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20 approximate measure of overall rock quality. RQD is most account for the effects of discontinuities, rock quality, and useful when combined with other parameters accounting for other factors. rock strength, deformability, and discontinuity characteris- tics. As discussed in subsequent sections of this report, many Table 7 lists the laboratory tests for intact rock most com- of the rock mass classification systems in use today incorpo- monly done for foundation design and gives the ASTM rate RQD as a key parameter. Standard Designation for each test. More thorough coverage of laboratory testing of intact rock is given by Mayne et al. Rock Mass Description RQD (2001), the Rock Testing Handbook (1993), and the Excellent 90100 AASHTO Manual on Subsurface Investigations (1988). Good 7590 Fair 5075 Engineering properties of intact rock that are used most Poor 2550 often for foundation design are uniaxial compressive Very Poor <25 strength (qu) and elastic modulus (ER). The compressive strength of intact rock is determined by applying a vertical ENGINEERING PROPERTIES OF ROCK compressive force to an unconfined cylindrical specimen prepared from rock core. The peak load is divided by the Laboratory Tests on Intact Rock cross-sectional area of the specimen to obtain the uniaxial compressive strength (qu). The ASTM procedure (D2938) Intact rock refers to the consolidated and cemented assem- specifies tolerances on smoothness over the specimen blage of mineral particles forming the rock material, ex- length, flatness of the ends, the degree to which specimen cluding the effects of macro-scale discontinuities such as ends are perpendicular to the length, and length-to-diameter joints, bedding planes, minor faults, or other recurrent pla- ratio. Uniaxial compressive strength of intact rock is nar fractures. The term rock mass is used to describe the sys- used in empirical correlations to evaluate ultimate side tem comprised of intact rock and discontinuities. The char- and base resistances under axial loading; ultimate limit acteristics of intact rock are determined from hand pressure under lateral loading; and, by contractors, to as- specimens or rock core. Properties of intact rock required for sess constructability. proper characterization of the rock mass and that are rele- vant to foundation design include strength and deformabil- Elastic modulus of intact rock is measured during conduct ity. For some rock types, the potential for degradation on ex- of the uniaxial compression test by measuring deformation as posure to atmospheric conditions may also need to be a function of load. It is common to measure both axial and di- evaluated. Some design methods incorporate properties of ametral strain during compression to determine elastic mod- intact rock directly; for example, correlations between ulti- ulus and Poisson's ratio. Test procedures are given in ASTM mate unit side resistance and uniaxial compressive strength. Standard (D3148) and discussed further by Wyllie (1999). It However, most analytical treatments of foundation capacity is important to note that the ASTM procedure defines several and load-deformation response incorporate the strength and methods of determination of modulus, including tangent deformability of intact rock into rock mass models that also modulus at a specified stress level, average modulus over the TABLE 7 COMMON LABORATORY TESTS FOR INTACT ROCK Test Category Name of Test and ASTM Designation Comments Uniaxial Unconfined compressive strength of intact Primary test for strength and deformability compression rock core specimen (D2938) of intact rock; input parameter for rock mass classification systems Split tensile Splitting tensile strength of intact rock core Splitting tensile strength of a rock disk under specimens (D3967) a compression line load Point load Determination of the point load strength index Index test for rock strength classification; strength of rock (D5731) can be performed in field on core pieces unsuitable for lab testing Direct shear Laboratory direct shear strength tests for rock Applies to intact rock strength or to shear specimens under constant normal stress strength along planes of discontinuities, (D5607) including rockconcrete interface Strength- Elastic moduli of intact rock core specimens in Young's modulus from axial stressstrain deformation uniaxial compression (D3148) curve; Poisson's ratio can also be determined Durability Slake durability of shales and similar weak Index test to quantify the durability of weak rocks (D4644) rocks under wetting and drying cycles with abrasion

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21 linear portion of the stressstrain curve, and secant modulus C is a correlation factor that should be established on a site- at a fixed percentage of maximum strength. For rocks that specific basis by conducting a limited number of uniaxial exhibit nonlinear stressstrain behavior, these methods may compression tests on prepared core samples. If a site-specific provide significantly different values of modulus and it is value of C is not available, the ASTM Standard recommends important to note which method was used when reporting val- approximate values based on core diameter. For a 54 mm ues of modulus. core (NX core size), the recommended value of C is 24. The principal advantages of the point load test are that it can The point load test is conducted by compressing a core be carried out quickly and inexpensively in the field at the sample or irregular piece of rock between hardened steel site of drilling and that tests can be conducted on irregular cones (Figure 13), causing failure by the development of ten- specimens without the preparation required for uniaxial com- sile cracks parallel to the axis of loading. The uncorrected pression tests. point load strength index is given by Split tensile strength (qt) of rock (ASTM D4644) is deter- Is = P/D2 (4) mined by compressing a cylindrical disk under a compressive line load. Split tensile strength has been correlated with unit where P = load at rupture, and D is the distance between the side resistance; for example, by McVay et al. (1992) for point loads. The point load index is reported as the point load drilled shafts in Florida limestone. strength of a 50 mm core. For other specimen sizes a correc- tion factor is applied to determine the equivalent strength of Direct shear testing is applicable to determination of the a 50 mm specimen. The point load index is correlated to uni- MohrCoulomb shear strength parameters cohesion, c, and axial compressive strength by friction angle, , of discontinuity surfaces in rock (ASTM D5607). Shear strength of discontinuities may govern capac- qu = C Is(50) (5) ity in certain conditions; for example, base capacity of sock- eted foundations when one or two intersecting joint sets are where qu is the unconfined compressive strength, Is(50) is the oriented at an intermediate angle to horizontal. The other no- point load strength corrected to a diameter of 50 mm, and table application of this test is in simulating the shear strength at the rockconcrete interface for evaluation of side resistance of socketed shafts under axial loading. However, for this application, the constant normal stiffness (CNS) di- rect shear test described by Johnston et al. (1987) is more ap- plicable. Instead of a constant normal load, normal force is applied through a spring that increases or decreases the ap- plied force in proportion to the magnitude of normal dis- placement (dilation). Dilatancy of the interface is a major factor controlling strength and stiffness of socketed shafts under axial load. The slake durability test (ASTM D4644) provides an index for identifying rocks that will weather and degrade rapidly. The test is appropriate for argillaceous sedimentary rocks (mudstone, shale, clayshales) or any weak rock. Representa- tive rock fragments are placed in a wire mesh drum and dried in an oven to constant weight. The drum is partially sub- merged in water and rotated at 20 revolutions per minute for a period of 10 min. The drum and its contents are then dried a second time and the loss of weight is recorded. The test cycle is repeated a second time and the slake durability index, ID, is calculated as the ratio (reported as a percentage) of final to ini- tial dry weights of the sample. Rocks with ID < 60 are consid- ered prone to rapid degradation and may indicate a suscepti- bility to degradation of the borehole wall when water is introduced during drilling, potentially leading to formation of a "smear zone." Hassan and O'Neill (1997) define the smear zone as a layer of soil-like material along the socket wall and demonstrate that smearing can have a significantly negative FIGURE 13 Point load test setup. effect on side load transfer of shafts in argillaceous rock.

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22 In Situ Tests for Rock rock modulus from laboratory uniaxial compression tests. The borehole jack was recommended as a field test that, with In situ testing can be used to evaluate rock mass deformation proper analysis (Heuze 1984), yields values of rock mass modulus and, in some instances, RMS. In situ testing meth- modulus that are consistent with results from large plate bear- ods with potential applications to rock-socket design are ing tests. The borehole jack designed for NX sized borings presented in Table 8. In situ testing of rock is not performed (75 mm or 3 in. diameter) affects a "test volume" of approxi- routinely for rock-socket design by most of the agencies mately 0.14 m3 (5 ft3). Borehole jack devices are available surveyed for this study. The survey responses indicate that commercially with limit pressures of up to 69 MPa, allowing five state DOTs currently use the pressuremeter test (PMT) the test to reach stress levels beyond the elastic limit and, for to obtain design parameters. Of these, all five use the test some weak rock masses, to ultimate strength. to obtain rock mass modulus. One state reported the use of PMT to evaluate RMS in weak rocks. Four states use the Studies on the use of PMTs for determination of rock mass PMT for correlating test results with the parameters that de- modulus include those of Rocha et al. (1970), Bukovansky fine p-y curves for analysis of shafts under lateral loading (1970), Georgiadis and Michalopoulos (1986), and Littlechild (chapter four). The term dilatometer is also used to describe a et al. (2000). Results have been mixed, with some research- pressuremeter intended for use in rock but should not be con- ers indicating a high degree of agreement between PMT fused with the flat plate dilatometer used for in situ testing of modulus and other in situ tests (e.g., Rocha et al. 1970) and soil. One state (Massachusetts) reported using the borehole others reporting PMT modulus values significantly lower jack to measure rock mass modulus. No states reported using than modulus measured by plate-load and borehole jack tests the plate load test for rock-socket design. Information on (e.g., Bukovansky 1970). Littlechild et al. (2000) concluded conduct and interpretation of the tests identified in Table 8 that PMTs, using the Cambridge High Pressure Dilatometer, and other in situ tests for rock are given in the relevant were not useful for determination of rock mass modulus for ASTM standards, Rock Testing Handbook (1993) and Mayne design of deep foundations in several rock types in Hong et al. (2001). Kong. In strong and massive rocks such as metasiltstone and tuff, the device did not have sufficient capacity to measure Heuze (1980) investigated the effect of test scale on the modulus, which typically was around 10 GPa. In highly frac- modulus of rock masses. Several types of field tests, includ- tured granodiorite, membrane failures were problematic. ing borehole jack and plate load tests at different scales, were Commercially available pressuremeter devices for rock are included and results were compared with those of laboratory currently limited to maximum pressures of around 30 MPa. compression tests. It was observed that in situ rock mass Additional discussion of rock mass modulus is presented modulus values generally range from 20% to 60% of intact later in this chapter. TABLE 8 IN SITU TESTS WITH APPLICATIONS TO ROCK-SOCKET DESIGN Method Procedure Rock Properties Limitations/Remarks Pressuremeter Pressuremeter is lowered to the Rock mass modulus; Test affects a small area of rock (includes devices test elevation in a prebored rock mass strength mass; depending on joint referred to as hole; flexible membrane of in weak rocks spacing, may or may not rock dilatometer) probe is expanded exerting a ASTM D4719 represent mass behavior; limited uniform pressure on the to soft or weak rocks sidewalls of the borehole Borehole jack Jacks exert a unidirectional Rock mass modulus; Measured modulus value must pressure to the walls of a rock mass strength be corrected to account for borehole by means of two in weak rocks stiffness of steel platens; test opposed curved steel platens ASTM D4971 method can be used to provide an estimate of anisotropy Plate load test Load is applied to a steel plate Rock mass modulus; Loaded area is limited, so may or concrete foundation using a rock mass strength not be effectively testing rock system of hydraulic jacks and a in weak rocks mass if joints are widely spaced; reaction frame anchored to the modulus values corrected for foundation rock plate geometry, effect of rock breakage, rock anisotropy, and steel plate modulus; not common for deep foundations Texas cone Steel cone is driven by a drop Correlated to Limitations similar to those of penetration test hammer; number of blows per compressive strength Standard Penetration Test; 300 mm of penetration is TCPT of weak rocks currently used by Texas and N-value; depth of penetration encountered in Oklahoma DOTs for direct per 100 blows is penetration Texas and Oklahoma correlation to side and base resistance (PR) resistance of shafts in weak rock Notes: Adapted from Geotechnical Engineering Circular No. 5 (Sabatini et al. 2002). TCPT = Texas Cone Penetration Test.

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23 An example of an in situ test that is used in a specific re- described by Bieniawski (1976, 1989) and the Rock Quality gion of the country is the Texas Cone Penetration Test Tunneling Index described by Barton et al. (1974). Both sys- (TCPT). A 76-mm-diameter solid steel cone is driven by a tems were developed primarily for application to tunneling 77 kg (170 lb) drop hammer. The number of blows required in rock, but have been extended to other rock engineering to drive 300 mm (12 in.) is recorded and the results are given problems. The application of classification systems to rock- in one of two ways: (1) number of blows per 300 mm of pen- socket design has been limited to correlations between clas- etration or TCPT N-value, or (2) the depth of penetration per sification parameters and RMS and deformation properties. 100 blows, referred to as the penetration resistance or PR. To facilitate such correlations, Hoek et al. (1995) introduced The Texas and Oklahoma DOTs use empirical correlations the GSI. Relationships were developed between GSI and the between the TCPT parameters and drilled shaft side and base rock mass classifications of Bieniawski and Barton et al. The resistances in soil and soft rock. The test procedure and principal characteristics of the two classification systems are correlations are available in the Texas DOT Geotechnical summarized, followed by a description of their relationship Manual, which can be accessed online. Some researchers to GSI. For more detailed discussion, including limitations have developed empirical correlations between TCPT mea- and recommended applications, consult the original refer- surements and properties of soft rock. For example, Cavu- ences and Hoek et al. (1995, 2002). soglu et al. (2004) show correlations between compressive strength of upper Cretaceous formation clay shales (UU tri- The Geomechanics Classification is based on determina- axial tests) and limestone (unconfined compression) and PR tion of the RMR, a numerical index determined by summing measurements conducted for Texas DOT projects. The cor- the individual numerical ratings for the following five cate- relations are highly formation-dependent and exhibit a high gories of rock mass parameters: degree of scatter, but provide first order estimates of rock strength based on TCPT resistance in formations where sam- Strength of intact rock, ple recovery is otherwise difficult. Drill core quality (in terms of RQD), Spacing of discontinuities, In addition to the tests identified as being applicable to Condition of discontinuities, and rock, it is common practice to use in situ tests for soil to Groundwater conditions. define the contact boundary between soil and rock. Of the agencies surveyed, 21 reported using the Standard Penetra- An adjustment is made to the RMR for the degree to tion Test (SPT) and 3 reported using the Cone Penetration which joint orientation may be unfavorable for the problem Test (CPT) to define the top-of-rock elevation. "Refusal" of under consideration. The classification system is presented in the SPT or CPT penetration is the method most often used to Table 9. Based on the RMR value, a rock mass is identified identify rock. Limitations of this approach include the possi- by one of five rock mass classes, ranging from very poor rock bility of mistaking cobbles or boulders for the top-of-rock to very good rock. The draft 2006 Interim AASHTO LRFD and the lack of consistency in SPT blowcounts in weak or Bridge Design Specifications recommends determination of weathered rock. RMR for classification of rock mass in foundation investiga- tions. Seventeen states reported using RMR either always or Six states reported using the SPT in soft or weak rock to sometimes for rock mass classification associated with obtain rock properties (unconfined compressive strength) or drilled shaft design. for correlating SPT N-values directly to design parameters, principally unit side resistance. For example, the Colorado Barton and co-workers at the Norwegian Geotechnical In- SPT-Based Method is used by the Colorado DOT to estab- stitute proposed a Tunneling Quality Index (Q) for describing lish design values of both unit side resistance and base resis- rock mass characteristics and tunnel support requirements tance for shafts socketed into claystones when the material (Barton et al. 1974). The system is commonly referred to as cannot be sampled in a way that provides intact core speci- the NGI-Q system or simply the Q-system. The numerical mens adequate for laboratory uniaxial compression tests value of the index Q varies on a log scale from 0.001 to 1,000 (Abu-Hejleh et al. 2003). O'Neill and Reese (1999) correlate and is defined as: unit side resistance with N-values for shafts in cohesionless IGMs, defined as materials with N > 50. Direct correlations RQD J r J Q= w (6) between design parameters and N values are considered fur- Jn J a SRF ther in chapter three. where RQD = rock quality designation, Rock Mass Classification Jn = joint set number, Jr = joint roughness number, Several empirical classification systems have been proposed Ja = joint alteration number, for the purpose of rating rock mass behavior. The most Jw = joint water reduction factor, and widely used systems are the Geomechanics Classification SRF = stress reduction factor.

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24 TABLE 9 GEOMECHANICS CLASSIFICATION SYSTEM FOR DETERMINATION OF ROCK MASS RATING (RMR) A. Classification Parameters and Their Ratings (after Bieniawski 1989) Parameter Ranges of Values 1 Strength For this low of Point load range, uniaxial intact strength >10 410 24 12 rock index, MPa comp. test is material preferred Uniaxial comp. strength, >250 100250 50100 2550 525 15 <1 MPa Rating 15 12 7 4 2 1 0 2 Drill core quality, RQD (%) 90100 7590 5075 2550 <25 Rating 20 17 13 8 3 3 Spacing of discontinuities >2 m 0.62 m 200600 mm 60200 mm <60 mm Rating 20 15 10 8 5 4 Condition of discontinuities Slightly Slickensided Very rough rough Slightly rough surfaces or Soft gouge >5 surfaces, surfaces, surfaces, gouge <5 mm mm thick or not continuous, separation separation <1 thick or separation >5 no separation, <1 mm, mm, highly joints open 1 to mm unweathered slightly weathered 5 mm continuous wall rock weathered walls continuous walls Rating 30 25 20 10 0 5 Ground- water Inflow per 10 m None 125 tunnel length Ratio: Joint water pressure/ major principal 0 0.5 stress General Completely dry Damp Wet Dripping Flowing conditions Rating 15 10 7 4 0 B. Rating Adjustment for Joint Orientations Strike and dip Very Very orientations favorable Favorable Fair Unfavorable Unfavorable Ratings Foundations 0 2 7 15 25 C. Rock Mass Classes Determined from Total Ratings RMR 100 to 81 80 to 61 60 to 41 40 to 21 <20 Class Number I II III IV V Very good Description rock Good rock Fair rock Poor rock Very poor rock Three states reported using the Q-system in connection GSI = 9LogeQ ' + 44 (9) with rock-socket design. A modified Tunneling Quality In- dex (Q') is utilized to determine the GSI, as described Table 10 gives the values of the parameters used to evaluate subsequently. Q ' by Eq. 8. The Geomechanics Classification can be used to estimate the value of GSI for cases where RMR is greater than 23, as Engineering Properties of Rock Mass follows: Shear Strength GSI = RMR89 5 (7) Geotechnical evaluation of foundation ultimate capacity un- der axial and lateral loading is calculated on the basis of shear in which RMR89 is the RMR according to Bieniawski (1989) strength along assumed failure surfaces in the rock or at the as presented in Table 9. For RMR89 values less than 23, the concreterock interface. Depending on the failure mode, the modified (Q) is used to estimate the value of GSI, where: strength may need to be defined at one of three levels: (1) in- tact rock, (2) along a discontinuity, and (3) representative of RQD Jr a highly fractured rock mass. Figure 14 illustrates these cases Q' = (8) Jn Ja for a socketed foundation in rock. For example, bearing

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25 TABLE 10 JOINT PARAMETERS USED TO DETERMINE Q ' 1. No. of Sets of Discontinuities = Jn 3. Discontinuity Condition & 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. Modified from Barton et al. (1974). capacity at the base of a socketed foundation in massive rock most common test for intact rock is the uniaxial (unconfined) would be evaluated in terms of the strength of the intact rock. compression test, which can be considered a special case of If the rock has regular discontinuities oriented as shown in triaxial testing with zero confining stress. The strength pa- level 2, base capacity may be controlled by the strength along rameter obtained is the uniaxial compressive strength, qu, the joint surfaces. If the rock is highly fractured (level 3), which is related to the MohrCoulomb strength parameters by bearing capacity would have to account for the overall strength of the fractured mass. qu = 2c tan (45 + 1/2 ) (11) For each of the three cases, shear strength may be ex- However, the strength of intact rock is normally given simply pressed within the framework of the MohrCoulomb failure in terms of qu. Stability analyses of rock sockets governed by massive rock are normally evaluated directly in terms of qu. criterion, where shear strength () is given by When rock core is not sufficient for uniaxial compression = c' + ' tan ' (10) testing, or sometimes for convenience, qu is correlated to re- sults of point load tests. Uniaxial compressive strength is also in which c' = effective stress cohesion intercept, ' = effec- one of the parameters used for evaluating the strength of tive stress angle of friction, and ' = effective normal stress highly fractured rock masses, as discussed later. on the failure plane. Evaluation of shear strength for each of the three cases is summarized as follows. Shear strength of discontinuities can be determined using laboratory direct shear tests. The apparatus is set up so that For intact rock the parameters c' and ' can be determined the discontinuity surface lies in the plane of shearing between from laboratory triaxial shear tests on specimens prepared the two halves of the split box. Both peak and residual val- from core samples. Triaxial testing procedures are given by ues of the strength parameters (c' and ') are determined. ASTM D2664 and AASHTO T226. The survey of state Discussion of direct shear testing of discontinuities, includ- DOTs indicates that triaxial testing is not used routinely. The ing its limitations, is given by Wyllie and Norrish (1996). For a planar, clean fracture (no infilling), the cohesion is zero and the shear strength is defined only by the friction angle. The roughness of the surface has a significant effect on the value of friction angle. If the discontinuity contains infilling, the strength parameters will be controlled by the thickness and properties of the infilling material. Compilations of typical representative ranges of strength parameter values for discon- tinuities are summarized in Mayne et al. (2001). The survey re- sults indicate that direct shear testing of joints is not conducted routinely by DOT agencies for rock-socket design. Shear failure along joint For intact rock masses and for fractured or jointed rock (a) Massive rock (b) Jointed rock (c) Highly fractured rock masses, Hoek and Brown (1980) proposed an empirical crite- FIGURE 14 Base failure modes illustrating different operational rion for characterizing RMS. Since its appearance, this criterion shear strength conditions. has been applied widely in practice and considerable experience

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26 has been gained for a range of rock engineering problems. Based (1988) suggested that the constants mb, s, and a could be related on these experiences, the criterion has undergone several stages empirically to the RMR described previously. Hoek et al. (1995) of modification, most significantly by Hoek and Brown (1988), noted that this process worked well for rock masses with RMR Hoek et al. (1995, 2002), and Marinos and Hoek et al. (2000). greater than about 25, but not well for very poor rock masses. The nonlinear RMS is given by: To overcome this limitation, the GSI was introduced. Sug- a gested relationships between GSI and the parameters mb/mi, s, ' and a, according to Hoek et al. (2002) are as follows: 1 ' = 3 ' + qu mb 3 + s (12) qu GSI - 100 = exp mb 28 - 14 D (13) where mi '1 and '3 = major and minor principal effective stresses, GSI - 100 respectively; s = exp (14) qu = uniaxial compressive strength of intact rock; 9 - 3D and mb, s, and a are empirically determined strength parame- 1 1 -15 GSI -20 a= + e -e 3 (15) ters for the rock mass. 2 6 The value of the constant m for intact rock is denoted by in which D is a factor that depends on the degree of disturbance mi and can be estimated from Table 11. Hoek and Brown to the rock mass caused by blast damage and stress relaxation. TABLE 11 VALUES OF THE CONSTANT mi BY ROCK GROUP (Hoek et al. 1995) Rock Class Group Texture Type Coarse Medium Fine Very fine Conglomerate Sandstone Siltstone Claystone (22) 19 9 4 Clastic (18) Sedimentary 7 Organic (821) Non-clastic Sparitic Micritic Breccia Carbonate limestone limestone (20) (10) 8 Gypstone Anhydrite Chemical 16 13 Marble Hornfels Quartzite Non-foliated 9 (19) 24 Metamorphic Migmatite Amphibolite Mylonites Slightly foliated (30) 31 (6) Gneiss Schists Phyllites Slate Foliated* 33 (10) (10) 9 Granite Rhyolite Obsidian 33 (16) (19) Granodiorite Dacite Light (30) (17) Diorite An desite Igneous (28) 19 Dark Gabbro Dolerite Basalt 27 (19) (17) Norite 22 Agglomerate Breccia Tuff Extrusive pyroclastic type (20) (18) (15) *These values are for intact rock specimens tested normal to foliation. The value of mi will be significantly different if failure occurs along a foliation plane. Note: Values in parentheses are estimates.

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27 The damage factor D ranges from zero for undisturbed in situ Kulhawy (1978), Wyllie (1999), and the AASHTO LRFD rock masses to 1.0 for very disturbed rock masses. Hoek et al. Bridge Design Specifications (2004). These values should (2002) provide guidance on values of D for application to tun- be considered as general guidelines to expected ranges of nel and rock slope problems, but no work has been published values for different rock types and serve to illustrate the relating D to drilled shaft construction. magnitude of variation that is possible. Rock mass modulus can vary from less than 1 MPa to greater than 100 GPa and Some problems involving fractured rock masses (e.g., bear- depends on intact rock modulus, degree of weathering, and ing capacity) are more readily analyzed in terms of the characteristics of discontinuities. Compiled values provide MohrCoulomb strength parameters than in terms of the guidance for very preliminary evaluations, but should not be HoekBrown criterion. Hoek and Brown (1997) noted that relied on for final design. Values of Poisson's ratio exhibit a there is no direct correlation between the two sets of strength narrow range of values, typically between 0.15 and 0.3. parameters. However, they describe a procedure that involves simulating a set of triaxial strength tests using the HoekBrown Various authors have proposed empirical correlations criterion (Eq. 12) then fitting the MohrCoulomb failure en- between rock mass modulus and other rock mass proper- velope to the resulting Mohr's circles by regression analysis. ties. Table 12 presents, in chronological order, some of the Values of the strength parameters c' and ' defining the in- most widely cited expressions found in the literature. The tercept and tangent slope of the envelope (which is nonlin- earliest published correlations (expressions 1 and 2 of ear) can thus be determined. Hoek et al. (2002) presented the Table 12) relate EM to modulus of intact rock, ER, and RQD. following equations for the angle of friction and cohesive In subsequent correlations (expression 3), RQD is replaced strength of fractured rock masses: by RMR, providing a more comprehensive empirical ap- proach because six rock mass parameters (including RQD) 6amb ( s + mb '3n ) a -1 are incorporated to evaluate the RMR. This was followed ' = sin -1 a -1 (16) 2 1 + a 2 + a + 6amb ( s + mb '3n ) ( ) ( ) by correlations relating EM directly to rock mass indexes, including RMR and Q (expressions 4, 5, and 6). Hoek et al. (1995) show the graph given in Figure 15 with curves given qu [(1 + 2a ) s + (1 - a ) mb '3n ]( s + mb '3n ) a -1 c' = by expressions 4, 5, and 6 of Table 12, along with case his- a -1 (1 + a ) ( 2 + a ) 1 + 6amb ( s + mb '3n ) (17) tory observations. The figure suggests that expression 4 of (1 + a ) ( 2 + a ) Table 12 provides a reasonable fit to the available data and offers the advantage of covering a wider range of RMR val- Applications of the HoekBrown criterion to rock-socket ues than the other equations. The draft 2006 Interim design are discussed further in chapter three (bearing AASHTO LRFD Bridge Design Specifications recommend capacity) and chapter four (lateral capacity). The draft 2006 use of either expression 4 of Table 12 or a method recom- Interim AASHTO LRFD Bridge Design Specifications rec- mended by O'Neill et al. (1996) based on applying a mod- ulus reduction ratio (EM/ER) given as a function of RQD in ommend the HoekBrown strength criterion for RMS char- Table 13. acterization, but the earlier version (Hoek and Brown 1988) is presented rather than the updated version based on GSI. Beginning with Hoek and Brown (1997), proposed corre- lation equations have been based on relating EM to GSI and Deformation Properties properties of intact rock, either uniaxial compressive strength (qu) or intact modulus (ER). In expression 7, EM is reduced Rock mass deformation properties are used in analytical progressively as the value of qu falls below 100 MPa. This re- methods for predicting the load-deformation behavior of duction is based on the reasoning that deformation of better rock-socketed foundations under axial and lateral loads. The quality rock masses is controlled by discontinuities, whereas parameters required by most methods include the modulus of for poorer quality rock masses deformation of the intact deformation of the rock mass, EM, and Poisson's ratio, v. rock pieces contributes to the overall deformation process Methods for establishing design values of EM include: (Hoek and Brown 1997). The version given in Table 12 is updated by Hoek et al. (2002) to incorporate the damage Estimates based on previous experience in similar rocks factor, D. or back-calculated from load tests, Correlations with seismic wave velocity propagation The final correlation (expression 8) in Table 12 was pro- (e.g., Eqs. 13), posed based on analyses by Yang (2006). Figure 16 shows a In situ testing, and comparison of the regression equation (expression 8) to data Empirical correlations that relate EM to strength or mod- from field observations of Bieniawski (1978) and Serafim and ulus values of intact rock (qu or ER) and/or rock mass Pereira (1983), as well as modulus values measured by PMTs characteristics. reported by Yang (2006). Expression 8 was applied to der- ivation of p-y curves for analysis of laterally loaded rock Compilations of typical values of rock mass modulus sockets, described further in chapter four. Additional discus- and Poisson's ratio are given in several sources, including sion of empirical equations for rock mass modulus and their

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28 TABLE 12 EMPIRICAL METHODS FOR ESTIMATING ROCK MASS MODULUS Expression Notes/Remarks Reference Reduction factor on intact Coon and Merritt 1. EM = ER[0.0231(RQD) 1.32] rock modulus; (1969); LRFD Bridge EM/ER > 0.15 Design . . . (2004) 2. For RQD < 70: EM = ER (RQD/350) Reduction factor on intact Bieniawski (1978) For RQD > 70: EM = ER [0.2 + (RQD 70)/37.5] rock modulus RMR Reduction factor on intact 3. E = E 0.1 + rock modulus; Kulhawy (1978) M R 1150 11 .4RMR EM/ER < 1.0 RMR 10 Serafim and Pereira 4. E M (GPa ) = 10 40 0 < RMR < 90 (1983) 5. EM (GPa) = 2 RMR 100 45 < RMR < 90 Bieniawski (1984) 6. EM (GPa) = 25 log10 Q 1 < Q < 400 Hoek et al. (1995) GSI 10 7. E (GPa ) = 1 D qu for qu < 100 MPa 10 40 Adjustment to Serafim M 2 100 Hoek and Brown and Pereira to account for (1997); Hoek et al. D GSI 10 rocks with qu < 100 MPa; E M (GPa ) = 1 10 40 for qu > 100 MPa (2002) note qu in MPa 2 8. E = E R e 21.7 Reduction factor on intact GSI M Liang and Yang (2006) 100 modulus, based on GSI Notes: ER = intact rock modulus, EM = equivalent rock mass modulus, RQD = rock quality designation, RMR = rock mass rating, Q = NGI rating of rock mass, GSI = geological strength index, qu = uniaxial compressive strength. application to foundation engineering is given by Littlechild jack test. At least three other states using PMT for rock did et al. (2000), Gokceoglu et al. (2003), and Yang (2006). not respond to the survey. The principal limitation of in situ testing is whether the volume of rock being tested is represen- Rock mass modulus is a key parameter for rock-socket tative of the in situ rock mass. Factors such as degree of rock load-deformation analysis, which is a key step in the design disturbance, anisotropy, and spacing of discontinuities relative process depicted in Figure 3. Several methods are identified in to the dimensions of the apparatus will determine the degree this chapter for establishing values of EM. These include geo- to which test results represent the response of rock mass to physical methods based on p-wave and s-wave velocities (Eqs. foundation loading. As noted earlier in this chapter, rock mass 1 and 2) or shear wave frequency (Eq. 3), in situ testing meth- modulus measured by pressuremeter shows varying levels of ods (Table 8), and the correlation equations given in Table 12. agreement with other in situ testing methods. The full range of The survey shows that correlation equations are the most application and limitations of PMTs for rock mass modulus widely used method for estimating modulus for rock-socket and its application to rock-socket design have yet to be deter- design, followed by in situ testing. The most common in situ test mined. Correlation equations for rock mass modulus have (used by five states) is pressuremeter (rock dilatometer), with evolved over the years as illustrated by the relationships sum- a single state (Massachusetts) reporting use of the borehole marized in Table 12. Correlations are attractive because they are based on more easily measured properties of intact rock and rock mass indexes, but caution must be exercised because most of the correlations were developed specifically for appli- cations to tunneling. Calibration studies aimed at the applica- tion of correlation equations for rock mass modulus to load- deformation analysis of rock-socketed foundations are largely lacking at the present time. Studies by Littlechild et al. (2000) and Liang and Yang (2006) are exceptions and illustrate the type of additional work that is needed. TABLE 13 ESTIMATION OF MODULUS RATIO (EM /ER) BASED ON RQD (O'Neill et al. 1996) EM/ER RQD (percent) Closed Joints Open Joints 100 1.00 0.60 70 0.70 0.10 50 0.15 0.10 FIGURE 15 Rock mass modulus versus rock mass rating 20 0.05 0.05 (Hoek et al. 1995). RQD = rock quality designation.