.1 Basic concept of rock mechanicsRock mechanics is the theoretical and applied science of the mechanical behavior of rock and rock masses.Compared to geology, it is that branch of mechanics concerned with the response of rock and rock masses to the force fields of their physical environment.Rock mechanics forms part of the broader subject of geomechanics(地质力学) , which is concerned with the mechanical responses of all geological materials, including soils.1.2 Rock mechanics historyRock mechanics is a new branch of science which develops accompany of the building and progression of the mathematics, mechanics and rock engineering containing mining, civil engineering, water conservancy project and traffic.1.2 Rock mechanics cavalcade (history)(1) first time (end of nineteenth century till early of twentieth century)In this time primary theory appeared to solve the mechanics calculation of excavation(挖掘) of the rock mass.Its development could divide into four steps:China's ancient water wells1.2 Rock mechanics cavalcade (history)(2) Empirical theory(twentieth century till thirty years)Lithostatic pressure theory地压理论appeared to analyze the supported problems of the underground excavation using mechanics of materials and structure mechanics according to production empiricism 观察实验法.foundation pitIt’s an important stage for the form of the rock mechanics. In this stage elasticity and plasticity were introduced into rock mechanics, confirming a lot of classic equations and the function of surrounding rock and supporting rock. Structural plane was thought more of the infection in rock characters.1.2 Rock mechanics cavalcade (history)(3) Classic theory (twentieth century thirty years till sixtieth years)v The theory of elasticity is used widely in rock mechanics to predict how rock masses respond to loads and excavation (surface and underground). The assumptions inherent to the theory of elasticity are:•the material is elastic (linear or non-linear) which implies an immediate response during loading and a fully reversible response upon unloading,•the material behaves as a continuum.If time is involved (time-deferred response), the theory of viscoelasticity should be used instead.1.2 Rock mechanics cavalcade (history) (3) Classic theory(twentieth century thirty years till sixtieth years) Document and monograph was published.Test method was improved.Technical of engineering problem was solved.In this stage rock mechanics had developed to be an independent subject. Continuous medium theory and geologic mechanics theory were founded.It’s an important times for rock mechanics to develop in the field of theory and practice.Complicated mechanical model was used to solve the problem of rock mechanics. The latest results in fieldsof mechanics, physics, system engineering, modern mathematical statistics and information technology were introduced into rock mechanics.(4) Modern times(twentieth century sixty years till now)It’s possible for theory including rheology, fracture mechanics, discontinuum mechanics, numerical method, fuzzy(模糊)theory, artificial intelligence and nonlinear theory to be introduced in to rock mechanics and engineering as result of the development of technical of computer.(4) Modern times(twentieth century sixty years till now)Chapter 1 Introduction to Rock Mechanics1.3 Research content and method(1) research content(2) research methodsØgeologic character of rock or rock mass content ：①material component and structural feature ；②structural plane feature with its impact on mechanics characters of rock mass ；③structure of rock mass and its mechanics characters ；④classification of rock mass engineering.1.3 Research content and method(1) research contentØphysical characters, water physical property and thermodynamic behaviour of rockThe physical characters of rock is a total of porosity, permeability , compressibility , electrical conductivity and heat transmissibility .1.3 Research content and method(1) research contentporosity1.3 Research content and method(1) research contentØphysical characters, water physical property and thermodynamic behavior of rockWater physical property of rock is the character of rock interacting with water, including water absorbing quality, hydraulic permeability, dehardening quality and antifreezing quality.1.3 Research content and method(1) research contentØfundamental mechanical property of rock content：①deformation and strength feature and mechanics exponent parameter under any kinds of force；②main factors impacting on rock mechanics characters include condition of loading, temperature and humidity；③rock deformation failure mechanism and failure criterion。
A fractal analysis of permeability for fractured rocks
A fractal analysis of permeability for fracturedrocksTongjun Miao a ,b ,Boming Yu a ,⇑,Yonggang Duan c ,Quantang Fang caSchool of Physics,Huazhong University of Science and Technology,1037Luoyu Road,Wuhan 430074,Hubei,PR ChinabDepartment of Electrical and Mechanical Engineering,Xinxiang Vocational and Technical College,Xinxiang 453007,Henan,PR China cState Key of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,8Xindu Road,Chengdu 610500,Sichuan,PR Chinaa r t i c l e i n f o Article history:Received 6September 2013Received in revised form 28March 2014Accepted 5October 2014Keywords:Permeability Rock Fractal FracturesFracture networksa b s t r a c tRocks with shear fractures or faults widely exist in nature such as oil/gas reservoirs,and hot dry rocks,etc.In this work,the fractal scaling law for length distribution of fractures and the relationship among the fractal dimension for fracture length distribution,fracture area porosity and the ratio of the maxi-mum length to the minimum length of fractures are proposed.Then,a fractal model for permeability for fractured rocks is derived based on the fractal geometry theory and the famous cubic law for laminar flow in fractures.It is found that the analytical expression for permeability of fractured rocks is a function of the fractal dimension D f for fracture area,area porosity /,fracture density D ,the maximum fracture length l max ,aperture a ,the facture azimuth a and facture dip angle h .Furthermore,a novel analytical expression for the fracture density is also proposed based on the fractal geometry theory for porous media.The validity of the fractal model is verified by comparing the model predictions with the available numerical simulations.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionFractured media and rocks with shear fractures or faults widely exist in nature such as oil/gas reservoirs,and hot dry rocks,ually,the fractures are embedded in porous matrix with micro pores,which play negligible effect on the seepage characteristic,and randomly distributed fractures dominate the seepage charac-teristic in the media.The randomly distributed fractures are often connected to form irregular networks,and the seepage character-istic of the fracture networks has the significant influence on nuclear waste disposal [1],oil or gas exploitation [2],and geother-mal energy extraction [3].In this work,we focus our attention on the seepage characteristics of fracture networks in fractured rocks and ignore the seepage performance from micro pores in porous matrix.Over the past four decades,many investigators studied the seepage characteristics of fracture networks/rocks and proposed several models.Snow [4]developed an analytical method for per-meability of fracture networks according to parallel plane model.Kranzz et al.[5]studied the permeability of whole jointed granite and tested the parallel plane model by experiments.Koudina et al.[6]investigated the permeability of fracture networks with numer-ical simulation method in the three-dimensional space,they assumed that fracture network consists of polygonal shape frac-tures and fluid flow in each fracture meets the Darcy’s law.Dreuzy et al.[7]studied the permeability of randomly fractured networks by numerical and theoretical methods in two dimensions,and they verified the validity of the model by comparing to naturally frac-tured networks.Klimczak et al.[8]obtained the permeability of a single fracture by parallel plate model with the fracture length and aperture satisfying power-law and verified by the numerical simulation.However,these models did not provide a quantitative relationship among the permeability of fracture networks,poros-ity,fracture density and microstructure parameters of fractures,such as fracture length,aperture,inclination,orientation etc.Fractures in rocks are usually random and disorder and they have been shown to have the statistically self-similar and fractal characteristic [3,9–13].Chang and Yortsos [10]studied the single phase fluid flow in the fractal fracture networks.Watanabe and Takahashi [3]investigated the permeability of fracture networks and heat extraction in hot dry rock by using fractal method.But,they did not propose an expression of permeability with micro-scopic parameters included.Jafari and Babadagli [14]obtained the permeability expression with multiple regression analysis of random fractures by the fractal geometry theory according to observed data in the well logging.In addition,their expression with several empirical constants does not include the orientation factor and microstructure parameters of fracture networks.The tree-like fractal branching networks were often considered as/10.1016/j.ijheatmasstransfer.2014.10.0100017-9310/Ó2014Elsevier Ltd.All rights reserved.⇑Corresponding author.E-mail address:yubm_2012@ (B.Yu).fracture networks by many investigators.Xu et al.[15,16]studied the seepage and heat transfer characteristics of fractal-like tree networks.Recently,Wang et al.[17]studied the starting pressure gradient for Binghamfluid in a special dual porosity medium with randomly distributed fractal-like tree network embedded in matrix porous media.Most recently,Zheng and Yu[18]investigated gas flow characteristics in the dual porosity medium with randomly distributed fractal-like tree networks.However,the fractal-like tree network is a kind of ideal and symmetrical network.The purpose of the present work is to derive an analytical expression and establish a model for permeability of fracture rocks/media based on the parallel plane model(cubic law)and frac-tal geometry theory.The proposed permeability and the predicted fracture density will be compared with the numerical simulations.2.Fractal characteristics for fracture networksMany investigators[3,9–13,19–23]reported that the relation-ships between the length and the number of fractures exhibit the power-law,exponential and log-normal types.Torabi and Berg [19]made a comprehensive review on fault dimensions and their scaling laws,and they summarized several types of scaling laws such as the length distributions for faults and fractures in siliciclas-tic rocks from different scales and tectonic settings.The power-law exponents of the scaling-law between the fault length and the number of faults were found to be in the range of1.02–2.04and are probably influenced by factors such as stress regime,linkage of faults,sampling bias,and size of the dataset.Interested readers may consult Refs.[3,9–13,19–23]for detail.In addition,the self-similar fractal structures of fracture net-works were extensively studied[22,23],and the application in complex rock structures with the fractal technique was recently reviewed by Kruhl[24].Velde et al.[25]and Vignes-Adler et al.[26]studied the data at several length scales with fractal method and found that the fracture networks are fractal.Barton and Zoback [27]analyzed the2D maps of the trace length of fractures spanning ten orders,ranging from micro to large scale fractures and found that D f=1.3–1.7.The width between two plates/walls of a fracture,i.e.the paral-lel plate model is used to represent the effective aperture of a frac-ture.Generally,the relationship between the effective aperture a and the fracture length l is given by[28,29]a¼b l nð1Þwhere b and n are the proportionality coefficient and a constant according to fracture scales,respectively.The value of n=1is important,which indicates a linear scaling law,and the fracture network is self-similarity and fractal[19,29].Thus,in the current work the value of n=1is chosen for fractures with fractal characteristic.Thus,Eq.(1)can be rewritten asa¼b lð2ÞEq.(2)will be used in this work.It is well-known that the cumulative size distribution of islands on the Earth’s surface obeys the fractal scaling law[30]NðS>sÞ/sÀD=2ð3aÞwhere N is the total number of island of area S greater than s,and D is the fractal dimension for the size distribution of islands.The equality in Eq.(3a)can be invoked by using s max to represent the largest island on Earth to yield[31]NðS>sÞ¼s maxsD=2ð3bÞEq.(3b)implies that there is only one largest island on the Earth’s surface,and Majumdar and Bhushan[31]used this power-law equation to describe the contact spots on engineering surfaces,where s max¼g k2max(the maximum spot area)and s¼g k2(a spot area),with k being the diameter of a spot and g being a geometry factor.It has been shown that the length distribution of fractures sat-isfies the fractal scaling law[3,9–13,19,22,23,32],hence,Eq.(3b) for description of islands on the Earth’s surface and spots on engi-neering surfaces can be extended to describe the area distribution of fractures on a fractured surface,i.e.NðS!sÞ¼a max l maxalD f=2ð3cÞwhere a max l max represents the maximum fracture area with a max and l max respectively being the maximum aperture and maximum fracture length,and al refers to a fracture area with the aperture and length being a and l,respectively.Inserting Eq.(2)into Eq.(3c),we obtainNðS!sÞ¼b l2maxb l!D f=2ð3dÞThen,from Eq.(3d),the cumulative number of fractures whose length are greater than or equal to l can be expressed by the follow-ing scaling law:NðL!lÞ¼l maxD fð4Þwhere D f is the fractal dimension for fracture lengths,0<D f<2(or 3)in two(or three)dimensions;and Eq.(4)implies that there is only one fracture with the maximum length.Some investigators [3,9–13,19,32]reported that the length distribution of fractures in rocks has the self-similarity and the fractal scaling law can be described by N/ClÀD f,where C is afitting constant,D f is the fractal dimension for the length(l)distribution of fractures and N is the number of fractures,and this fractal scaling law is similar to Eq.(4).Eq.(4)is also the base of the box-counting method[33]for mea-suring the fractal dimension of fracture lengths in fracture net-works,and Chelidze and Guguen[9]applied the box-counting method and found that the fractal dimension of fracture network (described by Nolen-Hoeksema and Gordon[34])in a2D cross sec-tion is1.6.Since there usually are numerous fractures in fracture net-works,Eq.(4)can be considered as a continuous and differentiable function.So,differentiating Eq.(4)with respect to l,we can get the number of fractures whose lengths are in the infinitesimal rang l to l+dl:ÀdNðlÞ¼D f l D fmaxlÀðD fþ1Þdlð5ÞEq.(5)indicates that the number of fractures decreases with the increase of fracture length andÀdN(l)>0.The relationship among the fractal dimension,porosity and the ratio k max=k min for porous media was derived based on the assump-tion that pores in porous media are in the form of squares with self-similarity in sizes in the self similarity range from the mini-mum size k min to the maximum size k max,i.e.[35]D f¼d Eþln emax minð6Þwhere e is the effective porosity of a fractal porous medium,d E is the Euclid dimension,and d E=2and3respectively in two and three dimensions.It has been shown that Eq.(6)is valid not only for exactly self-similar fractals such as Sierpinski carpet and Sierpinski gasket but also for statistically self-similar fractal porous media.Fractures in rocks or in fractured media are analogous to pores in porous media.Therefore,Eq.(6)can be extended to describe the76T.Miao et al./International Journal of Heat and Mass Transfer81(2015)75–80relationship among the fractal dimension for length distribution, porosity of fractures and the ratio l max/l min of fractures in rocks,i.e.D f¼d Eþln/lnðl max=l minÞð7Þwhere l max and l min are the maximum and the minimum fracture lengths,respectively,and/is the effective porosity of fractures in a rock.The area porosity/of fractures is defined as/¼A PAð8Þwhere A is the area of a unit cell,A P is the total area of all fractures in the unite cell.Based on Eq.(5),the total area of all fractures in the unite cell can be obtained asA p¼ÀZ l maxl min aÁlÁdNðlÞ¼b D f l2max2ÀD f1Àl minl max2ÀD f"#ð9ÞInserting Eq.(7)into Eq.(9)yieldsA p¼b D f l2max2ÀD f1À/ðÞð10Þwhere porosity/is applied in Eq.(7)in two dimensions,i.e.d E=2is used.3.Relationship between fracture density and fractal dimensionThe total fracture lengths in a unit cell of area A can be obtained byl total¼ÀZ l maxl min lÁdNðlÞ¼D f l max1ÀD f1Àl minl max1ÀD f"#ð11ÞThe fracture density is defined by[36]D¼l totalð12Þwhere l total is the total length of all fractures(not a single fracture) which may be connected to form a network in the unit cell.Inserting Eqs.(7),(8)and(11)into Eq.(12)results in the fracture densityD¼ð2ÀD fÞ/1Àl minl max1ÀD fð1ÀD fÞb l max1Àl minmax2ÀD fð13aÞInserting Eq.(7)into Eq.(13a),the fracture density can also bewritten asD¼ð2ÀD fÞ1À/ðÞ1ÀD ff"#/ð1ÀD fÞb l max1À/ðÞð13bÞIt is evident that the fracture density D of fractures is a functionof the fractal dimension D f for fracture area,area porosity/,proportionality coefficient b and l max.Fig.2compares the predictions by the present fractal model(Eq.(13a))with numerical simulations of four groups of randomfracture networks by Zhang and Sanderson[36],who proposed anew numerical method for producing the self-avoiding randomgenerations,and the parameters such as the lengths of fracturescan be controlled.In their simulations,the lengths of fractures liefrom0.0005to1.5m,and the averaged fractal dimension D f is1.3.So,in this work we take the maximum length and minimumlength of fractures are1.5m and0.0005m,respectively,and theaveraged fractal dimension D f=1.3.The average porosity/is0.018calculated by Eq.(7).It can be seen from Fig.2that the pre-dictions are in good agreement with the numerical simulations.Fig.2clearly indicates that the fracture density increases withthe increase of the fractal dimension,and this is consistent withpractical situation.Fig.3presents the fracture density versus porosity of fracturenetworks as l max=1.5m,b=0.01.It can be seen from Fig.3thatthe fracture density increases with porosity.This can be explainedthat the pore area of fractures increasing with porosity means thatthe fracture density increases with porosity.This result is in agree-ment with the Monte Carlo simulations by Yazdi et al.[37].4.Fractal model for permeability of fractured rocksThe orientation of each fracture in fracture networks is definedby two angles,the fracture azimuth and fracture dip angle,whichsignificantly affect theflow and transport properties.The orienta-tions of fractures in a fracture network are non-uniform,but usu-ally with a preferred orientation[38,39].In general,the numberof fractures in fracture networks is very large.Based on generalpractice,the fracture azimuths of all fractures are taken as aver-aged/mean angle,for instance,Massart et al.[40]showed a meandip angle of70°,mean N–S(North–South)orientation from thetotal number of1878fractures.In this work,the mean dip angleof fractures between fracture orientations andfluidflow direction,and the mean azimuth of fractures perpendicular tofluidflowdirection are assumed to be h and a,respectively(see Fig.1(a)).(a)(b)T.Miao et al./International Journal of Heat and Mass Transfer81(2015)75–8077Therefore,the scalar quantity of permeability alongflow direction needs to be calculated.Iffluidflow through fractures is assumed to be laminarflow,the flow rate along theflow direction through a fracture can be described by the famous cubic law[41,42]qðlÞ¼a3l12lD PL0ð14Þwhere L0is the length of the structural unit,l is the fracture trace length,a is the fracture aperture,and D P is the pressure drop across a fracture alongflow direction.If the single fracture forms an angle with theflow direction,due to the projection on theflow direction of the fracture,theflow rate through the fracture can be written by[43,44]qðlÞ¼a3l1Àcos2a sin2h12lD PL0ð15Þwhere a and h are respectively the mean facture azimuth and facture dip angle.When a=0,Eq.(15)is reduced toqðlÞ¼a3l cos2h12lD PL0ð16ÞThis is the famous Parsons’model.See Fig.1(b)[43,44].The totalflow rate through all the fractures can be obtained by integrating Eq.(16)from the minimum length to the maximum length in a unit cross section,i.e.Q¼ÀZ l maxl minqðlÞdNðlÞ¼b3128lD f1Àcos2a sin2h4ÀD fD PL0l4max1Àl minl max4ÀD f"#ð17Þwhere D f represents the fractal dimension for the length distribu-tion of fractures.In general,l min<<l max.Since0<D f<2in two dimensions,andðl min=l maxÞ4ÀD f<<1,so that Eq.(17)can be simplified as:Q¼b3128lD f1Àcos2a sin2h4ÀD fD PL0l4maxð18ÞEq.(18)indicate that the totalflow rate through the fracture net-work is related to the fractal dimension D f of the fracture lengths, the facture azimuth a and facture dip angle h.Eq.(18)also indicates that theflow rate is very sensitive to the maximum fracture length l max.Darcy’s law for Newtonianfluidflow in porous media is given byQ¼KAlD PL0ð19ÞComparing Eq.(18)to Eq.(19),we can obtain the permeability for Newtonianfluidflow through the fracture networks asK¼b3128AD f1Àcos2a sin2h4ÀD fl4maxð20ÞInserting Eqs.(12)and(13b)into Eq.(20),the permeability for Newtonianfluidflow through fracture networks can be written asK¼b3D1281ÀD f4ÀD fl3max1Àcos2a sin2h1À/ðÞ1ÀD ff"#ð21ÞEq.(21)shows that the permeability is a function of the fractal dimension D f for the fracture length distribution,the structural parameters(maximum fracture length l max,fracture density D,fac-ture azimuth a and facture dip angle h)and fracture porosity/of fracture networks.Eq.(21)also reveals that the permeability strongly depends on the maximum fracture length l max,and the longer fracture with wider apertures conduct the higher volume offluid and higher permeability.As a result,the present fractal model can well reveal the mechanisms of seepage characteristics78T.Miao et al./International Journal of Heat and Mass Transfer81(2015)75–80in fracture networks than conventional methods.For example, many investigators proposed fracture network models by assum-ing that the media have ideal structures such as the parallel frac-ture network[4,5,8,45],the orthogonal plane network cracks [46,47],alternate level matrix layer and fractures[48]etc.The frac-ture network permeability was often expressed as K=/a2/12, where/is fracture porosity and a is fracture aperture.Recently, Jafari and Babadagli[14]obtained an expression(with several empirical constants)by fractal geometry for fracture networks according to the well logging and observation data.Therefore,it is clear that Eq.(21)has the obvious advantages over the conven-tional models/methods.5.Results and discussionIn this section,the model predictions will be compared with the simulated data and the effects of model parameters on the perme-ability will be discussed.The procedures for determination of the relevant parameters in Eq.(21)are as follows:(1)Given the fracture network parameters(such as l max,/,a,hand b)based on a real sample.(2)Find the fractal dimension D f of fracture lengths in a fracturenetwork by the box-counting method or by Eq.(7).(3)Determine the fracture density D by Eq.(13b).(4)Finally,calculate the permeability by Eq.(21).Jafari and Babadagli[49]obtained the fractal dimensions D f of2D maps from22different nature fracture networks by box-counting method,and then they calculated the equivalent fracture network permeability by a3D model with a block size of100Â100Â10m simulated/constructed.The maximum fracture length was taken to be2m and dip angle h=0.In comparison,the fracture density D and permeability are calculated by procedures3and4,respec-tively.Fig.4shows that the present model predictions are in good agreement with the simulation results[49].Fig.5depicts the permeability for Newtonianfluid through frac-ture networks against porosity of fracture networks at different dip angles at l max=10mm,b=0.01.It is seen from Fig.5that the per-meability for fracture networks increases with porosity.This is consistent with practical situation.From Fig.5,we can also see that the permeability decreases as the fracture plane dip angle increases.This can be explained that a higher fracture plane dip angle leads to an increase of theflow resistance.Fig.6plots the permeability versus the fracture density of the fracture networks at l max=10mm,a=0,h=p/4and b=0.01.It suggests that the permeability of the fracture networks increases with the increases of fracture density.The reason is that when the fracture density D increases,the area of fracture networks increases and thus results in increasing the permeability.This result agrees with the numerical simulation results in Ref.[50]. 6.ConclusionsIn this paper,the fractal geometry theory has been applied to describe the fractal fracture system,and the fractal scaling law for length distribution of fractures and the relationship among the fractal dimension for fracture length distribution,fracture area porosity and the ratio of the maximum length to the minimum length of fractures have been proposed.Then,a model for perme-ability of fractured rocks has been derived based on the famous cubic law,fractal geometry theory and technique.A novel expres-sion for the fracture density has also been proposed based on the fractal scaling law of length distribution of fractures.The present results show that the permeability of fracture networks increases with the increases of porosity and fracture density.Our results agree well the available numerical simulations.This verifies the validity of the proposed models.It should be point out that the percolation and critical behavior are not involved in this work.In this paper,we focus on the perme-ability that all fractures are assumed to be connected to form frac-ture network,which contributes the permeability of the fracture system.This means that we have ignored the interaction between fractures.The permeability after including the interaction and con-nectivity between fractures and critical behavior of fractures near the threshold undoubtedly is an interesting topic,and this may be our next workConflict of interestNone declared.AcknowledgmentThis work was supported by the National Natural Science Foundation of China through Grant Number10932010. 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Hoek-Brown_Failure_Criterion-2002_Edition
HOEK-BROWN FAILURE CRITERION – 2002 EDITIONEvert HoekConsulting Engineer, Vancouver, CanadaCarlos Carranza-TorresItasca Consulting Group Inc., Minneapolis, USABrent CorkumRocscience Inc., Toronto, CanadaABSTRACT: The Hoek-Brown failure criterion for rock masses is widely accepted and has been applied in a large number of projects around the world. While, in general, it has been found to be satisfactory, there are some uncertainties and inaccuracies that have made the criterion inconvenient to apply and to incorporate into numerical models and limit equilibrium programs. In particular, the difficulty of finding an acceptable equivalent friction angle and cohesive strength for a given rock mass has been a problem since the publication of the criterion in 1980. This paper resolves all these issues and sets out a recommended sequence of calculations for applying the criterion. An associated Windows program called “RocLab” has been developed to provide a convenient means of solving and plotting the equations presented in this paper.1.INTRODUCTIONHoek and Brown [1, 2] introduced their failure criterion in an attempt to provide input data for the analyses required for the design of underground excavations in hard rock. The criterion was derived from the results of research into the brittle failure of intact rock by Hoek [3] and on model studies of jointed rock mass behaviour by Brown [4]. The criterion started from the properties of intact rock and then introduced factors to reduce these properties on the basis of the characteristics of joints in a rock mass. The authors sought to link the empirical criterion to geological observations by means of one of the available rock mass classification schemes and, for this purpose, they chose the Rock Mass Rating proposed by Bieniawski [5].Because of the lack of suitable alternatives, the criterion was soon adopted by the rock mechanics community and its use quickly spread beyond the original limits used in deriving the strength reduction relationships. Consequently, it became necessary to re-examine these relationships and to introduce new elements from time to time to account for the wide range of practical problems to which the criterion was being applied. Typical of these enhancements were the introduction of the idea of “undisturbed” and “disturbed” rock masses Hoek and Brown [6], and the introduction of a modified criterion to force the rock mass tensile strength to zero for very poor quality rock masses (Hoek, Wood and Shah, [7]).One of the early difficulties arose because many geotechnical problems, particularly slope stability issues, are more conveniently dealt with in terms of shear and normal stresses rather than the principal stress relationships of the original Hoek-Brown riterion, defined by the equation:c(1)where '1σand '3σ are the major and minor effectiveprincipal stresses at failureciσis the uniaxial compressive strength of the intact rock material andm and s are material constants, where s = 1 for intact rock.An exact relationship between equation 1 and the normal and shear stresses at failure was derived by J. W. Bray (reported by Hoek [8]) and later by Ucar [9] and Londe1 [10].Hoek [12] discussed the derivation of equivalent friction angles and cohesive strengths for various practical situations. These derivations were based1 Londe’s equations were later found to contain errors although the concepts introduced by Londe were extremely important in the application of the Hoek-Brown criterion to tunnelling problems (Carranza-Torres and Fairhurst, [11])upon tangents to the Mohr envelope derived by Bray. Hoek [13] suggested that the cohesive strength determined by fitting a tangent to the curvilinear Mohr envelope is an upper bound value and may give optimistic results in stability calculations. Consequently, an average value, determined by fitting a linear Mohr-Coulomb relationship by least squares methods, may be more appropriate. In this paper Hoek also introduced the concept of the Generalized Hoek-Brown criterion in which the shape of the principal stress plot or the Mohr envelope could be adjusted by means of a variable coefficient a in place of the square rootterm in equation 1.(5)D is a factor which depends upon the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock masses. Guidelines for the selection of D are discussed in a later section.The uniaxial compressive strength is obtained bysetting in equation 2, giving:0'3=σaci c s .σσ=(6) Hoek and Brown [14] attempted to consolidate all the previous enhancements into a comprehensive presentation of the failure criterion and they gave a number of worked examples to illustrate its practical application.(7)Equation 7 is obtained by setting in equation 2. This represents a condition of biaxial tension. Hoek [8] showed that, for brittle materials, the uniaxial tensile strength is equal to the biaxial tensile strength. t σσσ=='3'1In addition to the changes in the equations, it was also recognised that the Rock Mass Rating of Bieniawski was no longer adequate as a vehicle for relating the failure criterion to geological observations in the field, particularly for very weak rock masses. This resulted in the introduction of the Geological Strength Index (GSI) by Hoek, Wood and Shah [7], Hoek [13] and Hoek, Kaiser and Bawden [15]. This index was subsequently extended for weak rock masses in a series of papers by Hoek, Marinos and Benissi [16], Hoek and Marinos [17, 18] and Marinos and Hoek [19].Note that the “switch” at GSI = 25 for the coefficients s and a (Hoek and Brown, [14]) has been eliminated in equations 4 and 5 which give smooth continuous transitions for the entire range of GSI values. The numerical values of a and s , given by these equations, are very close to those given by the previous equations and it is not necessary for readers to revisit and make corrections to old calculations.The Geological Strength Index will not be discussed in the following text, which will concentrate on the sequence of calculations now proposed for the application of the Generalized Hoek Brown criterion to jointed rock masses.Normal and shear stresses are related to principal stresses by the equations published by Balmer [20].2. GENERALIZED HOEK-BROWN CRITERION(9)(2) wherewhere m b is a reduced value of the material constant m i and is given by(3)3. MODULUS OF DEFORMATIONThe rock mass modulus of deformation is given by:s and a are constants for the rock mass given by the following relationships: (11a)The equivalent plot, in terms of the major and minor principal stresses, is defined by: Equation 11a applies for ≤ci σ 100 MPa. For >ci σ 100 MPa, use equation 11b.(15)Note that the original equation proposed by Hoek and Brown [14] has been modified, by the inclusion of the factor D , to allow for the effects of blast damage and stress relaxation.4. MOHR-COULOMB CRITERIONSince most geotechnical software is still written in terms of the Mohr-Coulomb failure criterion, it is necessary to determine equivalent angles of friction and cohesive strengths for each rock mass and stress range. This is done by fitting an average linear relationship to the curve generated by solving equation 2 for a range of minor principal stress values defined by '3max 3σσσ<<t , as illustrated in Figure 1. The fitting process involves balancing the areas above and below the Mohr-Coulomb plot. This results in the following equations for the angle of friction and cohesive strength : 'φ'cFigure 1: Relationships between major and minorprincipal stresses for Hoek-Brown and equivalentMohr-Coulomb criteria.5. ROCK MASS STRENGTHThe uniaxial compressive strength of the rock mass c σ is given by equation 6. Failure initiates at the boundary of an excavation when c σ is exceeded by the stress induced on that boundary. The failurepropagates from this initiation point into a biaxialstress field and it eventually stabilizes when the local strength, defined by equation 2, is higher than the induced stresses and . Most numericalmodels can follow this process of fracturepropagation and this level of detailed analysis isvery important when considering the stability ofexcavations in rock and when designing supportsystems. '1σ'3σNote that the value of 'max 3σ, the upper limit ofconfining stress over which the relationship between the Hoek-Brown and the Mohr-Coulomb criteria is considered, has to be determined for each individual case. Guidelines for selecting thesevalues for slopes as well as shallow and deeptunnels are presented later.The Mohr-Coulomb shear strength τ, for a given normal stress σ, is found by substitution of these values of and 'c 'φ in to the equation:''tan φστ+=c (14)However, there are times when it is useful to consider the overall behaviour of a rock mass rather than the detailed failure propagation process described above. For example, when consideringthe strength of a pillar, it is useful to have anestimate of the overall strength of the pillar ratherthan a detailed knowledge of the extent of fracture propagation in the pillar. This leads to the concept of a global “rock mass strength” and Hoek and Brown [14] proposed that this could be estimated(16)with and determined for the stress range 'c 'φ4/ci t σσσ<'3< giving(17)6. DETERMINATION OF σ′3MAXThe issue of determining the appropriate value of for use in equations 12 and 13 depends upon the specific application. Two cases will be investigated: 'max 3σ1. Tunnels − where the value of is that which gives equivalent characteristic curves for the two failure criteria for deep tunnels or equivalent subsidence profiles for shallow tunnels.'max 3σ2. Slopes – here the calculated factor of safety and the shape and location of the failure surface have to be equivalent.For the case of deep tunnels, closed form solutions for both the Generalized Hoek-Brown and the Mohr-Coulomb criteria have been used to generatehundreds of solutions and to find the value of that gives equivalent characteristic curves. 'max 3σFor shallow tunnels, where the depth below surface is less than 3 tunnel diameters, comparative numerical studies of the extent of failure and the magnitude of surface subsidence gave an identical relationship to that obtained for deep tunnels, provided that caving to surface is avoided.The results of the studies for deep tunnels are plotted in Figure 2 and the fitted equation for both cases is:94.0'''max347.0−=H cm cmγσσσ (18)where is the rock mass strength, defined by equation 17, 'cm σγis the unit weight of the rock massand H is the depth of the tunnel below surface. In cases where the horizontal stress is higher than the vertical stress, the horizontal stress value should be used in place of H γ.''3σσFigure 2: Relationship for the calculation of σ′3max for equivalent Mohr-Coulomb and Hoek-Brown parameters for tunnels.Equation 18 applies to all underground excavations, which are surrounded by a zone of failure that does not extend to surface. For studies of problems such as block caving in mines it is recommended that no attempt should be made to relate the Hoek-Brown and Mohr-Coulomb parameters and that the determination of material properties and subsequent analysis should be based on only one of these criteria.Similar studies for slopes, using Bishop’s circular failure analysis for a wide range of slope geometries and rock mass properties, gave:91.0'max 72.0−=H cmcmγσ (19)where H is the height of the slope.7. ESTIMATION OF DISTURBANCE FACTOR DExperience in the design of slopes in very large open pit mines has shown that the Hoek-Brown criterion for undisturbed in situ rock masses (D = 0) results in rock mass properties that are too optimistic [21, 22]. The effects of heavy blastdamage as well as stress relief due to removal of the overburden result in disturbance of the rock mass. It is considered that the “disturbed” rock mass properties [6], D = 1 in equations 3 and 4, are more appropriate for these rock masses.Lorig and Varona [23] showed that factors such as the lateral confinement produced by different radii of curvature of slopes (in plan) as compared with their height also have an influence on the degree of disturbance.Sonmez and Ulusay [24] back-analysed five slope failures in open pit coal mines in Turkey and attempted to assign disturbance factors to each rock mass based upon their assessment of the rock mass properties predicted by the Hoek-Brown criterion. Unfortunately, one of the slope failures appears to be structurally controlled while another consists of a transported waste pile. The authors consider that the Hoek-Brown criterion is not applicable to these two cases.Cheng and Liu [25] report the results of very careful back analysis of deformation measurements, from extensometers placed before the commencement of excavation, in the Mingtan power cavern in Taiwan. It was found that a zone of blast damage extended for a distance of approximately 2 m around all large excavations. The back-calculated strength and deformation properties of the damaged rock mass give an equivalent disturbance factor D = 0.7.From these references it is clear that a large number of factors can influence the degree of disturbance in the rock mass surrounding an excavation and that it may never be possible to quantify these factors precisely. However, based on their experience and on an analysis of all the details contained in these papers, the authors have attempted to draw up a set of guidelines for estimating the factor D and these are summarised in Table 1.The influence of this disturbance factor can be large. This is illustrated by a typical example in which ciσ = 50 MPa, m i = 10 and GSI = 45. For an undisturbed in situ rock mass surrounding a tunnel at a depth of 100 m, with a disturbance factor D = 0, the equivalent friction angle is 47.16° while the cohesive strength is c 0.58 MPa. A rock mass with the same basic parameters but in highly disturbed slope of 100 m height, with a disturbance factor of D = 1, has an equivalent friction angle of27.61° and a cohesive strength of 0.35 MPa.='φ='='φ='cNote that these are guidelines only and the reader would be well advised to apply the values given with caution. However, they can be used to provide a realistic starting point for any design and, if the observed or measured performance of the excavation turns out to be better than predicted, the disturbance factors can be adjusted downwards.8.CONCLUSIONA number of uncertainties and practical problems in using the Hoek-Brown failure criterion have been addressed in this paper. Wherever possible, an attempt has been made to provide a rigorous and unambiguous method for calculating or estimating the input parameters required for the analysis. These methods have all been implemented in a Windows program called “RocLab” that can be downloaded (free) from . This program includes tables and charts for estimating the uniaxial compressive strength of the intact rock elements (ciσ), the material constant m i and the Geological Strength Index (GSI).9.ACKNOWLEDGEMENTSThe authors wish to acknowledge the contributions of Professor E.T. Brown in reviewing a draft of this paper and in participating in the development of the Hoek-Brown criterion for the past 25 years.able 1: Guidelines for estimating disturbance factor D TAppearance of rock mass Description of rock massSuggestedvalue of DExcellent quality controlled blasting or excavation byTunnel Boring Machine results in minimal disturbanceto the confined rock mass surrounding a tunnel.D = 0Mechanical or hand excavation in poor quality rock masses (no blasting) results in minimal disturbance tohe surrounding rock mass.tWhere squeezing problems result in significant floorheave, disturbance can be severe unless a temporaryinvert, as shown in the photograph, is placed.D = 0D = 0.5No invertVery poor quality blasting in a hard rock tunnel results in severe local damage, extending 2 or 3 m, in the surrounding rock mass.D = 0.8Small scale blasting in civil engineering slopes resultsin modest rock mass damage, particularly if controlled blasting is used as shown on the left hand side of the photograph. However, stress relief results in somedisturbance. D = 0.7 Good blastingD = 1.0 Poor blastingVery large open pit mine slopes suffer significantdisturbance due to heavy production blasting and also due to stress relief from overburden removal.In some softer rocks excavation can be carried out byripping and dozing and the degree of damage to the slopes is less. D = 1.0 Productionblasting D = 0.7 Mechanicalexcavation10.REFERENCES1.Hoek, E. and Brown, E.T. 1980. Empirical strengthcriterion for rock masses. J. Geotech. Engng Div., ASCE 106 (GT9), 1013-1035.2.Hoek, E. and Brown, E.T. 1980. UndergroundExcavations in Rock, London, Instn Min. Metall.3.Hoek, E. 1968. Brittle failure of rock. In Rock Mechanicsin Engineering Practice . (eds K.G. Stagg and O.C.Zienkiewicz), 99-124. London: Wiley4.Brown, E.T. 1970. Strength of models of rock withintermittent joints. J. Soil Mech. Foundn Div., ASCE 96, SM6, 1935-1949.5.Bieniawski Z.T. 1976. Rock mass classification in rockengineering. In Exploration for Rock Engineering, Proc.of the Symp., (ed. Z.T. Bieniawski) 1, 97-106. Cape Town, Balkema.6.Hoek, E. and Brown, E.T. 1988. The Hoek-Brown failurecriterion - a 1988 update. Proc. 15th Canadian Rock Mech. Symp. (ed. J.C. Curran), 31-38. Toronto, Dept.Civil Engineering, University of Toronto.7.Hoek, E., Wood D. and Shah S. 1992. A modified Hoek-Brown criterion for jointed rock masses. Proc. Rock Characterization, Symp. Int. Soc. Rock Mech.: Eurock ‘92, (ed. J.A. Hudson), 209-214. London, Brit. Geotech.Soc.8.Hoek, E. 1983. Strength of jointed rock masses, 23rd.Rankine Lecture. Géotechnique33 (3), 187-223.9.Ucar, R. (1986) Determination of shear failure envelopein rock masses. J. Geotech. Engg. Div. ASCE.112, (3), 303-315.10.Londe, P. 1988. Discussion on the determination of theshear stress failure in rock masses. ASCE J Geotech Eng Div, 14, (3), 374-6.11.Carranza-Torres, C., and Fairhurst, C. 1999. Generalformulation of the elasto-plastic response of openings in rock using the Hoek-Brown failure criterion. Int. J. Rock Mech. Min. Sci., 36 (6), 777-809.12.Hoek, E. 1990. Estimating Mohr-Coulomb friction andcohesion values from the Hoek-Brown failure criterion.Intnl. J. Rock Mech. & Mining Sci. & Geomechanics Abstracts.12 (3), 227-229.13.Hoek, E. 1994. Strength of rock and rock masses, ISRMNews Journal, 2 (2), 4-16.14.Hoek, E. and Brown, E.T. 1997. Practical estimates ofrock mass strength. Intnl. J. Rock Mech. & Mining Sci. & Geomechanics Abstracts.34 (8), 1165-1186.15.Hoek, E., Kaiser P.K. and Bawden W.F. 1995. Support ofunderground excavations in hard rock. Rotterdam, Balkema.16.Hoek, E., Marinos, P. and Benissi, M. 1998. Applicabilityof the Geological Strength Index (GSI) classification for very weak and sheared rock masses. The case of the Athens Schist Formation. Bull. Engg. Geol. Env. 57(2), 151-160. 17.Marinos, P and Hoek, E. 2000. GSI – A geologicallyfriendly tool for rock mass strength estimation. Proc.GeoEng2000 Conference, Melbourne.18.Hoek, E. and Marinos, P. 2000. Predicting TunnelSqueezing. Tunnels and Tunnelling International. Part 1 – November 2000, Part 2 – December, 200019.Marinos. P, and Hoek, E. 2001. – Estimating thegeotechnical properties of heterogeneous rock masses such as flysch. Accepted for publication in the Bulletin of the International Association of Engineering Geologists 20.Balmer, G. 1952. A general analytical solution for Mohr'senvelope. Am. Soc. Test. Mat. 52, 1260-1271.21.Sjöberg, J., Sharp, J.C., and Malorey, D.J. 2001 Slopestability at Aznalcóllar. In Slope stability in surface mining. (eds. W.A. Hustrulid, M.J. McCarter and D.J.A.Van Zyl). Littleton: Society for Mining, Metallurgy and Exploration, Inc., 183-202.22.Pierce, M., Brandshaug, T., and Ward, M. 2001 Slopestability assessment at the Main Cresson Mine. In Slopestability in surface mining. (eds. W.A. Hustrulid, M.J.McCarter and D.J.A. Van Zyl). Littleton: Society for Mining, Metallurgy and Exploration, Inc., 239-250.23.Lorig, L., and Varona, P. 2001 Practical slope-stabilityanalysis using finite-difference codes. In Slope stability in surface mining. (eds. W.A. Hustrulid, M.J. McCarter andD.J.A. Van Zyl). Littleton: Society for Mining,Metallurgy and Exploration, Inc., 115-124.24.Sonmez, H., and Ulusay, R. 1999. Modifications to thegeological strength index (GSI) and their applicability to the stability of slopes. Int. J. Rock Mech. Min. Sci., 36 (6),743-760.25.Cheng, Y., and Liu, S. 1990. Power caverns of theMingtan Pumped Storage Project, Taiwan. In Comprehensive Rock Engineering. (ed. J.A. Hudson), Oxford: Pergamon, 5, 111-132.。
围岩扰动系数D的量化取值
围岩扰动系数D的量化取值崔明;李淼【摘要】Based on empirical equation,visualized chart and graph was created for estimating rock mass deformation modulus,which was greatly influenced by the degree of disturbance D.the value of D is related to influence degree and range.The quantitative formulas of D value is presented in the form of integral and distance normalization for the distributions of elastic modulus of rock core.The mechanical parameters of rock masses of deep tunnel was estimated based on geological strength index GSI,degree of disturbance D and strength criterion.WithFLAC3D,these parameters were adopted to judge the law of stress, displacement,and plasticity range of rockmass.The relative error of below is 1 1% between calculated value and experimental value of plasticity range,and,1 5% for displacement values.The comparison of calculated results with measured data verified that the quantitative method is feasible and correct in rock engineering.%本文根据 Hoek-Diederichs公式，直观给出巷道围岩变形模量估计图表，计算出不同扰动参数 D 对岩体变形模量的影响。
岩体力学与工程实践岩体力学的概念Rockmass
第一节岩体力学与工程实践一、岩体力学的概念（Rockmass mechanics）力学的一个分支学科，是研究岩体在各种力场作用下变形与破坏规律的理论及其实际应用的基础学科。
（1）研究对象各类岩体（岩体：地质体的一部分，它位于一定的地质环境之中，是在各种宏观地质界面（断层节理、破碎带、接触带、片理等）分割下形成的有一定结构的地质体。
）（2）服务对象涉及许多领域和学科。
如水利水电工程、采矿工程、道路交通工程、国防工程、海洋工程、重要工厂（如核电站、大型发电厂及大型钢铁厂等）以及地震地质学、地球物理学和构造地质学等地学学科都应用到岩体力学的理论和方法。
但不同的领域和学科对岩体力学的要求和研究重点是不同的。
概括起来，可分为三个方面：①为各类建筑工程及采矿工程等服务岩体力学；（工程岩石力学）②为掘进、钻井及爆破工程服务的岩体力学；③为构造地质学、找矿及地震预报等服务岩体力学。
（3）（工程）岩体力学研究的根本目的和任务准确地预测岩体在各种应力场作用下的变形与稳定性，进而从岩体力学观点出发，选择相对优良的工程场址，防止重大事故，为合理的工程设计提供岩体力学依据。
（以露天采矿边坡坡角选择为例，符合''安全、经济和正常运营''的原则）二、工程实践（Engineering practices）岩体力学的发展是和人类工程实践分不开的。
（1）发展进程：最初，岩体工程数量少，规模也小，多凭经验解决工程中遇到的岩体力学问题。
因此，岩体力学20世纪50年代末（1957年法国的塔罗勃J.Talobre《岩石力学》的出版））的形成与发展要比土力学（18世纪七十年代（1773〜1776年）库仑Coulomb提出的土的抗剪强度和滑动土壤的土压力理论，标志着土力学进入古典理论时期）晚得多。
随着生产力水平及工程建筑事业的迅速发展，提出了大量的岩体力学问题。
对工程建设的安全性与经济性产生显着的影响，甚至带来严重的后果。
岩体完整性系数确定及应用中的几个问题探讨
21( 4) 段世委等: 岩体完整性系数确定及应用中的几个问题探讨
549
1引言
岩体完整性系数是表征岩体完整程度的地质术 语，其物理含义是岩体相对于岩石的完整程度。岩 体完整性系数是通过获取岩体和岩石的纵波速度进 行计算得到的。岩体内存在的各种结构面及充填物 质使得弹性波在岩体内的传播速度降低，岩体弹性 纵波速度反映了由于岩体的不完整性而降低了的物 理力学性质； 岩块则认为基本上不包含明显的结构 面，测得的岩块的弹性纵波速度反映的是完整岩石 的物理力 学 性 质［1］。 岩 体 完 整 性 系 数 是 一 个 与 岩 体质量和强度有关的参数，因此，很多工程岩体质量 评价方法中，都将岩体完整性系数作为影响岩体质 量的一个重要指标［1 ～ 5］。我国现行的《工程岩体分 级标准》中将岩体完整性系数作为计算岩体质量指 标 BQ 的 2 个参数之一［1］； 《水利水电工程地质勘 察规范》中坝基和围岩工程地质分类都将岩体完整 性系数作为一个重要指标［2，6，7］。但 是，不 同 的 规 范对确定岩体完整性系数的规定存在一定的分歧。 实际勘察工作中，在波速测试方法、测试岩块的选择 以及采用体积节理数确定岩体完整性系数等方面也 存在一些问题。以上原因可能造成计算的岩体完整 性系数不能真实地反映岩体的完整程度，进而影响 到岩体质量的准确评价。本文对岩体完整性系数确 定及应用中可能存在的几个问题进行探讨。
由于以上原因，在计算岩体完整性系数时，若岩 块与岩体分别采用不同类型的纵波速度是不合理 的，应根据 不 同 情 况 对 岩 块 或 岩 体 波 速 进 行 修 正。 笔者认为，由于地震波测试范围大，能够更好的反映 岩体的情况，计算岩体完整性系数时，岩体波速最好 采用地震波速度。当岩体的波速采用地震波速度 时，应 对 岩 块 声 波 速 度 进 行 修 正，修 正 系 数 为 0. 91［13］； 对 于 声 波 测 井 成 果，由 于 其 测 试 范 围 小 （ 更接近岩块） ，应通过建立工程区声波测井成果与 地震波测试成果之间的关系，对其进行修正，然后再 计算岩体完整性系数。
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• PROJECT SPECIFIC SYSTEMS
Development of Rock Mass Rating System
Rock Mass Rating System
(After Beiniawski 1989)
Guidelines for excavation and support of 10m span rock tunnels in accordance with the RMR system
‘Q‟ Classification System
• consists of two stress parameters • SRF can be regarded as a total stress parameter measure of – loosening load as excavated through shear zones – rock stress in competent rock – squeezing loads in plastic incompetent rock • JW is a measure of water pressure
Rock Quality Designation Index (RQD) (Deere et al. 1967)
• Aim : to provide a quantitative estimate of rock mass
quality from drill logs
• Equal to the percentage of intact core pieces longer than 100mm in the total length of core
ROCK MASS CLASSIFICATION
Presented by:
Neil Benson
Rock Mass Classification
• Why? • How does this help us in tunnel design?
Rock Mass Classification
WHY?
Engineering Rock Mass Classification Schemes
• Developed for estimation of tunnel support • Used at project feasibility and preliminary design stages • Simple check lists or detailed schemes • Used to develop a picture of the rock mass and its variability • Used to provide initial empirical estimates of tunnel support requirements
Q Classification Scheme
Resolves to three parameters • Block size • Interblock shear strength • Active stress ( RQD / Jn ) ( Jr / Ja ) ( Jw / SRF )
‘Q‟ Classification System
(After Barton et al. 1974)
‘Q‟ Classification System
• represents the structure of the rockmass • crude measure of block or particle size
(After Beiniawski 1989)
Rock Tunnelling Quality Index Q
• Based on case histories in Scandinavia • Numerical values on a log scale • Range 0.001 to 1000
(After Wickham et al. 1972)
Geomechanics Classification or Rock Mass Rating System (RMR) (Bieniawski 1976)
Based upon • uniaxial compressive strength of rock material • rock quality designation (RQD) • spacing of discontinuities
Procedure for Measurement and Calculation of RQD
Weathering of Basalt with depth
Multi parameter Rock Mass Classification Schemes
• Rock Mass Structure Rating (RSR)
a numerical value
• Demonstrates the logic in a quasi-quantitative rock mass classification • Has limitations as based on small tunnels supported by steel sets only • RSR = A + B + C
• condition of discontinuities
• groundwater conditions • orientation of discontinuities
Rock Mass Rating System
• Rock mass divided into structural regions • Each region is classified separately • Boundaries can be rock type or structural, eg: fault • Can be sub divided based on significant changes, eg:
Classification of individual parameters used in the Tunnelling Quality Index Q (cont‟d)
Q Classification Scheme
Resolves to three parameters • Block size • Interblock shear strength • Active stress ( RQD / Jn ) ( Jr / Ja ) ( Jw / SRF )
Rock Structure Rating
Parameter A: General area geology
Considers
(a) rock type origin (b) rock „hardness‟ (c) geotechnical structure
Rock Structure Rating
discontinuity spacing
Rock Mass Rating System
Rock Mass Rating System
BUT: 1976 to 1989 Bienawski • System refined by greater data • Ratings for parameters changed • Adapted by other workers for different situations
Ground interaction
Summary of rock mass characteristics, testing methods and theoretical considerations
Hale Waihona Puke Types of failure which occur in rock masses under low and high in-situ stress levels
(After Barton et al. 1974)
‘Q‟ Classification System
• represents roughness and frictional characteristics of joint walls or infill material
(After Barton et al. 1974)
RQD
• Directionally dependant parameter
• Intended to indicate rock mass quality in-situ
• Adapted for surface exposures as „Jv‟ number of discontinuities per unit volume • Used as a component in the RMR and Q systems
RSR support estimates for a 7.3m diameter circular tunnel
Examples RSR = 62 2” shotcrete 1” rockbolts @ 5ft centres
RSR = 30 5” shotcrete 1” rockbolts @ 2.5ft centres OR 8WF31 steel sets @ 3ft centres
Parameter B: Geometry : Effect of discontinuity pattern
Considers
(a) joint spacing (b) joint orientation (strike and dip) (c) direction of tunnel drive
Terzaghi‟s Rock Mass Classification (1946)