Manual on Subsurface Investigations (2019)

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206 C H A P T E R 1 0 Evaluation of Rock Mass Properties Introduction The engineering behavior of rock masses under loading depends upon the assemblage of composite components, including (i) intact rock material and (ii) the set of discontinuities, fissures, joints, and cracks that separate the intact rock. While the rock material itself is quite strong, the fissures and joints permit movement that can adversely affect the performance and integrity of the rock mass. For highway construction, this may result in rock falls, falling boulders or stones, talus, and collection of debris along the roadway, as well as possible instability, collapse, or loss of bridge foundations in the extreme cases. In assessing the quality of the rock mass, it is important to document both components in a classification scheme. The classification of the rock type, mapping of the discontinuities, jointing, shear zones, and fault features is best handled by an experienced engineering geologist and may require field work in the form of site reconnaissance, geophysical testing, and coring of rock samples. The extent of this work will depend on the size of the project, possible consequences, risks associated with construction, and other factors. For highways and roadways, rock mass classification will be necessary on projects involving tunnels, foundations, slopes, and excavations. Calculations will be required to evaluate the strength of the rock mass to quantify the potential for instability and level of support needed. This may necessitate the design of anchors, drainage ducts, rock bolts, shotcrete, fences, netting, cut slope angles, and other measures, such as long-term monitoring and instrumentation programs. The United States covers an immense area with many varied and diverse types of geomaterials (Figure 10-1). Each color represents a distinct unit of the 154 various geologic formations found in the United States. Thus, it is necessary to recognize the importance of understanding local and site-specific geologic settings. Often, the state geological survey provides summary reports on the types of geomaterials, including soils, rocks, and minerals, as well as mining operations found in the local vicinity. These documents should be sought out and reviewed for common performance expectations, including known problems encountered on past civil engineering projects, such as landslides, rockfalls, and sinkholes.

207 Source: William Menke Figure 10-1. Diversity of rock types found in the conterminous United States. Note: each color represents one of 154 different geologic formations Intact Rock Classification Intact rock should be described in terms of its geologic origin (sedimentary, metamorphic, or igneous), color, size of the mineral grains (fine, medium, coarse), strength (i.e., qu = uniaxial compressive strength), and stiffness (i.e., E50 = elastic modulus at 50 percent ultimate strength). Additional factors describing the intact rock may include hardness, age, porosity, and seismic velocities. The primary rock types defined according to geologic origin and mineral grain size are given in Table 10-1. The number in parentheses following the type of rock is a material constant for the intact rock type assigned according to the GSI, which is a rock mass classification system discussed in Section 10.4.3 (Marinos et al. 2005, Hoek 2007). Table 10-1. Primary rock types classified by geologic origin and mineral grain size Grain Aspects Sedimentary Metamorphic Igneous Clastic Carbonate Foliated Non- foliated Intrusive Extrusive Coarse Conglomerate (22) Breccia (20) Limestone (10) Gneiss (33) Amphibolite (31) Marble (9) Migmatite (30) Granite (33) Granodiorite (30) Diorite (28) Volcanic Breccia or Agglomerate (20)

208 Grain Aspects Sedimentary Metamorphic Igneous Clastic Carbonate Foliated Non- foliated Intrusive Extrusive Medium Sandstone (19) Siltstone (9) Greywacke (18) Chalk (7) Schist (10) Phyllite (10) Quartzite (24) Dolerite (19) Basalt (17) Fine Shale (4) Claystone (4) Calcareous Mudstone (8) Slate (9) Mylonite (6) Rhyolite (16) Obsidian (19) Tuff (15) *Note: number in parentheses is the GSI material constant (mi) for the intact rock type (Marinos et al. 2005, Hoek 2007) Source: after Mayne et al. (2002) Alternate rock classification systems have been devised, such as those based on behavioral response (e.g., Goodman 1989). A detailing of the rock mineralogy may be necessary on large and critical projects, thereby requiring the attention of an engineering geologist. Guidance can be found in published field guides on rock types and minerals (e.g., Pough 1988). The type of rock and its mineralogy can be used to infer possible problems that may be encountered in construction, and thus, should be considered in engineering design (Mayne et al. 2002). Notable issues and problems are often found with limestones because of water solubility. These issues include the development of sinkholes, caves, and erosional features associated with karst topography (e.g., voids, vugs, subsidence). Similarly, serpentine is associated with slippage and low frictional characteristics, while bentonitic shales can exhibit high swelling and expansive clay characteristics, thereby having concerns with shallow foundations of light structures and issues with slope instability. In the case of diabase, the residual formation of boulders may be important during construction, particularly in the case of driven pilings and drilled shaft foundations. The deterioration of the shale-claystone-mudstone family of rocks and weakly cemented friable sandstones is the cause of many maintenance problems, particularly with respect to slope cuts, excavations, roadway construction using rockfill, and foundations. For instance, cut slopes in shales will expose these rocks to air, water, wind, and solar processes that trigger weathering and disintegration, eventually resulting in flatter slopes and possible instability (Hoek 2007). Shale rockfill used in embankments may break down during compaction operations and result in a material less pervious and less strong than the original borrow source materials. Maintenance problems for slopes can be mitigated by a variety of solutions, including using flatter design slopes, installing horizontal drains, applying gunite or shotcrete and mesh. In certain cases, more elaborate structural supports are required (e.g., anchors, rock bolts, retention walls, and use of walls with drilled shafts). After the excavation for a structural foundation is made, the bearing level must be protected against slaking, deterioration, and expansion. This can be accomplished by spraying a protective coating on the freshly exposed rock surface, such as gunite or shotcrete (Wyllie 1992). Geologic time plays a role in the characteristics of rock materials. In general, the age of the rock affects its strength and stiffness (i.e. the older the rock, the stronger and stiffer it will be in relation to similar rock types that are younger). Figure 10-2 shows the geologic time scale with corresponding era, epoch, and periods. Excepting recent volcanics as a general guide, sedimentary geomaterials that are Cretaceous age or younger are considered unconsolidated in the geologic sense, thus are soil-like, whereas older sediments are rock-like.

209 Source: Paul Mayne Figure 10-2. Geologic time scale and associated age of rocks Intact Rock Properties Intact rock material can be quantified in terms of density, strength, stiffness, and other properties, as discussed in this section. 10.3.1 Specific Gravity of Solids The specific gravity of solids ( ) of various rock types depends on the constituent mineralogy and their relative composition. Values of for select minerals are presented in Figure 10-3. For common minerals (quartz, feldspar, calcite, chlorite, illite, kaolinite, mica), the overall bulk value gives an average = 2.7 ± 0.1 for many rock types. Exceptions include areas that contain appreciable amounts of rock salt (halite) that has a low specific gravity, or heavy metals such as ore deposits and mining operations (e.g., iron, lead) that have high values of . 0.0 0.1 0.2 0.3 0.4 0 2 4 6 8 10 12 14 16 Re sid ua l S tr en gt h, S r (a tm ) SPT Resistance, (N1)60 (bpf) Geologic Age Geologic Age Earth Begins Precambrian Cambrian Ordovician Silurian Devonian Carboniferous Permian Triassic Jurassic Cretaceous Paleocene Eocene Oligocene Miocene Pliocene Pleistocene Holocene 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 4,700,000,000 3,900,000,000 570,000,000 470,000,000 425,000,000 413,000,000 355,000,000 265,000,000 230,000,000 185,000,000 130,000,000 65,000,000 54,000,000 38,000,000 26,000,000 5,000,000 2,000,000 10,000 Logarithm of Time (years) Ge ol og ic Ti m e in Ye ar s Geologic Period or Epoch Mezozoic Cenozoic Paleozoic Quatenary Tertiary Era

210 Source: Paul Mayne Figure 10-3. Specific gravity of solids of common rock minerals 10.3.2 Unit Weight The unit weight of rock depends upon its porosity (n) and specific gravity of solids. The dry unit weight ( ) is determined as: = ∙ (1 − ) where = unit weight of water (= 9.81 kN/m3 = 64.3 pcf). The variation of saturated unit weight ( ) of rock with porosity is shown in Figure 10-4 and given by: = (1 − ) +

211 Source: Paul Mayne Figure 10-4. Unit weight of saturated rock vs. porosity The unit weight of rock can be indirectly estimated from the in situ shear wave velocity. Results of empirical relationships from a variety of different rock types are presented in Figure 10-5. The overall trend can be expressed as follows: (pcf) = 38.0 . where is the shear wave velocity (ft/s) kN m3⁄ = 7.165 . where is the shear wave velocity (m/s)

212 Source: Paul Mayne Figure 10-5. Trend for rock unit weight with in situ shear wave velocity It is also possible to estimate the unit weight of rock from compression wave velocity. Mavko et al. (1998) summarize representative empirical correlations developed for different rock types by Gardner et al. (1974) and Castagna et al. (1993). 10.3.3 Seismic Velocities The shear and compression wave velocities can be measured in the laboratory on small rock specimens using ultrasonic tests. These velocities can serve as indicators as to the soundness of the rock and degree of weathering, as well as an index of their strength. Surface and borehole geophysical methods can also be used to measure the seismic velocities of intact and fractured rocks, thereby allowing a better quantification of in situ conditions. For a wide range of rock types, Figure 10-6 provides a summary of data compiled from several sources: • Intact rocks tested in the laboratory (Mayne et al. 2002) • Field measurements on basalt, gneiss, and quartzite in India (Wadhwa et al. 2010) • Weathered tuff, andesites, granite, and felsite in South Korea (Cha et al. 2006) The trend relates the measured shear wave velocity ( ) to the measured compression wave velocity ( ) of the rock. The general trend for intact rocks is reported as (Wadhwa et al. 2010): = 1.21 ∙ . where and (ft/s) = 1.10 ∙ . where and (m/s) This is applicable to the specified ranges of wave velocities indicated in the figure. For weathered rocks, these expressions tend to overestimate the shear wave velocity.

213 Source: data from Mayne et al. (2002), Wadhwa et al. (2010), Cha et al. (2006) Figure 10-6. Trends between measured Vs and Vp for various types of rocks 10.3.4 Uniaxial Compressive Strength The uniaxial compressive strength ( = ) is a basic index parameter quantifying the intact rock strength. As described in Section 8.11.6, it is classically measured in the laboratory on small cylindrical specimens of rock (diameter = 2 in. [50 mm]; length = 4 in. [100 mm]) as the peak value of stress ( ) from a stress-strain curve. As the differences between hard soil and soft rock can be unclear, the boundary can be defined using compressive strength. For instance, rock typically has a uniaxial compressive strength greater than approximately 10 tsf (≈ 1 MPa) (Mayne et al. 2002). An illustrative example of the measured stress-strain curve on schistose gneiss is presented in Figure 10-7. The maximum measured stress gives = 964 tsf (92.4 MPa) and the tangent Young's modulus at 50 percent of ultimate is = 402,506 tsf (38.5 GPa). The ratio of modulus to strength is = ⁄ = 417 and is an indicator of the quality of the intact rock; in the case illustrated, very good to excellent rock. Alternate means of approximately assessing the magnitude of in the field are afforded via point load index tests or Schmidt hammer (FHWA 2016).

214 Source: Paul Mayne Figure 10-7. Measured stress-strain response on intact gneissic rock A selection of measured properties on a varied assortment of intact rocks is listed in Table 10-2, including uniaxial compressive strength, elastic modulus, tensile strength, and Poisson's ratio, as well as their respective sources of data. From these results, the mean value of uniaxial compressive strength is 1,094 tsf (105 MPa) with a standard deviation of 787 tsf (75.4 MPa). For any rock formation, the measured properties may vary significantly across the site due to heterogeneity and site variability. This may be caused by natural features in the rocks, including weathering, extent of discontinuities, changes in porosity, composition, mineralogy, and other factors. Furthermore, certain rocks (e.g., schist, phylite) exhibit strong anisotropy manifested as vastly different strengths and moduli in orthogonal directions of loading. Therefore, it is prudent to test a large number of rock specimens to evaluate the degree of variability and express the results in terms of the mean and variance. 10.3.5 Elastic Modulus of Intact Rock The elastic Young's modulus of intact rock is defined as a tangent value taken at 50 percent ultimate strength. For the data set reviewed in Table 10-2, the mean value was found to be = 408,206 atm with a standard deviation = 247,860 atm. Regression results from best fit line (r2 = 0.430) give: = 326 ∙ Table 10-2. Strength and stiffness properties of select intact rocks measured in laboratory tests Rock Type Intact Rock Material Reference Source σu = qu (atm) ER (atm) σt = T0 (-) Igneous Cedar City Tonalite John Day Basalt Goodman (1989) Goodman (1989) 1,002 3,504 189,341 826,909 63 143 0.17 0.29

215 Rock Type Intact Rock Material Reference Source σu = qu (atm) ER (atm) σt = T0 (-) Chehalis Basalt Chehalis Basalt Chehalis Basalt Chehalis Basalt Nevada Basalt Oregon Tuff Nevada Granite Nevada Tuff Mexico Andesite Mexico Breccia Mexico Tuff Palisades Diabase Pikes Peak Granit HDR-S&W (2015) HDR-S&W (2015) HDR-S&W (2015) HDR-S&W (2015) Goodman (1989) Mackiewicz and Rippe (2010) Goodman (1989) Goodman (1989) Filloy et al. (2015) Filloy et al. (2015) Filloy et al. (2015) Goodman (1989) Goodman (1989) 1,406 1,774 1,044 1,208 1,461 316 1,393 112 841 364 742 2,379 2,231 607,687 690,272 551,020 517,007 344,739 98,640 728,360 36,025 490,539 155,946 294,126 806,369 695,953 129 115 11 78 30 99 113 117 0.27 0.32 0.27 0.36 0.32 0.22 0.29 0.28 0.18 Metamorphic Baraboo Quartzite Cherokee Marble Dworshak Dam Gneiss Quartz Mica Schist Taconic Marble Lasa Marble Carrara Marble Pentelikon Marble Homblende Gneiss Homblende Gneiss Homblende Gneiss Homblende Gneiss Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) Cravero et al (2003) Cravero et al (2003) Cravero et al. (2003) Thompson et al. (2012) Thompson et al. (2012) Thompson et al. (2012) Thompson et al. (2012) 3,158 660 1,599 545 612 755 997 710 535 476 768 567 871,718 550,693 529,249 204,309 473,030 534,954 586,278 756,042 70,068 50,340 372,789 265,646 109 18 68 5 12 73 98 60 0.11 0.25 0.34 0.31 0.40 0.24 0.27 0.21 0.14 0.22 0.34 Sedimentary Bedford Limestone Berea Sandstone Flaming Gorge Shale Hackensack Siltstone Oregon Sandstone Oregon Siltstone Lockport Dolomite Micaceous Shale Navajo Sandstone Oneota Dolomite Solenhofen Limestone Tavermalle Limestone Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) Mackiewicz and Rippe (2010) Mackiewicz and Rippe (2010) Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) Goodman (1989) 503 728 347 1,211 395 331 891 742 2,112 858 2,418 966 281,384 190,114 54,546 291,863 88,560 102,960 503,562 109,849 386,529 433,140 628,719 550,776 16 12 2 29 30 20 80 44 39 39 0.29 0.38 0.25 0.22 0.34 0.29 0.34 0.29 0.30 Notes: (a) 1 atm = 1.01 bar = 101.3 kPa = 1.058 tsf = 14.7 psi (b) qu = σu = uniaxial compressive strength (c) E50 = tangent modulus at 50% ultimate strength (d) T0 = σt = tensile strength (e) ν = Poisson's ratio

216 10.3.6 Poisson’s Ratio The Poisson's ratio ( ) is a necessary material input into elasticity solutions for various problems encountered in rock mechanics (Poulos and Davis 1974). Values of Poisson's ratio on intact rocks are determined as the ratio of horizontal-to-vertical strain. For the data listed in Table 10-2, the following guidelines for mean value (±1 standard deviation) can be recommended: • Sedimentary rocks: ѵ = 0.300 ± 0.048 • Metamorphic rocks: ѵ = 0.257 ± 0.087 • Igneous rocks: ѵ = 0.270 ± 0.059 10.3.7 Tensile Strength The tensile strength of rock ( = ) is considerably less than its compressive strength. For the data in Table 10-2, the mean value was determined to be = 59 atm with a standard deviation = 42 atm. From regression analyses on the data available, a weak trend (r2 = 0.449) between uniaxial compressive strength and tensile strength was found to be: = 0.044 ∙ More specifically, the trends can be separated by types of rocks based on geologic origins (Figure 10-8). Weak trends from the regression results for best fit lines give the following: • Sedimentary rocks: = 0.028 • Metamorphic rocks: = 0.043 • Igneous rocks: = 0.054 Source: Paul Mayne Figure 10-8. General trends between tensile and compressive strengths for intact rock according to geologic origin

217 10.3.8 Shear Strength of Intact Rock The shear strength is most commonly expressed in terms of the Mohr-Coulomb criterion that is a linear approximation to the strength envelope: = + ∙ where = maximum shear stress (= shear strength) = effective cohesion intercept = effective normal stress = effective stress friction angle The interrelationships between shear strength, uniaxial compressive strength, tensile strength, and general triaxial mode of shearing are depicted in Figure 10-9. Shear strength parameters for rock are used in the geotechnical analysis of slope stability, tunnel support, design of excavations, and foundations. For massive rock with only one or two joint sets, the analyses are usually conducted using wedge analyses and block theory. For highly fractured rock with extensive sets of discontinuities, stability will be evaluated using either limit equilibrium or numerical analyses, or both. Source: Paul Mayne Figure 10-9. General interrelationships between strength parameters of intact rock There are four approaches for assessing of rock strength: (i) in situ testing of rock joint strength, (ii) lab testing of strength, (iii) empirical strength estimations, and (iv) selection of strength parameters based on index tests and rock mineralogy. For the intact rock, triaxial compressive strength tests can be conducted at increasing confining stresses to define the Mohr-Coulomb envelope and corresponding and

218 parameters. This will be required on large highway projects with appreciable levels of overburden stress such as large slopes and deep tunnels. For small to medium projects, it may be possible to use empirical methods based on the type of rock material and its measured uniaxial compressive strength that are available for evaluating the shear strength parameters of intact rock (Hoek 2007), as discussed in Section 10.5.1. This approach is versatile as it has been calibrated to account for the degree of fracturing and weathering, thus, also used to represent the shear strength of rock masses. Laboratory DS testing can be used to determine the shear strength of a joint of discontinuity and the infilling material found within the joints. The split box of the DS device is orientated with the axis along the preferred plane of interest. The shear strength of the discontinuity surface will determine either a representative peak or residual value of the frictional component of shear strength. Peak values can be conceived as the sum of the residual shear strength plus an additional strength component that depends on the asperities and roughness on the plane of shearing. Relatively small movements can reduce shear strength from peak to residual values. For highway cuts and excavations in fresh rocks where no movement has occurred before, the peak shear strengths are applicable. In contrast, for restoration and remedial work involving rockslides and slipped wedges or blocks of rock, the residual shear strengths are appropriate. Table 10-3 lists values of peak friction angle of various rock surface types, rock minerals (that may coat the joints), and infilling materials (such as clays and sands). If the joints are sufficiently open, the infilling of clay or other soils may control the shear strength behavior. Table 10-4 presents selected values of residual frictional angle ( , assuming = 0) for various types of rock. These values can give an approximate guide in selecting interface and joint strengths. Additional guidelines for selecting Mohr-Coulomb parameters are given by Wyllie (1992), Hoek (2007), and FWHA (2016). Table 10-3. Selected guideline values of peak friction angles for rocks, joints, and minerals Field Condition Type of Geomaterial Friction Angle, (degrees) (assuming = 0) Rock Joints Crystalline limestone 42–49 Sandstone 32–35 Gabbro 33 Schist 32–40 Chalk 30–40 Clay shale or mudstone 22–37 Bentonitic shale 9–27 Rock Minerals Quartz 33 Feldspar 24 Serpentine 16 Mica (muscovite) 13 Talc 9 Calcite 8 Mica (biotite) 7 Infilling and soil Quartz sand 33–45 Chlorite 20–30 Kaolinite 15–28 Illite 16–26 Source: after Olson (1974) and Mayne et al. (2002)

219 Table 10-4. Selected guideline values of residual friction angles for rock Type of Rock Friction Angle, (degrees) (assuming = 0) Limestone 33–40 Basalt 31–38 Chalk 30 Granite 29–35 Dolomite 27–31 Schistose Gneiss 23–29 Source: after Olson (1974) and Mayne et al. (2002) Rock Mass Classification The natural rock mass is composed of intact rock material separated by discontinuities in the form of joints, fissures, cracks, and shear planes. This assemblage results in a complex arrangement that requires caution while evaluating the important and dominant features controlling possible modes of displacement, movement, and in some cases, collapse. An experienced engineering geologist or geological engineer may be required on critical projects and large civil engineering works. There are varied types of discontinuities, planar features, and variability that can be expected in the site characterization of these geomaterials. Quantifying the network and extent of the fissures and discontinuities is perhaps even more important than classifying the intact rock material itself, as the joints, planar surfaces, and shear zones offer considerably more potential for movement and slippage than the intact rock. As such, rock mass classification systems have been developed to address these features. For instance, the RQD is an early rock mass quantification scheme. However, additional details on the rock features and jointing characteristics need to be properly assessed for engineering purposes (ASTM D5878). 10.4.1 Rock Mass Rating The geomechanics system for RMR was developed for the stability of tunnels and openings for diamond and gold mines in South Africa (Bieniawski 1989). The basic system depends upon five parameters that are assessed independently and then summed to form a rating on the quality of the overall rock mass components. Later, a sixth factor was included to better calibrate the performance of the RMR, specifically related to the orientation of the discontinuities for applications involving tunnels, foundations, and slopes. The five basic factors are as follows: 1. Uniaxial compressive strength 2. RQD 3. Spacing of the discontinuities 4. Condition of the discontinuities and joints 5. Groundwater conditions The five parameters (R1, R2, R3, R4, R5) are each presented in Figure 10-10. The RMR is the sum of these factors and ranges from 0 to 100 percent: = + + + + The first four terms can be expressed in equation form: = 0.948 + ( 113⁄ ) − ( 875⁄ ) ≤ 15 where = uniaxial compressive strength (atm)

220 = 5⁄ ≤ 20 where RQD is expressed in percent (%) = 10.39 ∙ . ≤ 20 where DS = discontinuity spacing (ft) = 30 − 152 ∙ > 0 where JS = joint or gouge thickness (in.) The fifth parameter (R5) is related to water conditions and can be assessed by one of two alternate methods: (i) using ratio of pore pressure to overburden stress ( ⁄ ) and (ii) water inflow measured in gallons per minute per 10-yard (9-m) length, designated INF. These can also be represented in equation form: = 22 − 15 ∙ ( ѵ⁄ )0.55 > 0 Ratio ( ⁄ ) is dimensionless and R5 < 15 ≈ 11 − 6 ∙ ( ) > 0 with INF in gallons/minute and R5 < 15 More recently, it has been noted that parameters R2 and R3 provide redundant measures on the frequency of fractures and fissures (Lowson and Bieniawski 2013); thus, it has been recommended to combine these two parameters into a single variable (R23 = R2 + R3), as presented in Figure 10-11. Moreover, there is evidence that the RQD is not the best or most reliable measure of fracturing (Pells et al. 2016). In fact, the new parameter R23 is more easily determined than either R2 or R3 because the natural cracks and discontinuities merely need to be counted and averaged over a 3.3-ft (1-m) length. The parameter R23 can be expressed as follows: 0 ≤ = 40 − 6.4 ∙ . ≤ 40 where ND = number of discontinuities per yard The updated value of RMR is then calculated from: = + + +

221 Source: based on Bieniawski (1989, 2011) Figure 10-10. Basic components for RMR system

222 Source: modified from Lowson and Bieniawski (2013) Figure 10-11. New RMR component R23 = R2 + R3 for number of discontinuities Finally, the orientation of the joints, discontinuities, and fissures may affect the overall performance of the rock mass during construction and application of structural loading. This can be illustrated for a cut slope in rock with various scenarios including massive rock with little jointing, favorable joint sets, unfavorable joint sets, and high-fractured rock mass (Figure 10-12). For tunnels, the relative strike and dip orientations of the discontinuities with respect to the tunnel axes can be used to assess the favorable- unfavorable rating (Table 10-5). Source: Paul Mayne Figure 10-12. Depictions of massive, favorable, unfavorable, and highly fractured rock mass scenarios for rock slope cuts Once an assessment of the joint orientation is made, the value of the sixth RMR parameter (R6) can be assigned. Table 10-6 provides a guide on the evaluation of R6 for foundations, tunnels, and rock slopes. The final assessment of an adjusted RMR′ is made from: ʹ = + + + + 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 R M R C om bi ne d R at in g: R 23 = R 2 + R 3 Number of Discontinuities per Length, ND Lowson & Bieniawski (2013) for meters Lowson & Bieniawski (2013) for yards R23 = 40 - 6.6∙(ND)0.46 for ND in meters Note: 0 ≤ R23 ≤ 40 R23 = 40 - 6.4∙(ND)0.48 for ND in yards

223 Additional details may be found in Bieniawski (2011) and Lowson and Bieniawski (2013). Table 10-5. Assessment of discontinuity orientation for tunneling in fractured rock Strike perpendicular to tunnel axis Strike parallel to tunnel axis Drive with dip; Dip 45°–90° Drive with dip; Dip 20°–45° Dip 45°–90° Dip 20°–45° Very favorable Favorable Very unfavorable Fair Drive against dip; Dip 45°–90° Drive against dip; Dip 20°–45° Dip 0°–20° irrespective of strike Fair Unfavorable Fair Source: after Bieniawski (1989) and Hoek (2007) Table 10-6. RMR parameter R6 adjustment for orientation of discontinuities Strike and dip orientations of joints Slopes Foundations Tunnels Very favorable 0 0 0 Favorable -5 -2 -2 Fair -25 -7 -5 Unfavorable -50 -15 -10 Very unfavorable -60 -25 -12 Source: ASTM D5878 10.4.2 Norwegian Geotechnical Institute Q-Rating System for Rock Masses The Norwegian Geotechnical Institute (NGI) developed a system for rating rock mass formations, primarily for designing and constructing highway and railroad tunnels (Barton et al. 1974). In this NGI Q- rating system, six parameters are used: 1. RQD 2. Number of sets of discontinuities or joint sets, 3. Interface roughness of the joints and fissures, 4. Condition of the joints and fractures, 5. Groundwater effects, 6. Stress reduction factor, SRF The parameters are individually cited in Figure 10-13 with their associated values and criteria. The Q-rating is calculated from the following: = ∙ ∙ A number of studies have correlated Q and RMR (e.g., Milne et al. 1998, Palmström A. 2009). For instance, Barton and Bieniawski (2008) have established an approximate relationship: ≈ 15 ∙ + 50

224 Source: after Barton et al. (1974) and Barton and Bieniawski (2008) Figure 10-13. Outline and components of the Q systems for RMR 10.4.3 Geological Strength Index The GSI was originally developed as a hybrid of the RMR and Q systems for evaluating rock mass quality and the shear strength of fractured rocks. A GSI rating from 0 to 100 is calculated by comparing the rock mass structure with the conditions of the joints and discontinuities, using a chart as shown in Figure 10-14. Complete details on the GSI are given by Marinos et al. (2005) and Hoek (2007). A simple conversion from RMR to GSI rating is given by (Hoek and Diederichs 2006): = − 5 NGI Q-System Rating for Rock Masses Norwegian Geotechnical Institute, Oslo Classification for Rock Masses Q - Value Quality of Rock Mass < 0.01 Exceptionally Poor 4. Discontinuity Condition & Infilling = Ja 0.01 to 0.1 Extremely Poor 4.1 Unfilled Cases 0.1 to 1 Very Poor Healed 0.75 1 to 4 Poor Stained, no alteration 1 4 to 10 Fair Silty or Sandy Coating 3 10 to 40 Good Clay coating 4 40 to 100 Very Good 4.2 Filled Discontinuities 100 to 400 Extremely Good Sand or crushed rock infill 4 < 400 Exceptionally Good Stiff clay infilling < 0.2 in 6 Soft clay infill < 0.2 in thick 8 PARAMETERS FOR THE Q-Rating of Rock Masses Swelling clay < 0.2 in 12 Stiff clay infill > 0.2 in thick 10 1. RQD = Rock Quality Designation = sum of cored pieces Soft clay infill > 0.2 in thick 15 > 4 inches (100 mm) long, divided by total core run length Swelling clay > 0.2 in 20 *Note: 0.2 inches = 5 mm 2. Number of Sets of Discontinuities (joint sets) = Jn 5. Water Conditions Massive 0.5 Dry 1 One set 2 Medium Water Inflow 0.66 Two sets 4 Large inflow in unfilled joints 0.5 Three sets 9 Large inflow with filled joints Four or more sets 15 that wash out 0.33 Crushed rock 20 High transient flow 0.2 to 0.1 High continuous flow 0.1 to 0.05 3. Roughness of Discontinuities* = Jr Noncontinuous joints 4 6. Stress Reduction Factor** = SRF Rough, wavy 3 Loose rock with clay infill 10 Smooth, wavy 2 Loose rock with open joints 5 Rough, planar 1.5 Shallow rock with clay infill 2.5 Smooth, planar 1 Rock with unfilled joints 1 Slick and planar 0.5 Filled discontinuities 1 **Note: Additional SRF values given *Note: add +1 if mean joint spacing > 3 yards (3 m) for rocks prone to bursting, squeezing and swelling by Barton et al. (1974)                   = SRF J J J J RQDQ w a r n

225 Source: after Hoek (2007) Figure 10-14. Chart for assessing the GSI rating and quality of rock masses 10.4.4 Estimating Quality of Rock Mass from Seismic Velocity Barton (2002) showed that the Q rating for hard rocks is related to the compression wave velocity ( ), approximately expressed by: ≈ 10 . ∙ . where is given in ft/s ≈ 10 . where is given in km/s In addition, the relationship was adjusted for weaker rocks by inclusion of the uniaxial compressive strength ( ) in a modified form of the Q-rating. S U R FA C E C O N D IT IO N S VE R Y G O O D - Ve ry R ou gh - f re sh u nw ea th er ed G O O D - R ou gh , s lig ht ly w ea th er ed , i ro n- st ai ne d FA IR - Sm oo th , m od er at el y w ea th er ed a nd al te re d PO O R - Sl ic ke ns id ed , hi gh ly w ea th er ed w ith fil lin g VE R Y PO O R - Sl ic ke ns id ed w ith s of t cl ay c oa tin g ROCK STRUCTURE INTACT or MASSIVE rock with few widely spaced discontinuities BLOCKY - well interlocked undisturbed rock mass composed of cubical blocks with 3 sets of intersecting discontinuities VERY BLOCKY - interlocked partially-disturbed rock mass with multi-faceted blocks having 4+ joint sets DISTURBED-BLOCKY- SEAMY: folded with angular blocks formed by many intersecting joint sets with bedding planes or schistocity DISINTEGRATED ROCK: Poorly interlocked and heavily broken with mix of angular & rounded pieces LAMINATED-SHEARED: lack of blockiness due to close spacing of weak schistocity or shear planes Geological Strength Index (GSI) 90 80 70 60 50 40 30 20 10 Not applicable Not applicable De cr ea sin g In te rlo ck in g of R oc k Pi ec es Decreasing Surface Quality of Discontinuities

226 Using measurements of shear wave velocity ( ) obtained by suspension logging, Cha et al. (2006) suggested a relationship between rock mass quality and . Figure 10-15 shows data from two sites indicating the relationship: = 250 − 67.7 ∙ log(3,600 − 0.3 ∙ ) where > 3,000 ft/s = 250 − 67.7 ∙ log(3,600 − ) where > 900 m/s Source: Paul Mayne Figure 10-15. Correlative trend for RMR in terms of shear wave velocity Rock Mass Parameters The RMR, Q, and GSI systems have found use in engineering analyses for tunnels, slope stability, shallow and deep foundations, excavations, mining, quarry, erosion, and other civil engineering applications. In terms of rock mass characterization, these ratings are also used to evaluate shear strength parameters of intact and fractured rock ( and ), elastic modulus, bearing capacity ( ), and unit side resistance ( ), as well as rippability using construction equipment. 10.5.1 Rock Mass Strength The rock mass strength is controlled by the composite structure of the intact rock and the discontinuities, fissures, and jointing. The rock mass strength can be determined in the field using large-scale DS tests, back calculation from failed slopes or rockslides, or estimated using empirical methods. For the latter, the well- known Hoek-Brown model (Hoek et al. 2002) has been developed which is based on seven rock parameters: 1. uniaxial compressive strength of the intact rock, 2. material constant for the intact rock, (reference Table 10-1)

227 3. geological strength index of the rock mass, GSI 4. material coefficient parameter for the rock mass, 5. variable associated with the rock mass, s 6. exponent parameter for the rock mass, a 7. measure of damage or disturbance to the rock mass caused by blasting or other factors, D The Hoek-Brown model can be used to represent intact rock or highly fractured rock masses. However, it should not be used for massive rocks with only one or two joint sets, as indicated by Table 10-7. In the case of intact rock masses having only one to two joint sets, wedge analyses should be used (Goodman 1989). The Q system provides a direct estimation of the rock joint strengths for these cases (assuming = 0): = arctan( ⁄ ) Additional details and recommendations on this approach are given by Barton (2002) and Barton and Bieniawski (2008). Table 10-7. Applicability of the Hoek-Brown model for intact and fractured rocks Case Applicability of GSI Equations Remarks Intact rock specimen Yes, use s = 1 Use GSI approach to fit laboratory stress-strain and strength data Massive rock with 1 joint set No, use strength from Jr/Ja ratio (Q-rating) Use in 2D wedge analysis or sliding block Sound rock with 2 joint sets No, use strength from Jr/Ja ratio (Q-rating) Use in 2D and 3D wedge analysis or sliding block Jointed rock mass with 3+ discontinuity sets Yes, use H-B model for estimating and Apply in limit equilibrium or numerical analyses Heavily jointed rock mass and/or partially weathered rock Yes, use H-B model for estimating and Apply in limit equilibrium or numerical analyses The generalized expression of the Hoek-Brown model for rock strength in terms of the major ( ) and minor ( ) effective principal stresses is given by: = + ∙ ∙ ′ + where is a reduced value of the material constant found from: = ∙ exp − 10028 − 14

228 The rock mass terms s and a are obtained from: = exp − 1009 − 3 = 12 + 16 exp − 15 − exp − 203 Finally, the disturbance factor D depends upon the means of care and quality of the rock extraction, ranging from 0 for undisturbed rock to 1 for completely damaged rock. Table 10-8 provides guidance on the value of D for certain cases: Table 10-8. Values of the disturbance factor D for GSI rock mass quality system Case - Condition of Rock Disturbance Factor, D Excellent quality rock, tunnel made using tunnel boring machine D = 0.0 Squeezing rock D = 0.5 Good blasting control on small projects D = 0.7 Mechanical excavation for rippable rock D = 0.7 Large open pit mining; poorly controlled blasting D = 1.0 Source: after Hoek et al. (2002) The Mohr-Coulomb criterion (Section 10.3.8) can be rearranged to provide the effective principal stresses in terms of effective friction angle ( ) and effective cohesion intercept ( ): = 2 cos1 − sin + 1 + sin1 − sin ∙ ′ 10.5.1.1 Example Calculations for Rock Mass Strength of Fractured Marble An example set of calculations to evaluate the effective principal stresses using the Hoek-Brown empirical model for rock mass strength is given here, using fractured marble bedrock that has a measured uniaxial compressive strength of = 386 tsf (37 MPa) and GSI = 45. Overburden stresses are calculated up to a depth of 16.4 ft (5 m) below grade with a groundwater table taken at 6.6 ft (2 m). The calculated GSI parameters and stresses are presented in Figure 10-16. A disturbance factor of D = 0 was used in this example. For marble, which is a metamorphic rock, the GSI material index is obtained from Table 10-1 with a value of = 9. This is used in conjunction with the reduction expression from the GSI rating to obtain a value of = 1.262 for the fractured marble. The GSI rating also determines the parameter values for s = 0.0022 and exponent a = 0.508. Then the Hoek-Brown equation can be used to produce values for

229 assumed values of . The latter values are taken at the corresponding overburden stresses for selected depths in the rock formation. Source: Paul Mayne Figure 10-16. Example calculations of rock mass strength of marble using Hoek-Brown model 10.5.1.2 Equivalent Mohr-Coulomb Parameters for Fractured Marble Five sets of effective principal stresses ( and ) were calculated at each of 3.3-ft (1-m) depth intervals, as shown in the figure. These can be plotted as Mohr's circles to obtain the strength parameters: and , as illustrated by Figure 10-17a. The corresponding values for this example are found as: = 275 kPa and = 58.9°. Alternatively, values can be calculated incrementally, as indicated in Figure 10-17a. Alternatively, the Mohr-Coulomb parameters can be obtained from a - plot as shown in Figure 10-16 and plotted in Figure 10-17b. Rock Mass Strength - Hoek - Brown Model (Hoek 2007) - Example Calculation for Marble PROBLEM DATA Calculated GSI Parameters GSI = 45 Equivalent RMR= 50 qu (MPa) = 37 mb/mi Reduction = 0.140 mi = 9 s (Rock Mass) = 0.00222 GWT depth(m) = 2 mb (Rock Mass) = 1.262 γ (kN/m3) = 25 a (exponent) = 0.508 Depth (m) = 5 D (disturbance) = 0 Effective Principal Stresses MIT Stress Space MOHR-COULOMB CRITERION Depth σ3 =σv σ1' uo σ3' σ1' q p' Ratio Secant Incremental Parameters z (m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) q/p' φ' c', kPa φ' ID (degrees) (degrees) 0 0 1966 0 0 1966 983 983 1.000 90.0 1 25 2345 0 25 2345 1160 1185 0.979 78.2 253 61.2 A 2 50 2677 0 50 2677 1314 1364 0.963 74.4 276 59.3 B 3 75 2863 10 65 2863 1399 1464 0.955 72.8 295 58.1 C 4 100 3040 20 80 3040 1480 1560 0.948 71.5 309 57.3 D 5 125 3209 29 96 3209 1556 1652 0.942 70.4 323 56.6 E MIT Parameters: q = (σ1'- σ3')/2 Mean = 291 58.5 p' = (σ1'+ σ3')/2 Values (kPa) (deg)

230 Source: Paul Mayne Figure 10-17. Example rock mass strength of fractured marble from Hoek-Brown model to determine c' and φ' using (a) Mohr's circles and (b) p'-q space 10.5.2 Rock Mass Modulus The rock mass modulus ( ) can be evaluated in situ using FJTs (Goodman 1989) or borehole dilatometer (Arsonnet et al. 2014), as well as by back-calculating Young's moduli using elastic continuum solutions from the measured movements and field performance of large structures (Poulos and Davis 1974). Alternatively, can be estimated using one or more of the rock mass classification systems. For the GSI system, Hoek and Diederichs (2006) have recommended a relationship between and the modulus for the intact rock ( ) that depends on the GSI and disturbance factor D: = 0.02 + 1 − /21 + exp 60 + 15 −11 A direct relationship for without the need to have the intact rock modulus has also been developed (Hoek and Diederichs 2006): (tsf) = 932,385 1 − 2⁄1 + exp 75 + 25 −11 (GPa) = 100 1 − 2⁄1 + exp 75 + 25 −11 For the RMR and Q systems, methods are also available (e.g., Barton and Bieniawski 2008). For instance, Figure 10-18 presents a simple relationship between and RMR: (tsf) = 10,440 ∙ 10( )⁄ ========= ========= 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Sh ea r S tr es s, τ (k Pa ) Effective Normal Stress, σ' (kPa) Hoek-Brown Rock Mass Model φ' = 58.9° c' = 275 kPa c' tanφ' = 1.65

231 (GPa) = 10( )⁄ Source: after Barton and Bieniawski (2008) Figure 10-18. Rock mass modulus estimated from the RMR and Q rating systems 10.5.3 Foundation Bearing Resistances For foundations bearing on rock, the RQD has served for many decades as a simple measure to estimate an allowable bearing stress, (Peck et al. 1974). While the original source provided a table of values associated with RQDs, the recommended can be graphed as shown in Figure 10-19, which is approximately given by the expression: = ∙ 10 + 0.625 1 ( + 1) − 0.0077⁄⁄ where = 1 atm = 0.101 MPa = 1.058 tsf

232 Source: after Peck et al. (1974) Figure 10-19. Allowable bearing stress for foundations on fractured rock A more substantiated approach for bearing capacity was completed by Zhang and Einstein (1998) who reviewed load test data from 39 drilled shaft foundations. The maximum measured bearing capacity ( ) was found to be related to the uniaxial compressive strength of the rock. Figure 10-20 shows their final summary trend, which can be expressed for drilled shaft foundations having embedment ratios greater than three (L/d > 3): = ∙ ∙ (10 ∙ ⁄ ) . where = empirical constant The mean trend is established with = 4.6 with upper and lower bounds corresponding to = 6.8 and = 3.0, respectively. Two additional recent values from Osterberg load tests are also included and are consistent with the mean trend (Thompson et al. 2012).

233 Source: after Zhang and Einstein (1998) Figure 10-20. Allowable bearing stress for drilled shaft foundations (L/d > 3) on rock 10.5.4 Unit Side Resistance for Socketed Drilled Shafts For drilled shafts and bored pile foundations that extend into rocks, the unit side resistance ( ) is related to the shear strength of the rock (Kulhawy and Phoon 1993). Figure 10-21 shows the general relationship with supporting data from their study plus an additional 64 case studies reported by Ng et al. (2001). The trends can be expressed by the following relationship: = ∙ ∙ 12 ⁄ . where Ψ = empirical coefficient that takes on a mean value Ψ = 2 in various rock types and has upper and lower limits of Ψ = 3 and Ψ = 1, respectively. Additional details on the behavior of foundations in rock and characteristics of rock masses for the design and evaluation of drilled shafts may be found in Turner (2006).

234 Source: after Kulhawy and Phoon (1993) Figure 10-21. Unit side resistance of drilled shaft foundations related to rock strength 10.5.5 Rock Rippability and Earthwork Factor In the case of massive rock, blasting may be required to excavate rock in highway cuts, tunnels, and slopes. In some cases, the rock is fractured sufficiently so that construction equipment may be able to remove the material without need for blasting, vibration monitoring, and damage control. In such cases, the compression wave velocity ( ) of the rock mass may prove useful in helping to assess whether the equipment is rippable or not. Figure 4-3 provides an example for a Caterpillar D8R, indicating expected criteria for rippable rock, marginal conditions, and nonrippable materials. Stephens (1978) developed empirical relationships between the compression wave velocity and the earthwork factor (i.e., the ratio of the volume after emplacement and compaction to the volume prior to excavation) for volcanic, sedimentary, and granitic rocks. The estimated earthwork factors were generally within ±5 percent of the actual factors. 10.5.6 Other Rock Parameters Additional parameters may be of concern in the site characterization of rock masses and, yet, are beyond the scope of this manual. For instance, the Q-rating and RMR systems were originally developed for tunneling and mining operations and, thus, have design charts for stand-up time and required support features (e.g., rock bolts, support pressure, shotcrete) on various size tunnels and underground openings (Barton and Bieniawski 2008). Additional studies have shown the use of Q-rating to estimate water inflow and hydraulic conductivity characteristics of rock masses (Barton 2002). Blasting and removal of rock has also been explored in terms of the rock mass quality and its importance in minimizing damage to the rock formation. Some rocks tend to weather rapidly and so must be considered in terms of their degradational characteristics with time, temperature, and exposure to the elements. In such cases, it is prudent to conduct

235 studies regarding disintegration rates, deterioration, and break-down of the materials, using slaking and abrasion tests, especially shales and mudstones. In addition, certain rocks (e.g., limestones, dolomite, gypsum) are prone to being water-soluble and can develop erosional and scour problems, leading to rockfalls, sinkholes, and other features that can cause maintenance problems. Special considerations should be given for these cases (Hoek 2007).

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