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40 1.8 Rock Classification and Properties 1.8.1 Overview A rock mass comprises blocks of intact rock that are sep- arated by discontinuities such as cleavage, bedding planes, joints, and faults. Table 8 provides a summary of rock mass discontinuity definitions and characteristics. These naturally formed discontinuities create weakness surfaces within the rock mass, thereby reducing the material strength. As previ- ously discussed, the influence of the discontinuities upon the material strength depends upon the scale of the foundation relative to the position and frequency of the discontinuities (Canadian Foundation Geotechnical Society, 2006). Figure 39. Lower bound solution for bearing capacity This section provides a short review of rock mass classi- (Carter and Kulhawy, 1988). fication/characterization systems and rock properties that are relevant to the methods selected for bearing capacity evaluation. Methods allowing engineering classification of rock mass are across the interface must be maintained and therefore the reviewed including the Rock Mass index (RMi) system, RMR bearing capacity of the strip footing may be evaluated from system and the Hoek-Brown GSI. Equation 81 (with 3 = s0.5qu) as 1.8.2 Engineering Rock Mass Classification ( qult = m + s qu ) (82a) 1.8.2.1 Classification Methods In an errata to Carter and Kulhawy (1988), Equation (82a) A number of classification systems have been developed was modified to the following: to provide the basis for engineering characterization of rock masses. A comprehensive overview of this subject is pro- ( )q vided by Hoek et al. (1995). Most of the classification sys- ( ) 0.5 qult = s + m s +s u (82b) tems incorporating various parameters were derived from civil engineering case histories in which all components of the engineering geological parameters of the rock mass were A similar approach to the bearing capacity analysis of a considered (Wickham et al., 1972; Bieniawski, 1973, 1979, strip footing was proposed by Carter and Kulhawy (1988) 1989; Barton et al., 1974). More recently, the systems have to be used for a circular foundation with an interface between been modified to account for the conditions affecting rock the two zones that was a cylindrical surface of the same diam- mass stability in underground mining. While no single clas- eter as the foundation. In this axisymmetric case, the radial sification system has been developed for or applied to foun- stress transmitted across the cylindrical surface at the point of dation design, the type of information collected for the two collapse of the foundation may be greater than qu s , without more common civil engineering classification schemes--the necessarily violating either radial equilibrium or the failure cri- Q system (Barton et al., 1974), used in tunnel design, and terion. However, because of the uncertainty of this value, the RMR (Bieniawski, 1989), used in tunnel and foundation radial stress at the interface is also assumed to be qu s for the design--are often considered. These techniques have been case of a circular foundation. Therefore, the predicted (lower applied to empirical design situations, where previous expe- bound) bearing capacity is given by Equations 82a and 82b. rience greatly affects the design of the excavation in the rock The m and s constants are determined by the rock type and mass. Table 9 outlines the many classification systems and their the conditions of the rock mass, and selecting an appropriate uses. Detailed descriptions of the different systems and the category is easier if either the Rock Mass Rating (RMR) sys- engineering properties associated with them are beyond the tem or the Geological Strength Index (GSI) classification data scope of this work and are restricted to the methods relevant are available as outlined below. Both bearing capacity formu- to the current research. lations expressed in Equations 82a and 82b were investigated The two most commonly used rock mass classification in this study. systems today are RMR, developed by Bieniawski (1973) and

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41 Table 8. Rock mass discontinuity descriptions (Hunt, 1986). Discontinuity Definition Characteristics A separation in the rock mass, a Signifies joints, faults, slickensides, foliations, Fracture break. and cleavage. Most common defect encountered. Present in most formations in some geometric pattern A fracture or crack in rock not related to rock type and stress field. Open joints Joint accompanied by dislocation. allow free movement of water, increasing decomposition rate of mass. Tight joints resist weathering and the mass decomposes uniformly. Fault zones usually consist of crushed and sheared rock through which water can move A fracture along which there has relatively freely, increasing weathering. Faults Fault been an observable amount of generally occur as parallel to sub-parallel sets of displacement. fractures along which movement has taken place to a greater or lesser degree. A smooth often striated surface Shiny, polished surfaces with striations. Often the produced on rock by movement Slickenside weakest elements in a mass, since strength is along a fault or a subsidiary often near residual. fracture. Can be present as open joints or merely Continuous foliation surface results orientations without openings. Strength and Foliation Plane from orientation of mineral grains deformation relate to the orientation of applied during metamorphism. stress to the foliations. The quality of a crystallized A fragment obtained by splitting along preferred Cleavage substance or rock of splitting along planes of weakness, e.g., diamond. definite planes. Any of the division planes which Often are zones containing weak materials such Bedding Plane separate the individual strata or as lignite or montmorillonite clays. beds in sedimentary or stratified. A fine-grained laminated rock Mylonite formed by the shifting of rock Fine-grained rock formed in shear zones. layers along faults. Openings in soluble rocks resulting In limestone, range from caverns to tubes. In Cavities from groundwater movement or in rhyolite and other igneous rocks, range from igneous rocks from gas pockets. voids of various sizes to tubes. adopted by the South African Council of Scientific and Indus- strength, joint distance, and ground water condition. It has trial Research (CSIR), and the Norwegian Geotechnical Insti- often been suggested that when using rock classification tute index (NGI-index or Q-system) (Barton et al., 1974). schemes--such as the RQD, RMR, and Q-system--only Both classification systems include Rock Quality Designation the natural discontinuities, which are of geological or geo- (RQD). In this study, the RMR geomechanics classification morphic origin, should be taken into account. However, it system was adopted because (1) the overwhelming majority of is often difficult, if not impossible, to judge whether a discon- states evaluate RQD and utilize the RMR system (this infor- tinuity is natural or artificial after activities such as drilling, mation is based on a questionnaire presented in Chapter 3) blasting, and excavation. and (2) it was favored by the available rock property data of the case histories. The Geological Strength Index (GSI), 1.8.2.2 Rock Quality Designation (RQD) based on the RMR system and the tables from the latest ver- sions of the Hoek-Brown failure criterion (e.g., Hoek et al., In 1964, D. U. Deere introduced an index to assess rock qual- 2002), was used. ity quantitatively called RQD. RQD is a core recovery percent- The systems presented in this report and utilized in the age that is associated with the number of fractures and the calibration (1) give a numerical value (have a numerical amount of softening in the rock mass that is observed from the form), (2) present a result that can be used to determine/ drill cores. Only the intact pieces with a length greater than estimate the strength, (3) have been successfully used in the 100 mm (4 in.) are summed and divided by the total length of past, and (4) are applicable to hard rock masses. The param- the core run (Deere, 1968). eters included in the classification systems resulting in a numerical value are presented in Table 10. The most com- RQD = Length of core pieces 10 cm 100 ( % ) (83) monly used parameters are the intact rock strength, joint total core length

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Table 9. Major rock classification/characterization systems (Edelbro, 2004, modified after Palstrm, 1995). Name of Author and Country of Form and Application Remarks classification first version origin type 1 Descriptive F, Terzaghi, 1946 Tunnels with steel Unsuitable for Rock Load Theory USA Behavior F, supports modern tunneling Functional T Lauffer, 1958 Descriptive F, Stand Up Time Austria Tunneling Conservative General T Rabcewicz, Tunneling in New Austrian Tunneling Descriptive F, 1964/65 and incompetent Utilized in squeezing Method (NATM) Austria Behavioristic F, 1975 (overstressed) ground conditions Tunneling concept ground Deere et al., Sensitive to Rock Quality Designation Core logging Numerical F, 1966 USA orientation effects. (RQD) tunneling General T In Deere, 1968 A Recommended Rock Coates and For input in rock Descriptive F, Classification for Rock Patching, 1968 mechanics General T Mechanical Purposes Deere et al., Based on particles The Unified Classification of Descriptive F, In Deere and Deere, 1966 USA and blocks for Soils and Rocks General T 1988 communication Rock Structure Rating (RSR) Wickham et al., Tunnels with steel Numerical F, Not useful with steel Concept2 USA 1972 supports Functional T fiber shotcrete Rock Mass Rating Bieniawski, (RMR)-System, Council of South Tunnels, mines, Numerical F, Unpublished base 1974 Scientific and Industrial Africa foundations, etc. Functional T case records Research (CSIR) Barton et al., Tunnels, large Numerical F, Q-System Norway 1974 chambers Functional T In Laubscher, Laubscher, 1975 Numerical F, Mining RMR (MRMR) Mining 1977 Functional T Matula and For use in Descriptive F, The Typological Classification Holzer, 1978 communication General T 3 Williamson, The Unified Rock For use in Descriptive F, In Williamson, 1984 1980 USA Classification System (URCS) communication General T Basic Geotechnical Description ISRM, 1981 Descriptive F, For general use (BGD) General T Stille et al., 1982 Numerical F, Rock Mass Strength (RMS) Sweden Modified RMR Functional T Cummings et al., Numerical F, Modified Basic RMR (MBR) 1982 Mining Functional T Brook and Dharmaratne, Numerical F, Modified RMR and Simplified Rock Mass Rating Mines and tunnels 1985 Functional T MRMR Slope Mass Rating Romana, 1985 Numerical F, Spain Slopes (SMR) Functional T Ramamurthy For intact and Numerical F, Modified Deere and Ramamurthy/Arora and Arora, 1993 India jointed rocks Functional T Miller approach Hoek et al., Numerical F, Geological Strength Index (GSI) Mines, tunnels 1995 Functional T Goel et al., 1995 Numerical F, Rock Mass Number (N) India Stress-free Q-system Functional T Rock engineering Numerical F, Rock Mass Index (RMi) Palmstrm, 1995 Norway communication, Functional T characterization 1 Descriptive F = Descriptive Form: the input to the system is mainly based on descriptions. Numerical F = Numerical Form: the input parameters are given numerical ratings according to their character. Behavioristic F = Behavioristic Form: the input is based on the behavior of the rock mass in tunnel. General T = General Type: the system is worked out to serve as a general characterization. Functional T = Functional Type: the system is structured for a special application (for example, for rock support) (Palmstrm, 1995). 2 RSR was a forerunner to the RMR system, although they both give numerical ratings to the input parameters and summarize them to a total value connected to the suggested support. 3 The Unified Rock Classification System (URCS) is associated with Casagrande's classification system for soils in 1948.

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43 Table 10. Parameters included in different classification systems resulting in a numerical value (Edelbro, 2004). Parameters RQD RSR RMR Q MRMR RMS MBR SRMR* SMR **RAC GSI N RMi Block size X X Joint orientation X X X Number of joint X X X X sets Joint length X Joint spacing X X X X X X X X X X X X X Joint strength X X X X X X X X X X X X Rock type X State of stress X X X Groundwater X X X X X X X X X condition Strength of intact X X X X X X X X X X X rock Blast damage X X X X *SRMR = Simplified Rock Mass Rating * *RAC - Ramamurthy and Arora Classification RQD is used as a standard quantity in drill core logging, (1982) presented the relationship between Jv and RQD in a and its greatest value is perhaps its simplicity, low cost, and clay free rock mass along a tunnel as the following: quick determination. RQD is simply a measurement of the percentage of "good" rock recovered from an interval of a RQD = 115 - 3.3 J v (86) borehole. The procedure for measuring RQD is illustrated in Figure 40. The recommended procedure for measuring where Jv is the volumetric joint count and the sum of the num- the core length is to measure it along the centerline of the ber of joints per unit length for all joint sets in a clay-free rock core. Core breaks caused by the drilling process should be mass. For Jv < 4.5, RQD = 100. fitted together and counted as one piece. The relationship The RQD is not scale dependent and is not a good measure between the numerical value of RQD and the engineering of the rock mass quality in the case of a rock mass with joint quality of the rock mass as proposed by Deere (1968) is given spacing near 100 mm. If the spacing between continuous in Table 11. joints is 105 mm (core length), the RQD value will be 100%. When no cores are available, one can estimate RQD from If the spacing between continuous joints is 95 mm, the RQD value will be 0%. For large-sized tunnels, RQD is of question- relevant information, for instance, joint spacing (Brady and able value. It is, as mentioned by Douglas and Mostyn (1999), Brown, 1985). Priest and Hudson (1976) found that an esti- unlikely that all defects found in the boreholes would be of mate of RQD could be obtained from joint spacing ( [number significance to the rock mass stability. of joints per meter]) measurements made on an exposure by using the following: 1.8.2.3 Rock Mass Rating (RMR) RQD = 100e -0.1 (0.1 + 1) (84) In 1973, Bieniawski introduced RMR as a basis for geo- mechanics classification. The rating system was based on For = 6 to 16 joints/meter, the following simplified equa- Bieniawski's experience in shallow tunnels in sedimentary tion can be used (Priest and Hudson, 1976): rocks. Originally, the RMR system involved 49 unpublished case histories. Since then, the classification system has under- RQD = -3.68 + 110.4 (85) gone several significant changes. In 1974, there was a reduc- tion of parameters from eight to six, and, in 1975, there was Equations 84 and 85 are probably the simplest ways of an adjustment of ratings and a reduction of recommended determining RQD, when no cores are available. Palmstrm support requirements.

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44 Figure 40. Procedure for measurement and calculation of rock quality designation (Sabatini et al., 2002). In 1976, a modification of rating class boundaries (as a The RMR system uses six parameters, which are rated. The result of 64 new case histories) to even multiples of 20 took ratings are added to obtain a total RMR value. The six param- place, and, in 1979, there was an adoption of the International eters are the following: Society for Rock Mechanics (ISRM) rock mass description. The newest version of RMR is from 1989, when Bieniawski 1. Unconfined compressive strength of intact rock material published guidelines for selecting rock reinforcement. In this (qu), version, Bieniawski suggested that the user could interpolate 2. RQD, the RMR values between different classes and not just use dis- 3. Joint or discontinuity spacing (s), crete values. Therefore, it is important to state which version 4. Joint condition, is used when RMR values are quoted. When applying this 5. Ground water condition, and classification system, one divides the rock mass into a num- 6. Joint orientation. ber of structural regions and classifies each region separately. The first five parameters represent the RMR basic parameters (RMRbasic) in the classification system. The sixth parameter is Table 11. Correlation treated separately because the influence of discontinuity ori- between RQD and rock entations depends upon the engineering application. Each of mass quality (Deere, 1968). these parameters is given a rating that symbolizes the RQD. RQD % Rock quality The first five parameters of all the ratings are algebraically < 25 Very Poor summed and can be adjusted, depending on the joint and 2550 Poor tunnel orientation, by the sixth parameter as shown in Equa- 5075 Fair tions 87a and 87b. 7590 Good 90100 Excellent RMR = RMR basic + adjustment for joint orientation (87a)

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45 Table 12. Meaning of rock mass classes and rock mass classes determined from total ratings (Bieniawski, 1978). Parameter/properties of Rock mass rating (rock class) rock mass Ratings 10081 8061 6041 4021 <20 Classification of rock mass Very Good Good Fair Poor Very Poor 10 years for 6 months for 1 week for 10 hours for 30 minutes Average stand-up time 15 m span 8 m span 5 m span 2.5 m span for 1 m span Cohesion of the rock mass > 400 300400 200300 100200 < 100 kPa (ksf) ( > 90) (67.4490) (4567.44) (22.4845) (< 22.48) Friction angle of the rock > 45o 35o45o 25o35o 15o25o < 15o mass RMR basic = parameters (1 + 2 + 3 + 4 + 5 ) (87b) If rock masses contain many discontinuities or are heavily jointed with discontinuities having similar strength charac- The final RMR value is grouped into five rock mass classes teristics, they can be treated as an isotropic continuum, and their strength can be estimated using methods based on a con- (see Table 12 and the relevant Table 10.4.6.4-3 in the AASHTO tinuum approach. The strength and deformation properties [2008] specifications). The various parameters in the system of jointed rock masses can, therefore, be estimated using the are not equally important for the overall classification of the Hoek-Brown failure criterion (Hoek and Brown, 1997) from rock mass, since they have been given different ratings. Higher three parameters (Hoek and Marinos, 2000; Marinos and RMA indicates better rock mass condition/quality. The RMR Hoek, 2001): system is very simple to use, and the classification parameters are easily obtained from either borehole data or underground The unconfined compressive strength of the intact rock mapping. Most of the applications of RMR have been in the elements contained within the rock mass. field of tunneling, but RMR has also been applied in the stabil- A constant, mi, which defines the frictional characteristics ity analysis of slopes and shallow foundations, caverns, and dif- of the component minerals within each intact rock element. ferent mining openings. The GSI, which relates the properties of the intact rock elements to those of the overall rock mass (see Table 13) 1.8.2.4 Geological Strength Index (GSI) (Canadian Geotechnical Society, 2006). Hoek et al. (1995) introduced the GSI as a complement to The generalized Hoek-Brown failure criterion is defined as their generalized rock failure criterion and as a way to esti- the following: mate the material constants s, a, and mb in the Hoek-Brown a failure criterion. GSI estimates the reduction in rock mass 3 = 3 1 + qu mb +s (88) strength for different geological conditions. The GSI has been qu updated for weak rock masses several times (1998, 2000, and where 2001) (Hoek et al., 2002). The aim of the GSI system is to 1 and 3 = the principal effective stresses at failure; determine the properties of the undisturbed rock mass. For qu = the unconfined compressive strength of the disturbed rock masses, compensation must be made for the intact rock pieces; lower GSI values obtained from such locations. mb = the value of the Hoek-Brown constant m for the The strength of the rock mass depends on factors such as the GSI - 100 shear strength of the surfaces of the blocks defined by disconti- rock mass, and mb = m1 exp ; 28 nuities, their continuous length, and their alignment relative to mi = the Hoek-Brown constant for the intact rock the load direction (Wyllie, 1992). If the loads are great enough (see Table 14) (Canadian Geotechnical Society, to extend fractures and break intact rock or if the rock mass 2006); and can dilate, resulting in loss of interlock between the blocks, s and a = constants that depend upon the rock mass then the rock mass strength may be diminished significantly characteristics. from that of the in situ rock. Where foundations contain poten- GSI - 100 tially unstable blocks that may slide from the foundation, the For GSI > 25, a = 0.5, and s = exp . For GSI < 25, 9 shear strength parameters of the discontinuities should be used GSI s = 0, and a = 0.65 - . in design, rather than the rock mass strength. 200

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46 Table 13. GSI estimates for rock masses (Hoek and Marinos, 2000). Geological Strength Index Smooth, moderately weathered or altered surfaces Slickensided, highly weathered surfaces with soft compact coatings or fillings of angular fragments Rough, slightly weathered, iron stained surfaces Slickensided, highly weathered surfaces with From the letter codes describing the structure and surface of the rock mass, select the appropriate box in this chart. Estimate the Very rough, fresh unweathered surfaces average value of the geological strength index (GSI) from the contours. Do not attempt to be too precise, i.e., quoting a range of GSI from 36 to 42 is more realistic than stating that GSI=38. clay coatings or fillings VERY GOOD VERY POOR GOOD POOR Fair STRUCTURE Decreasing Surface Quality BLOCKY very well interlocked 80 undisturbed rock mass consisting of Decreasing Interlocking of Rock Pieces cubical blocks formed by three 70 orthogonal discontinuity sets. 60 VERY BLOCKY interlocked, partially disturbed rock mass with multifaceted 50 angular blocks formed by four or more discontinuity sets. 40 BLOCKY/DISTURBED folded and/or faulted with angular blocks formed by many intersecting discontinuity sets. 30 DISINTEGRATED poorly 20 interlocked, heavily broken rock mass with a mixture of angular and rounded rock pieces. 10 The Hoek-Brown constant (mi) can be determined from technical Society, 2006). The ranges of values depend upon the triaxial testing of core samples using the procedure discussed granularity and interlocking of the crystal structure. Higher by Hoek et al. (1995) or can be determined from the values values are associated with tightly interlocked and more fric- given in Table 14 (Canadian Geotechnical Society, 2006). Most tional characteristics. of the values provided in Table 14 have been derived from triaxial testing on intact core samples. The ranges of values shown reflect the natural variability in the strength of earth 1.8.3 Current AASHTO (2008) Practice materials and depend upon the accuracy of the lithological description of the rock. For example, Marinos and Hoek The strength of intact rock material is determined using (2001) note that the term "granite" describes a clearly defined the results of unconfined compression tests on intact rock rock type that exhibits very similar mechanical characteristics, cores, splitting tensile tests on intact rock cores, or point load independent of origin. As a result, mi for granite is defined as strength tests on intact specimens of rock. The rock is classi- 323. On the other hand, volcanic breccia is not very precise fied using the RMR system as described in Table 15. For each in terms of mineral composition, with the result that mi is given of the five parameters in Table 15, the relative rating based on as 195, denoting a higher level of uncertainty (Canadian Geo- the ranges of values provided is to be evaluated. The RMR is

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47 Table 14. Values of the Hoek-Brown Constant (mi ) for intact rock by rock group (Marinos and Hoek, 2001). Silstone Claystone Conglomerate Sandstone (72) (42) Clastic Breccia1 (174) Greywacke Shale (62) (183) Marl (72) Crystalline Spartic Micritic Sedimentary Dolomite Carbonates Limestone Limestone Limestone (93) (123) (102) (92) Non-clastic Gypsum Anhydrite Evaporites (82) (122) Organic Chalk (72) Hornfels (194) Quartzite Non-foliated Marble (93) Meta (203) Sandstone Metamorphic (193) Slightly Migmatite Amphibolite Gneiss foliated (293) (266) (285) Schist Phyllite Foliated2 Slate (74) (123) (73) Granite (323) Diorite Light Granodiorite (255) Plutonic (293) Gabbro (273) Dolerite Dark Norite (205) (165) Porphyry Diabase Peridotite Hypabyssal Igneous (205) (155) (255) Ryolite Dacite (255) (253) Lava Andesite Basalt Volcanic (255) (255) Agglomerate Breccia Tuff Pyroclastic (193) (195) (135) Notes: Values in parentheses are estimates. 1 Conglomerates and breccias may have a wide range of values, depending on the nature of the cementing material and the degree of cementation. Values range between those of sandstone and those of fine-grained sediments. 2 These values are for intact rock specimens tested normal to bedding or foliation. Values of mi will be significantly different if failure occurs along a weakness plane. determined as the sum of all five relative ratings. The RMR where should be adjusted in accordance with the criteria in Table 16. Jn = number of sets of discontinuities, The rock classification should be determined in accordance Jr = roughness of discontinuities, and with Table 17. Emphasis is placed on visual assessment of Ja = discontinuity condition and infilling. the rock and the rock mass because of the importance of the discontinuities in rock. The geomechanics classification can GSI = 9 log e Q + 44 (91) be used to estimate the value of GSI for cases where RMR is Table 18 gives the values of the parameters used to evalu- greater than 23, as follows: ate Q in Equation 90. The determination of the shear strength of fractured GSI = RMR89 - 5 (89) rock masses is essential in foundation design analyses. The Hoek and Brown criteria can be used to evaluate the shear where RMR89 = RMR according to Bieniawski (1989) as pre- strength of fractured rock masses in which the shear strength sented in Table 17. For RMR89 values less than 23, the mod- is represented as a curved envelope that is a function of the ified Tunneling Quality Index (Q) is used to estimate the unconfined compressive strength of the intact rock, qu, and value of GSI: two dimensionless constants, m and s. The values of m and s as defined in Table 19 should be used. The shear strength RQD J r Q = (90) of the rock mass should be determined using the method Jn Ja

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48 Table 15. Geomechanics classification of rock masses (AASHTO, 2008, Table 10.4.6.4-1). PARAMETER RANGES OF VALUES Point load >175 85175 2045 For this low range, unconfined Strength strength 4585 ksf ksf ksf ksf compressive test is preferred of intact index 1 rock Unconfined 2,160 520 material >4,320 1,080 215 70215 compressive 4,320 1,080 2070 ksf ksf 2,160 ksf 520 ksf ksf strength ksf ksf Relative Rating 15 12 7 4 2 1 0 Drill core quality RQD 90% to 100% 75% to 90% 50% to 75% 25% to 50% <25% 2 Relative Rating 20 17 13 8 3 Spacing of joints >10 ft 310 ft 13 ft 2 in1 ft <2 in 3 Relative Rating 30 25 20 10 5 Very rough Slightly Slightly Slicken- Soft gouge surfaces rough rough sided >0.2 in Not surfaces surfaces surfaces or thick or continuous Separation Separation Gouge Joints open No 0.2 in Condition of joints separation Hard joint Soft joint thick or Continuous 4 Hard joint wall rock wall rock Joints open joints wall rock 0.050.2 in Continuous joints Relative Rating 25 20 12 6 0 Inflow per Ground 30 ft water None 2,000 gal/hr tunnel conditions length (use one of the three evaluation Ratio = 5 criteria as joint water appropriate pressure/ to the 0 0.00.2 0.20.5 >0.5 major method of principal exploration) stress General Completely Moist only Water under Severe water Conditions Dry (interstitial water) moderate pressure problems Relative Rating 10 7 4 0 Table 16. Geomechanics rating adjustment for joint orientations (AASHTO, 2008, Table 10.4.6.4-2). Strike and dip Very Very orientations of Favorable Fair Unfavorable favorable unfavorable joints Tunnels 0 2 5 10 12 Ratings Foundations 0 2 7 15 25 Slopes 0 5 25 50 60

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49 Table 17. Geomechanics rock mass classes determined from total ratings (AASHTO, 2008, Table 10.4.6.4-3). RMR rating 10081 8061 6041 4021 <20 Class No. I II III IV V Very good Good Poor Very Description Fair rock rock rock rock poor rock developed by Hoek (1983) and Hoek and Brown (1988, 1997) of a sample of rock core (Ei) or the modulus determined from as follows: one of the following equations: qu RMR-10 = ( cot i - cos i )m (92) Em = 145 10 40 (93) 8 where where = the shear strength of the rock mass (ksf), Em = elastic modulus of the rock mass (ksi), qu = average unconfined compressive strength of rock Em Ei, core (ksf), Ei = elastic modulus of intact rock from tests (ksi), and m, s = constants from Table 19, RMR = rock mass rating. n = effective normal stress (ksf), and i = the instantaneous friction angle of the rock mass or (degrees): E -1 Em = m Ei (94) -3 2 Ei i = tan -1 4h cos 2 30 + 0.33 sin -1 h 2 - 1 where Em is the elastic modulus of the rock mass (ksi), and + squ ) 16 (m n Em/Ei is a reduction factor based on RQD determined from h = 1+ 3m 2qu Table 20 (dim.). For critical or large structures, determination of rock mass When a major discontinuity with a significant thickness of modulus (Em) using in situ tests may be warranted. It is infilling is to be investigated, the shear strength is governed by extremely important to use the elastic modulus of the rock the strength of the infilling material and the past and expected mass for computation of displacements of rock materials future displacement of the discontinuity. The elastic modulus under applied loads. Use of the intact modulus will result in of a rock mass (Em) is taken as the lesser of the intact modulus unrealistic and unconservative estimates. Poisson's ratio for Table 18. Joint parameters used to determine Q' (Barton et al., 1974). 3. Discontinuity condition and 1. No. of sets of discontinuities = Jn infilling = Ja Massive 0.5 3.1 Unfilled cases One set 2 Healed 0.75 Two sets 4 Stained, no alteration 1 Three sets 9 Silty or sandy coating 3 Four or more sets 15 Clay coating 4 Crushed rock 20 3.2 Filled discontinuities Sand or crushed rock infill 4 2. Roughness of Discontinuities = Jr Stiff clay infilling < 5 mm 6 Noncontinuous joints 4 Soft clay infill < 5 mm thick 8 Rough, wavy 3 Swelling clay < 5 mm 12 Smooth, wavy 2 Stiff clay infill > 5 mm thick 10 Rough, planar 1.5 Soft clay infill > 5 mm thick 15 Smooth, planar 1 Swelling clay > 5 mm 20 Slick and planar 0.5 Filled discontinuities 1 Note: Add + 1 if mean joint spacing > 3 m.

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50 Table 19. Approximate relationship between rock mass quality and material constants used in defining nonlinear strength (Hoek and Brown, 1988; AASHTO, 2008, Table 10.4.6.4-4). Rock type A = Carbonate rocks with well developed crystal cleavage-- dolomite, limestone, and marble B = Lithified argrillaceous rocks--mudstone, siltstone, shale, and slate (normal to cleavage) C = Arenaceous rocks with strong crystals and Rock quality Constants poorly developed crystal cleavage-- sandstone and quartzite D = Fine grained polyminerallic igneous crystalline rocks-- andesite, dolerite, diabase, and rhyolite E = Coarse-grained polyminerallic igneous and metamorphic crystalline rocks-- amphibolite, gabbro, gneiss, granite, norite, quartz-diorite A B C D E INTACT ROCK SAMPLES Laboratory size m 7.00 10.00 15.00 17.00 25.00 specimens free from s 1.00 1.00 1.00 1.00 1.00 discontinuities. CSIR rating: RMR = 100 VERY GOOD QUALITY ROCK MASS Tightly interlocking undisturbed m 2.40 3.43 5.14 5.82 8.567 rock with unweathered s 0.082 0.082 0.082 0.082 0.082 joints at 310 ft. CSIR rating: RMR = 85 GOOD QUALITY ROCK MASS Fresh to slightly weathered rock, slightly m 0.575 0.821 1.231 1.395 2.052 disturbed with joints at 3 s 0.00293 0.00293 0.00293 0.00293 0.00293 10 ft. CSIR rating: RMR = 65 FAIR QUALITY ROCK MASS Several sets of m 0.128 0.183 0.275 0.311 0.458 moderately weathered joints s 0.00009 0.00009 0.00009 0.00009 0.00009 spaced at 13 ft. CSIR rating: RMR = 44 POOR QUALITY ROCK MASS Numerous weathered joints at 2 to 12 m 0.029 0.041 0.061 0.069 0.102 in; some gouge. Clean s 3 x 10-6 3 x 10-6 3 x 10-6 3 x 10-6 3 x 10-6 compacted waste rock. CSIR rating: RMR = 23 VERY POOR QUALITY ROCK MASS Numerous heavily weathered joints m 0.007 0.010 0.015 0.017 0.025 spaced < 2 in with gouge. s 1 x10-7 1 x10-7 1 x10-7 1 x10-7 1 x10-7 Waste rock with fines. CSIR rating: RMR = 3 rock is determined from tests on intact rock core. Where tests block size and shape, joint strength, and a scale factor are the on rock core are not practical, Poisson's ratio may be esti- most important parameters that should be used when esti- mated from Table 21. mating the rock mass strength. Based on findings, selected systems and criteria have been discussed in this chapter. These include RMR, GSI, and the Hoek-Brown criterion. 1.8.4 Summary GSI is similar to RMR, but incorporates newer versions of A common way of determining the rock mass strength is Bieniawski's original system (Bieniawski 1976, 1989). The by using a failure criterion. The existing rock mass failure Hoek-Brown criterion is the most widely used failure criterion criteria are stress dependent and often include one or sev- for estimating the strength of jointed rock masses despite its eral parameters that describe the rock mass properties. lack of a theoretical basis and the limited amount of exper- These parameters are usually based on classification or char- imental data that went into the first development of the cri- acterization systems. The unconfined compressive strength, terion (Sjberg, 1997).

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51 Table 20. Estimation of Em based on RQD (O'Neill and Reese, 1999; AASHTO, 2008, Table 10.4.6.5-1). RQD Em/Ei (percent) Closed joints Open joints 100 1.00 0.60 70 0.70 0.10 50 0.15 0.10 20 0.05 0.05 Table 21. Summary of Poisson's Ratio for intact rock (AASHTO, 2008, Table C10.4.6.5-2, modified after Kulhawy, 1978). No. of No. of Poisson's Ratio, Standard Rock type rock values Minimum Maximum Mean deviation types Granite 22 22 0.39 0.09 0.2 0.08 Gabbro 3 3 0.2 0.16 0.18 0.02 Diabase 6 6 0.38 0.2 0.29 0.06 Basalt 11 11 0.32 0.16 0.23 0.05 Quartzite 6 6 0.22 0.08 0.14 0.05 Marble 5 5 0.4 0.17 0.28 0.08 Gneiss 11 11 0.4 0.09 0.22 0.09 Schist 12 11 0.31 0.02 0.12 0.08 Sandstone 12 9 0.46 0.08 0.2 0.11 Siltstone 3 3 0.23 0.09 0.18 0.06 Shale 3 3 0.18 0.03 0.09 0.06 Limestone 19 19 0.33 0.12 0.23 0.06 Dolostone 5 5 0.35 0.14 0.29 0.08