ISRM Congress 2015 Proceedings - Int l Symposium on Rock Mechanics - ISBN: INTERPRETATION OF UCS TEST RESULTS FOR ENGINEERING DESIGN

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1 INTERPRETATION OF UCS TEST RESULTS FOR ENGINEERING DESIGN *R. P. Bewick Golder Associates Ltd Lorne Street Sudbury, Canada P3C 4R9 (*Corresponding author: F. Amann ETH Zurich, Department of Earth Science Sonneggstrasse Zürich P. K. Kaiser Laurentian University 935 Ramsey Lake Rd Sudbury, Canada P3E 2C6 C. D. Martin University of Alberta Department of Civil and Environmental Engineering Edmonton, Alberta T6G 2W2 1

2 INTERPRETATION OF THE UCS TEST FOR ENGINEERING DESIGN ABSTRACT This article focuses on the uniaxial compressive strength (UCS) of homogeneous and heterogeneous rocks. Critical factors impacting the UCS of rocks are reviewed and then separate assessments of UCS data from homogeneous and heterogeneous rocks are presented. The variability (coefficient of variation) of UCS test results for homogeneous rocks is found to be generally <25% while for heterogeneous rocks the variability is >35%. Failure mode variation is found to be the cause of the variability of UCS test results in heterogeneous rocks. Empirical engineering design methods that use UCS as an input parameter are discussed and suggestions are provided for selecting appropriate UCS values. KEYWORDS UCS, compressive strength, laboratory testing, interpretation, design INTRODUCTION The UCS is one of the most commonly used rock engineering parameters whether for rock mass classification or for strength determination. The mean UCS and its variability are often assumed to represent a reliable rock material property. For the reasons discussed in this article, UCS is rarely representative of the intact rock UCS. The UCS test simply records the collapse load during uniaxial loading of a cylindrical specimen. As suggested by many, the UCS is an index rather than a unique engineering parameter. The UCS is thus a proxy for rock strength which depends on the loading rate (e.g., Bieniawski 1967), specimen geometry (e.g., Hudson et al., 1971), specimen size (e.g., Bieniawski 1968), and many other factors. Furthermore, the UCS is not the same as the Hoek-Brown strength criterion parameter σ ci. There are differences in opinion on what is commonly considered to be intact rock. When sampling intact pieces of core from drillholes crossing blocks of rock bound by block forming discontinuities, samples will be intact but some samples will be veined, others will be damaged, and others will be neither. According to Hoek (1983), intact rock pieces are the unfractured blocks occurring between structural discontinuities in a typical rock mass and the σ ci parameter for intact rock is determined using the fitting procedure proposed by Hoek and Brown (1997) based on the data requirements outlined by Hoek (1983). Studies (e.g., Bewick and Kaiser 2014; Kaiser and Kim 2014) have shown that independently determined UCS and σ ci values for the same rock type are not equivalent. Thus, UCS data cannot be used as a replacement for σ ci. In this article, we focus on the UCS from unconfined tests and differentiate between UCS with failure through intact rock of predominately homogeneous specimens (called UCS ho=homogeneous ) and failure through combined failure modes such as shear on defects (such as veins) along with through intact rock (called UCS he=heterogeneous ). Both UCS ho and UCS he are representative of the strength distribution in intact rock blocks forming a rock mass. The UCS data from homogenous rock specimens generally provide a good estimate of the strength of the least defected part of the rock because the failure mode is minimally impacted by visually obvious heterogeneity and typically occurs through mostly intact rock material. For this reason, UCS ho is often called the intact strength and labelled UCS i. However, as stated above, UCS i is not to be confused with σ ci. 2

3 The UCS data from heterogeneous parts of the rock blocks, due to their inherent variability at both the field and laboratory scales, often are obtained from specimens that do not predominately fail through intact rock. Heterogeneous rocks exhibit a variety of failure modes such as axial splitting, combined shear and splitting rupture, shear along a single pre-existing discontinuity, and combinations of the previously listed failure modes as shown in Figure 1. As a consequence, the UCS data from heterogeneous rocks almost always includes a mixture of failure modes resulting in more variable UCS values (typically with Coefficient of Variation, CoV >35%). Thus, the UCS test results from heterogeneous rocks are representative of the UCS distribution in a heterogeneous rock block if a sufficiently large number of specimens are tested. Primarily for the variability in failure mode, leading to highly variable UCS data, the reported UCS he for heterogeneous rocks is often confusing, misleading and challenging to apply to many empirical design methods. One of the sources for this confusion originates in testing standards and suggested methods such as ASTM D and ISRM (1979; 1999) which are the industry standards for conducting and reporting laboratory uniaxial tests on rock cylinders for the purpose of estimating a rock s intact compressive strength. While these standards and suggested methods provide excellent guidance on how to prepare rock specimens for testing and how to monitor and conduct the tests so that the testing procedures are reliable, they provide insufficient guidance on how to: (1) report the results in a meaningful manner such that they can be properly processed outside the laboratory; and (2) interpret the results for the determination of reliable engineering parameters. Since the focus of the standards was the testing of homogeneous rocks that predominantly fail through intact rock material, modifications to the standards and suggested methods are required for heterogeneous rocks. In this article, focus is placed on Uniaxial Compressive Strength (UCS) testing procedures, test results and their interpretation, and guidance on the use of UCS data in some empirical design approaches for strong (UCS >25MPa) hard brittle rocks. The terminology adopted for this article is outlined in Appendix A. The reasons for variability in UCS and the number of specimens needed to obtain representative, statistically valid UCS values are investigated. It is shown that the UCS is not necessarily a unique engineering parameter for a given rock type and, depending on a rock s heterogeneity, different UCS values may need to be specified for various design aspects. Figure 1. Examples of common failure modes observed in hard brittle rocks loaded in compression showing before and after testing photographs (core specimens are ~63 mm in diameter); (a-b) intact axial splitting; (c-d) intact shear rupture; (e-f) combination of intact rock and pre-existing discontinuities; (g-h) failure along a pre-existing discontinuity; (i-j) failure around clasts or other specimen scale matrix elements; and (k-l) non-valid test result where failure occurred due to end sloughing. 3

4 UCS TESTING REQUIREMENTS ISRM (1979; 1999) provide suggestions for standardized testing of cylindrical rock specimens under laterally unconfined conditions with respect to specimen end preparation, slenderness, and diameter to grain size ratio. The significance of specimen end-face preparation and frictional constraints is often underestimated in routinely performed tests. Imperfections such as irregularities on both the platen and specimen face lead inevitably to local stress concentrations (e.g., point loads or line loads) that substantially influence the failure behaviour and decrease the peak strength of a rock specimen. This is illustrated by Figure 2 showing a fused quartz specimen (i.e., UCS=1000 MPa, E=72 GPa). The specimen was loaded under unconfined conditions. At a load of 50 MPa (i.e., 1/20 th of the UCS) tensile cracks emanated from an imperfection (i.e., a piece of particulate on loading platen) at the specimen end-face. The greater the stiffness and strength of the rock the less forgiving a UCS test is to imperfections in specimen preparation showing the need for carful adherence to testing procedures. Figure 2. Fused quartz specimen fractured at 1/20 th of its UCS due to a small particulate on the loading platen/specimen interface. (a) Isometric view and (b) Top view. (Photograph curtesy of F. Amann). Peng (1970) and Peng and Johnson (1972) analyzed experimentally and numerically the stress state within a rock specimen exposed to uniaxial loading considering various end-boundary conditions. They found that for increased friction between the platen and the rock specimen the non-uniformity of the stress state in the specimen increased, even though a uniform stress was applied. In compression, a rock specimen tends to expand laterally as it shortens axially. Frictional constraints at the specimen s end-faces tend to prevent lateral expansion causing the specimen s ends to be subjected to shear stress. As a consequence, the stress state in the specimen is neither uniform nor uniaxial (i.e., it is actually a triaxial stress state). In practice it is almost impossible to fully eliminate frictional constraints at the platen. However, the effect of frictional constraints on the non-uniformity of the stress state in the center of the specimen can be reduced by adjusting the slenderness ratio (height/diameter ratio). The effect of slenderness ratio on Young s Modulus, UCS, and strain at peak stress was analyzed in several studies on concrete and rock (e.g., Mogi 1966; Dhir and Sangha 1973). Figure 3a shows the relative strength in percent (i.e., UCS normalized by UCS with a slenderness ratio of 2.5) for different rock types and slenderness ratios (Mogi 1966; Dhir and Sangha 1973). For a slenderness ratio > 2.5, UCS changes slightly (i.e., by less than 2%). For smaller ratios the relative strength increases considerably depending on the tested material. The ISRM suggested methods account for this important effect by suggesting a heightto-diameter ratio between and the ASTM standard by suggesting a height-to-diameter ratio >2.0. 4

5 Figure 3. (a) Impact of slenderness ratio (height/diameter) on UCS relative to the UCS at a slenderness ratio of 2.5. The data shows that UCS is minimally influenced by slenderness at ratios >2.5. (b) Impact of the largest grain to specimen diameter ratio on UCS for concrete (modified from Blanks and McNamara 1935). The plot shows that at largest grain to specimen diameter ratios >10, UCS is minimally impacted. ISRM (1979) suggests that the specimen diameter should be 10 times larger than the size of the largest grain (i.e., 10:1). For determining the full stress strain curve ISRM (1999) suggests 20:1. Blanks and McNamara (1935) performed tests on cylindrical mass concrete specimens with a height to diameter ratio of 2:1, diameters ranging from 50 mm to 900 mm and ratios between the largest grain to specimen diameter ranging from 2:1 to 48:1 (Figure 3b). This unique series of tests suggests that for a ratio larger than 10:1 the UCS is only slightly affected by the grain size while for smaller ratios a large variability in UCS is to be anticipated. The reason for increasing the suggested ratio from 10:1 to 20:1 is not explored in ISRM (1999) but is possibly related to the fact that for determining the full stress-strain response, strain gauges mounted on the specimen surface are required. Even if the above listed effects on UCS and its variability have been minimized, most rocks show a natural variability that is relevant for engineering design purposes. The ISRM (1979) states that the number of tests should be determined from practical considerations but at least five are preferred; irrespectively if the rock is homogeneous or heterogeneous. To investigate the impact of specimen population effects on the mean and distribution of UCS values, a dataset of damaged Lac du Bonnet granite (Martin 1993) containing 69 UCS tests (mean 139 MPa; Standard Deviation 10 MPa; CoV 7%) was randomly sampled to obtain populations of 5, 10, 15, 20, and 30 UCS test results. The results of the random sampling are shown in Figure 4 as histograms of each of the data populations and a fit normal distribution to the data. While the mean and standard deviation values are generally comparable for the presented sample populations, visually a distribution of test results becomes apparent when the sample population is between 10 and 20. Based on this preliminary assessment, greater than five UCS tests are likely required to provide a meaningful representation of the UCS value and distribution for a given rock type. Ten tests appear to be a reasonable minimum for this relatively homogeneous rock (i.e., CoV 7%). While not presented for space considerations, more tests would be needed to define a reliable mean, standard deviation, and distribution of more heterogeneous rocks with CoV s greater than 25%. Initial testing of greater than 10 specimens should be considered for heterogeneous rocks. 5

6 Figure 4. Impact of specimen population on Lac du Bonnet Granite mean, standard deviation, and distribution of UCS test results with low CoV. (Stdev standard deviation; PDF Probability density function). UCS TESTING RESULTS FROM HOMOGENEOUS AND HETEROGENEOUS ROCKS Homogeneous Homogeneous rocks typically fail predominately through intact rock material and are well suited for the current standard and suggested methods as outlined above and ISRM (1979; 1999). Thus, the homogeneous test results (UCS ho ) in this section are representative of UCS i. To emphasize this, UCS test results for four homogeneous rock types are shown in Figure 5 with fitted normal distributions. The four homogeneous rock types are also summarized in Table 1. While these UCS test results were completed following standard and careful testing procedures, some but relatively constrained variability is evident in the results. This is highlighted by the CoV in Table 1 which ranges from 2% for Carrera marble, the most homogenous rock type presented in this article, to 15% for the Sandstone. For these four homogeneous rock types, based on specimen populations of 10 to 13, the CoV is 15%. The variability observed in homogeneous rocks is primarily due to two sources: (1) the quality of the standard and suggested testing procedures; and (2) variability in the homogeneous rock specimens. Based on the Carrera marble dataset containing 10 specimens, limited variability in the testing results is evident. This suggests that if the testing standards and suggested methods are adhered to, there should be minimal effects of the testing procedure on the UCS value and the resulting UCS ho = UCS i is a reliable engineering strength index. The variability in homogeneous rocks is thus predominately due to inherent specimen variability that depends on rock type. 6

7 Frequency Carrera Marble Granite (Franklin and Hoek 1970) Quartz Dolerite (Franklin and Hoek 1970) Sandstone (Franklin and Hoek 1970) PDF Figure 5. Histograms of UCS test results completed on some homogeneous rock datasets. Showing fit normal distributions to each dataset. Statistical summary provided in Table 1. PDF Probability Density Function. Table 1. Statistical summary of UCS results for compiled homogenous rocks in Figure 5. Lithology Average Standard CoV Minimum Maximum Population UCS (MPa) Deviation (%) UCS (MPa) UCS (MPa) (MPa) Carrera Marble Sandstone a Quartz Dolerite a Granite a a Franklin and Hoek (1970) UCS (MPa) Heterogeneous Unlike homogeneous rocks, heterogeneous rocks when tested exhibit a number of different failure modes as previously discussed and shown in Figure 1. Consequently, UCS test results for heterogeneous rocks are highly variable and are representative of UCS he (see Appendix A) and not of the homogeneous part UCS ho. As shown in the previous section for homogeneous rocks, if the standard and suggested testing methods are conformed to, variability in UCS test results appear directly related to variability in the material tested. In the case of heterogeneous rocks, the potential for various failure modes leads to increased variability. UCS test results for four heterogeneous rock types are shown in Figure 6 with fitted normal distributions and summarized in Table 2. While these UCS test results were completed following standard and suggested testing procedures, high variability is evident in the results (CoV in Table 2 ranging from 33% for Quintner Limestone to 84% for Sulfate-rich clay rock). For the three rock types with reasonable CoV values (i.e., <50%), the CoV is on average 38% (ranging from 33 to 42%). This is typical for heterogeneous rock types. The excessive CoV of 84% for the sulfate rich clay rock flags that the sample population is made of at least two unique groups and the reported mean and CoV are of little practical value. One of the main limitations of the standard and suggested methods is that they were predominately written for homogeneous rocks where failure is generally through homogeneous rock. When these standards and suggested methods are applied to heterogeneous rock test result summaries where only the mean, standard deviation, and CoV are to be reported for the core specimens tested (as per recommendations in ISRM 1979; ASTM D ), high variability is obtained with a relatively low average UCS value. If the heterogeneous rock test results are divided by failure types such as breaks along discrete planes of weakness, combinations of intact rock and defects, and through intact rock, the mean 7

8 intact compressive strength increases and the CoV for the intact failure mode tends to those found for the homogeneous part of the rocks. An example of this is shown in Table 3 where the UCS test results for a heterogeneous limestone have been summarized by the available UCS tests regardless of failure mode, UCS test results with breaks along discrete discontinuity planes removed, and finally failure involving predominately intact rock alone. As is evident in Table 3, the mean UCS increases and the CoV decreases to a value similar to the range of the presented homogeneous test results in Table 1. Figure 6. Histograms of UCS test results completed on some heterogeneous rock datasets. Showing fit normal distributions. Statistical summary provided in Table 1. Note that negative UCS values are suggested by the fit normal distributions. In reality, any fit distribution to UCS data needs to be constrained to values greater than 0 MPa. Table 2. Statistical summary of UCS results for compiled heterogeneous rocks in Figure 6. Lithology Average Standard CoV Minimum Maximum Population UCS he (MPa) Deviation (%) UCS (MPa) UCS (MPa) (MPa) Limestone Quintner Limestone b Sulfate-rich clay rock c Quartz Monzonite b Perras et al. (2012); c Amann et al. (2013) Table 3. Heterogeneous rock Impact of failure mode grouping on UCS and its variability. Parameter Complete Discrete discontinuity Intact breaks dataset breaks removed only (UCS ho ) Average UCS (MPa) Standard Deviation (MPa) CoV (%) Population The following example illustrates the need for careful data filtering. For the Quartzite described by Bewick et al. (2011), the UCS data is shown in Figure 7. The mean UCS for the available data is 118 MPa with a CoV of 59% leading to the normal distribution shown with black dashed line. This distribution, unless replaced by a skewed fit, suggests a high likelihood for extremely low (near zero) strengths or weak rock and a maximum strength of about 300 MPa. Upon examination and filtering by failure mode, it was 8

9 found that the dataset can be represented by two failure mode groupings with respective mean UCS and CoV. Respective normal distributions are shown by dotted and dashed green lines and the combined bimodal distribution is shown by the full green line. This distribution conforms to the binned data well and further illustrates the need for data filtering by failure mode. This example illustrates that the mean value and CoV for the available data is highly misleading as the rock is made up of a rock with high homogeneous strength (UCS ho = 215 MPa/37%) and a matrix of lower strength (UCS he = 95 MPa/42%). The practical consequences of this misrepresentation are significant as discussed in the section on UCS in rock engineering. Figure 7. Heterogeneous quartzite showing bi-modal distribution due to different failure modes in the dataset. Summary and recommendations The standard and suggested testing methods for the determination of the UCS provide excellent guidance on specimen preparation and testing procedure such that the UCS testing procedures minimally impact the variability of the test results. The methods also provide reliable results for homogeneous rocks where failure is through predominately intact rock thus producing UCS ho, which in this case is synonymous with the intact strength UCS i. For heterogeneous rocks, the UCS tests results when available failure modes are considered should be reported as a UCS for heterogeneous rock, UCS he. When the CoV exceeds 30 to 35%, further investigations into the cause for the high variability are suggested. It is likely that the underlying data is bi- or multi-modal and the source of the variability needs to be identified and reported. Filtering of the UCS test data is required to obtain estimates for each group of data making up the entire dataset family. If data is affected by defects causing various failure modes, each mode should be analyzed separately and reported separately. If other factors are identified, the data should be reported in a similar manner for each identified group. UCS IN ROCK ENGINEERING The basis for rock engineering designs are rooted in empirical approaches. One of the common input parameters used in these empirical approaches is the UCS and the UCS value is either used directly or indirectly. In this section, the role of the UCS in 3 commonly used empirical approaches in rock engineering is discussed and suggestions are provided for selecting appropriate UCS values. Empirical spalling assessment When the stresses on the boundary of an underground excavation reach the rock mass strength, failure occurs. In good quality hard rock, such as that found in many underground environments, the failure process is described as spalling and the associated rock mass strength as the spalling strength. 9

10 The term spalling is purposely used to indicate that the failure process involves extensional splitting/cracking first analyzed by Fairhurst and Cook (1966). This process is fundamentally different from that of shearing which is commonly observed in weak rocks. Consequently, the stress state that leads to spalling is in the region of low confinement where the laboratory rock strength is typically defined by the tensile strength and the uniaxial compressive strength. From a tunnel design perspective two issues must be addressed: (1) what procedure should be used during the site characterization phase to assess if spalling should be anticipated during construction; and (2) if spalling is expected, what design procedure should be used to assess the lateral and radial extent of the spalled zone. Martin (2014) reviewed the various approaches and suggested that spalling strength can be estimated by using the crack initiation (CI) determined using UCS tests. Nicksiar and Martin (2013) compiled the crack initiation stress for 336 specimens of low porosity Igneous, Metamorphic and Sedimentary rocks. They found the CI stress to UCS strength ratio (CIR) ranged from 0.42 to 0.47 regardless of the rock type in uniaxial compression and when confined CIR ranged from 0.50 to If the maximum tangential stress on the boundary of a tunnel exceeds CI, spalling should be expected. To predict the extent of spalling ( ) the empirical equation is often used: = ( / ) (1) where is the maximum tangential stress on the boundary of the tunnel and a is the tunnel radius. When establishing the CIR, Nicksiar and Martin (2013) used rocks that ranged in UCS values from 15 MPa to 375 MPa, yet the CIR only ranged from 0.42 to Hence it would appear that CIR is insensitive to the rock homogeneity. Spalling initiates as a strain localization phenomenon, which means that the spalling volume on the boundary of the tunnel is relatively small. If the rock contains defects the depth of spalling should be assessed using the UCS for the defected rock (UCS he ) and filtered for UCS ho to provide a bound to the range of potential strengths and depth of spalling. If homogeneous, the UCS of the homogeneous, intact rock, UCS ho, should be used. Experience selecting the UCS value for application in Equation 1, suggests it should be the mean value (Rojat et al., 2009). Empirical pillar design The extensive research of Salamon and Munro (1967), using 125 case histories involving coal pillar collapses, led to the well-known pillar strength formula: = (2) where σ p (MPa) is the pillar strength, K (MPa) is the strength of a unit volume of coal, and W and H are the pillar width and height in metres, respectively, and α and β are empirical constants. The formula in equation 2 expresses the pillar strength as a collapse load that is a function of geometry of the specimen and the strength of a unit volume of the material. The similarities between the loading path in a UCS test and the loading path experienced by a pillar in a mine, as extraction proceeds, are obvious. The major differences being, the rate of loading and the scale of the specimens with the UCS volume being only a small fraction of the pillar volume. While equation 2 was originally designed for coal, similar forms of the empirical equation have been proposed for various rock masses (Martin and Maybee, 2000). Figure 8a shows the various pillar formulas compiled by Martin and Maybee (2000) and possible pillar stability curves for pillars in stressed hard brittle rock (Figure 8b) with the pillar strength normalized to the uniaxial compressive strength. It is evident from Figure 8a that despite the uncertainty in empirical formulas derived from back analyses, scaling the pillar strength to the UCS shows considerable consistency between the pillar design curves for 10

11 narrow pillars (W/H<2). Hence there is an expectation that the pillar strength may be linked to the UCS strength. a) b) Figure 8. (a) Comparison of various empirical pillar strength formulas. (b) Empirical pillar database showing Hoek-Brown brittle parameter derived pillar stability curves (both [a] and [b] modified from Martin and Maybee 2000). The notion that the UCS could be linked to the pillar strength was explored by Košták (1971). Košták proposed that pillar strength should be based on a cumulative distribution of UCS values for heterogeneous rock. Košták recommended that a minimum of 40 specimens of rock that preserve defects in the correct proportion to the intact (homogeneous) rock was needed. By combining both the UCS results for the defected and intact specimens, Košták suggested that the strength magnitude corresponding to p = 11.5% for the cumulative distribution, could be taken as representative of the pillar strength for any particular rock. Using the data from Košták, the pillar strength at a cumulative probability of 11.5% is 116 MPa, which is approximately 57% of the mean UCS ho, 94% of the mean UCS he and 63% of mean, combined UCS ho and UCS he. While none of these values are in agreement with the empirical strength formulas provided in Figure 8a, using the UCS he gives the closest agreement. Hence in order to use the existing empirical pillar formulas it appears that UCS he provides the closest agreement with the empirical experience. Tunnel boring machine penetration Empirical penetration prediction models (PPM) have been derived through correlating rock mechanical data (i.e., UCS, degree of jointing, orientation of joints) and TBM specific parameters (i.e., cutter diameter, cutter spacing) with achieved penetration rates (Gehring 1995; 1997; Bruland 2000). In modern tunneling, where TBMs are frequently used, penetration prediction models are of key relevance for estimating the construction time and costs. In general, empirical PPMs are based upon a prediction of the base penetration rate (mm/rev) which is subsequently reduced to account for rock mass and TBM characteristics (Lislerud 1988; Gehring 1995; Bruland 2000). Many PPM s consider the UCS of the rock as one key parameter for predicting the base penetration rate. Since the cutting process itself occurs on the cm-scale, Gehring (1995) discusses the relevance of an accurately determined UCS where failure of the rock specimens is unaffected by any macroscopic flaws or discontinuities. Test results where flaws lead to an obvious strength reduction shall not be considered for penetration prediction. Gehring (1995) therefore used specimens with a slenderness ratio of 1.0 to minimize strength reduction effects associated with flaws. However, as discussed previously, for specimens with a slenderness ratio <2.5 the strength tends to increase substantially and thus the increase in UCS found by Gehring (1995) is a combined influence of eliminated flawed specimen results and an unknown stress state. TBM penetration is dependent on the cutting process which is not only affected by the rock strength on the cm-scale, but also on the spatial distribution of rock strength exposed on the tunnel face. The strongest rock at the tunnel face often determines the penetration rate. Hence, the relevant strength for TBM performance assessment should be chosen as the upper limit of strength data. The average strength would lead to a too optimistic prediction of the base penetration rate. Only UCS ho values or UCS he filtered 11

12 for the homogeneous parts with failure through homogeneous intact rock should be utilized. For defining a representative UCS for TBM penetration prediction in heterogeneous rocks a sufficient number (i.e., typically >10) of representative specimens per rock unit is required. CONCLUSIONS While the UCS test is one of the most common tests in site characterisation programs, producing meaningful results remains a challenge. It is evident from the previous sections that the indiscriminate use of UCS data reported without careful screening may be misleading. Based on the findings from the work used in this paper, the following recommendations should be considered when undertaking a testing program to determine the UCS: All testing should be carried out by a qualified laboratory using appropriate QA/QC procedures using the ISRM or ASTM methods and procedures. UCS from homogeneous rock: o Use a minimum of 5 to10 specimens to define UCS ho=i mean and CoV. UCS from heterogeneous rock: o A minimum of 10 to 40 specimens may be required to define UCS he mean and CoV. o If CoV exceeds 30 to 35%, the data is likely multi-modal and one needs to identify sources contributing to the multi-modal behavior and report respective mean strengths and CoVs for each unique dataset. o Filtering of testing data is required to get the intact strength (UCS ho ) of the homogeneous component of a rock block while the tested dataset is representative of the strength (UCS he ) and variability of a heterogeneous rock block. o Depending on the empirical design approach, either (UCS ho or UCS he ) or both may be relevant. REFERENCES Amann, F., Undul, O., Kaiser, P.K. (2013) Crack initiation and crack propagation in heterogeneous sulfaterich clay rocks. Rock Mech Rock Eng. doi: /s ASTM D (1991) Standard test method for unconfined compressive strenght of intact rock core specimens. Bewick, R.P., Kaiser, P.K., Valley, B. (2011) Interpretation of triaxial testing data for estimation of the Hoek-Brown strength parameter mi. Paper th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, June Bewick, R.P., Kaiser, P.K. (2013) Discussion on An Empirical Failure Criterion for Intact Rocks by Peng et al. (2013). Rock Mechanics and Rock Engineering. DOI /s Bieniawski, Z.T. (1967) Mechanism of brittle fracture of rock, parts I, II, III. Int. J. Rock Mech. Min. Sci. 4(4), Bieniawski, Z.T. (1968) The effect of specimen size on compressive strength of coal. Int. J. Rock Mech. Min. Sci. 5, Blanks, R., McNamara, C. (1935) Mass concrete tests in large cylinders. ACI Journal Proceedings, 31(1), Bruland, A. (2000) Hard Rock Tunnel Boring. Vol. 1. Trondheim: NTNU Trondheim. Dhir, R.K., Sangha, C.M. (1973) Relationships between size, deformation and strength for cylindrical specimens loaded in uniaxial compression. Int. J. Rock Mech. Min. Sci. 10, Franklin, J.A., Hoek, E. (1970) Developments in triaxial testing equipment. Rock Mech. 2, Fairhurst, C., N. G. W. Cook (1966). The phenomenon of rock splitting parallel to the direction of maximum compression in the neighbourhood of a surface. In Proc. of the 1st Congress of the International Society of Rock Mechanics, Lisbon, pp Gehring, K. (1995) Leistungs- Und Verschleißprognosen Im Maschinellen Tunnelbau. Felsbau 3. 12

13 Gehring, K. (1997) Classification of Drillability, Cuttability, Boreability and Abrasiveness in Tunnelling. Felsbau 3. Hoek, E., Brown, E.T. (1980) Underground excavations in rock. The Institution of Mining and Metallurgy, London. Hoek, E. (1983) Strength of jointed rock masses. Geotechnique, 23(3) Hoek, E., Brown. E.T. (1997) Practical estimates of rock mass strength. Int. J. Rock Mech. Min. Sci. 34(8), Hudson, J.A., Brown, E.T., Fairhurst, C. (1971) Shape of the complete stress strain curve for rock. Proc. Symp. Rock Mech. 13 th, Univ. Illinois, Urbana, IL. International Society for Rock Mechanics (1979) Suggested methods for determining the uniaxial compressive stregnth and deformability of rock materials. International Society for Rock Mechanics (1999) ISRM suggested method for the complete stress-strain curve for intact rock in uniaxial compression. Int. J. Rock Mech. Min. Sci. 36, Kaiser, P.K., Kim, B. (2014) Characterization of strength of intact brittle rock considering confinement dependent failure processes. Rock Mech Rock Eng. DOI /s Kaiser, P.K., Amann, F., Bewick, R.P. (2015) Overcoming challenges of rock mass characterization for underground construction in deep mines. 13 th International ISRM Congress Montreal, QC. Košták, B. (1971). Pillar strength prediction from representative sample of hard rock. Int. J Rock Mech, Min Sci. 8(5), doi: / (71) Lislerud, A. (1988) Hard Rock Tunnel Boring, Prognosis and Costs. Tunneling and Underground Space Technology 3 (1): Martin, C.D. (1993) Strength of massive Lac du Bonnet Granite around underground openings. Ph.D. Thesis. University of Manitoba, MB. Martin, C. D. (2014) The impact of brittle behaviour of rocks on tunnel excavation design. In L. R. Alejano, Á. Perucho, C. Olalla, & R. Jiménez, (pp ). In Proceedings EUROCK 2014, Rock Engineering and Rock Mechanics: Structures in and on Rock Masses, Vigo. Taylor and Francis Group, London, UK. Martin, C.D., Maybee, W. (2000) The strength of hard-rock pillars. Int J. Rock Mech. Min. Sci., 37(8), Mogi, K. (1966) Some precise measurements of fracture strength of rocks under uniform compressive stress. Rock Mech. Eng. Geol., 4: Nicksiar, M. & C. D. Martin (2013) Crack initiation stress in low porosity crystalline and sedimentary rocks. Engineering Geology 154(64 76). Peng, S.D. (1970) Failure and Fracture of Chelmsford Granite, PhD Thesis, Stanford University. Peng, S., Johnson, A.M. (1972) Crack growth and faulting in cylindrical specimens of Chelmsford Granite.Int. J. Rock Mech. Min. Sci. 9, Perras, M.A., Diederichs, M.S., Amann, F. (2012) Fracture initiation and propagation in the Quintner Limestone. ARMA th US Rock Mechanics Symp. Chicago, IL. June 24-27, Rojat, F., V. Labiouse, P. K. Kaiser, & F. Descoeudres (2009) Brittle rock failure in Steg Lateral Adit of the Lotschberg Base Tunnel. Rock Mech Rock Eng. 42, Salamon MDG, Munro AH. (1967) A study of the strength of coal pillars. J S Afr Inst Min Metall. 68: APPENDIX A - TERMINOLOGY For clarity the following terminology is used in this article starting from the definition of a rock mass through to UCS and specimen types. Rock mass: made up of rock blocks defined by block forming open discontinuities. Rock block: may be homogeneous (i.e., relatively similar properties throughout) or heterogeneous (i.e., with properties changing spatially within the rock block). Intact test specimen: typically obtained by coring, is a coherent piece of rock that could be sampled without breakage during drilling; it may be discontinuous and damaged at the micro-scale but it is intact. 13

14 Intact homogeneous rock (Figure A1a): Cylindrical rock specimens which visually appear to be homogeneous with limited variability in grain size distribution, mineral grain composition, or extent of micro-fracturing, such as Carrera Marble or Lac du Bonnet Granite (Martin 1993). Intact heterogeneous rock (Figure A1b): This satisfies the intact homogeneous rock definition except homogeneity. Cylindrical rock specimens which visually appear heterogeneous with evident veinlet stockworks or non-uniform grain size distribution at the specimen scale, variable mineral grain composition, or extent of micro-fracturing, such as quartz monzonite or sulfate rich clay rocks (Amann et al., 2013). UCS test: A test on a cylindrical rock core specimen that records the collapse load for a given loading condition that meets ASTM standard or ISRM suggested method requirements of: height to diameter ratio of ; diameter preferably of not less than NX core size (~54 mm); Specimens shall be tested at its natural water content; Loading rate MPa/s (total testing/loading time 5-10min). UCS value: The collapse stress regardless of failure mode calculated from the collapse load and cylindrical specimen loading area. Homogeneous rock UCS (UCS ho ): The UCS value obtained from failure through predominately homogeneous, intact parts of the rock. A small scatter (CoV <25%) in UCS values should be anticipated. UCS ho is often called UCS i, the strength of the intact part of the defected rock. Heterogeneous rock UCS (UCS he ): The strength based on UCS test results where available valid failure modes are considered regardless of failure type. A large scatter (CoV >25%) in UCS values should be anticipated. Coefficient of Variation (CoV): a measure of relative variation of a dataset given as the standard deviation as a percentage of the mean. Figure A1 Examples of homogeneous (a) and heterogeneous (63mm in diameter) (b) rock core specimens. 14