A comprehensive investigation of crack damage anisotropy in Cobourg limestone and its effect on the failure envelope

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1 A comprehensive investigation of crack damage anisotropy in Cobourg limestone and its effect on the failure envelope E. Ghazvinian, M. Perras, C. Langford & M. Diederichs GeoEngineering Centre, Queen s University, Kingston, ON, Canada D. Labrie CanmetMINING, Natural Resources Canada, Ottawa, ON, Canada ABSTRACT Crack damage anisotropy in the Cobourg limestone has been studied to understand the effect of argillaceous wisps and blebs (that mark the irregular apparent bedding) on the fabric-guided micro-fracturing phenomenon in argillaceous limestone. For this purpose a detailed testing program was carried out that includes uniaxial (Unconfined Compressive Strength or UCS), triaxial and indirect tensile (Brazilian) tests for five sets of specimens with different fabric orientations. The results are presented in this paper. RÉSUMÉ L anisotropie due à la propagation des fissures à l intérieur du calcaire de Cobourg a été étudiée pour comprendre l'effet des bandes foliées et des intrusions argileuses (qui forment le litage apparent irrégulier du calcaire) sur le phénomène de micro-fracturation liée à la texture dans les calcaires argileux. A cet effet, un programme d'essais détaillé a été réalisé lequel comprend des essais uniaxiaux (essais de résistance en compression non confinée ou C), triaxiaux et de tension indirecte (essai brésilien) sur cinq séries d'échantillons avec différentes orientations de texture. Les résultats sont présentés dans le présent document. 1 INTRODUCTION Many rocks show anisotropic mechanical properties, for example due to bedding, layering, foliation, fissuring and/or structures. The effect of layering on the ultimate strength and elastic constants of rock has been studied comprehensively in the past, for instance in Jaeger (19), Hoek (1964) and Amadei (1983, 1996). Fabricguided micro-fracturing phenomenon, however, that plays an important role on the Crack Initiation () and crack propagation () thresholds are still not well understood. The anisotropic behaviour in rock that includes a planar fabric can be attributed to the existence of one or a combination of fabric elements such as: grain shape orientation, mineral segregation or alternating depositional layers, crystallographic preferred orientation and aggregate shape orientation (Milnes et al 26). The presence of these elements can change the microfracturing behaviour in brittle rocks and consequently change the anisotropy model behaviour. The different anisotropy models are shown in Figure 1. Depending on the type of fabric element present in a rock, the rock can be completely anisotropic or isotropic at and/or stress levels while remaining anisotropic for peak strength (Hakala et al 25, Ghazvinian et al 213). This study addresses the crack damage anisotropy and the effect of fabric on the tensile strength and on Hoek- Brown (1997) failure envelopes of the Cobourg limestone. 2 COBOURG LIMESTONE The Cobourg Formation is an argillaceous limestone, which is Middle to Upper Ordovician in age and part of the Trenton Group. It is found in the Michigan Sedimentary Figure 1. Anisotropy models for different rock types (after Shea and Kronenberg 1993). Basin, and a similar formation, the Lindsay Formation, is found in the adjacent Appalachian Sedimentary Basin. These two basins were separated by the Algonquin arch during deposition, however the regional environment indicates that the larger limestone package (the Trenton Group) marks a transition from a restricted coastal to a shelf environment (Mazurek 24) and is applicable to both basins (Gartner Lee 28). The Cobourg is light gray

2 in colour and contains dark gray argillaceous wisps and blebs which loosely mark the irregular bedding. The light gray portions are fossil rich packstones and the dark gray portions are lime-mudstone. The latter is likely due to bioturbation shortly after deposition and/or compaction during diagenesis. Typically the argillaceous bedding grades into or abruptly changes to light gray fossiliferious limestone. The anisotropy in this rock is governed these features, which are shown in Figure 2. Figure 2. A 2 cm diameter core of the Cobourg limestone, from the Bowmanville quarry, Ontario. 3 EXPERIMENTAL METHODOLOGY To address the dependency of the mechanical properties of the Cobourg limestone on the orientation of the fabric in this rock with respect to the direction of the major principal stress (loading direction), large diameter cores (approximately 2 cm) were obtained from a quarry in Bowmanville, Ontario, courtesy of the Nuclear Waste Management Organization of Canada (NWMO). The large diameter cores were drilled in five different orientations with respect to the apparent bedding that resulted in 5 sets of specimens with beddings oriented at, 3, 45, and 9 degrees (Fig. 3). These specimens were used for Unconfined Compressive Strength (UCS), triaxial and indirect tensile (Brazilian) tests. Figure 4. The Cobourg limestone specimens with various fabric orientations prepared for UCS and triaxial tests. Loading was conducted under axial strain control mode while the specimen deformation was recorded by using 2 opposing axial and 2 lateral strain gauges for 4 out of the 6 specimens in each set. Deformation for the 2 remaining specimens in each orientation set was collected using LVDTs (for axial deformation) and a chain extensometer (for circumferential deformation). The Acoustic Emission (AE) activity of specimens was also monitored during the tests by using two PAC R15 AE transducers, and was used for the estimation of the crack damage thresholds. The testing setup is shown in Figure 5. Figure 3. Drilling of the large diameter Cobourg limestone cores with different orientations. 3.1 Unconfined Compressive Strength Testing For each orientation, 6 specimens with an average diameter of 54 mm and a length-to-diameter ratio of approximately 2.2 were prepared and tested for UCS according to ISRM (1999) and ASTM (213a, 213b) suggested methods. An example of the specimens prepared for compressive testing (UCS and triaxial) with various fabric orientations are shown in Figure 4. Figure 5. The setup used for testing the Cobourg limestone samples, with axial LVDTs, circumferential chain and AE sensors.

3 Poisson s ratio 3.2 Triaxial Testing Triaxial tests were completed for each orientation set included 2 specimens, one tested with a 4 MPa confining pressure and the other with a 1 MPa confinement. The specimens used for triaxial testing were prepared based on the same specifications used for preparing the UCS specimens, and the testing was completed according the ISRM (1983) suggested method and ASTM (213b) for triaxial testing. The specimens axial and lateral displacements were recorded by using LVDTS and a chain extensometer wrapped around the specimen circumference, respectively. The collected axial and lateral strains were used for identification of crack damage thresholds for the triaxial specimens. 4 TESTING RESULTS 4.1 Elastic Constants and Crack Damage Thresholds The Elastic constants (Young s modulus and Poisson s ratio) for the UCS specimens were calculated over an interval between 3 to 5% of the ultimate peak strength. The calculated Young s moduli and Possion s ratios for the UCS samples with different fabric orientations with respect to the loading direction are demonstrated respectively in Figures 8 and 9. Orientation 3.3 Indirect Tensile (Brazilian) Testing The Brazilian specimens were cut from the top and bottom part of the UCS and triaxial cores at the thickness of approximately 4 mm to satisfy the requirements of ISRM (1978) suggested method and ASTM (213c) for determining tensile strength of rock materials. The 45 specimens prepared for Brazilian testing are shown in Figure 6. E (GPa) E (GPa) Figure 8. Young s modulus for the Cobourg limestone specimens with different fabric orientations. Figure 6. Samples of 45 Brazilian testing. specimens prepared for The Brazilian specimens in each fabric-orientation set were divided into 3 groups to be tested under three different loading angles of, 45 and 9 degrees as illustrated in Figure 7. The tests were conducted under load control mode with a loading rate of.11 kn/sec. The mean Young s moduli for the different fabric orientations are represented by a bi-modal distribution, with the maximum value occurring at 3 and the second maximum at. The bi-modal distribution observed in Figure 8 can also be due to an inconsistent behaviour in specimens with a 45 orientation. A significant trend cannot be established between the fabric orientation and the mean Poisson s ratios, however; the maximum Poisson s ratio is observed, in Figure 9, to occur for specimens oriented at 3, similar to the maximum Young s modulus. Orientation Layering orientation Loading angle Figure 7. Schematic illustration of loading angle for a specimen with layering orientation of 45. Poisson s ratio Figure 9. Poisson s ratios for the Cobourg limestone specimens with different fabric orientations.

4 (MPa) The measured uniaxial peak strengths for the specimens with different layering orientations are shown in Figure 1. The range of strengths for the specimens in each orientation set is observed to be considerably wide. This will be further discussed in the next section. The trend that is established for the mean peak strengths shows that the maximum strength occurs for the 9 specimens, however, the classic U-shaped anisotropic behaviour (Figure 1) is not observed. The heterogeneous nature of the material certainly contributes to the variation in the results and possibly over shadows the classic U- shaped behaviour with respect to the orientation. UCS (MPa) y = 4E-5x x x Figure 1. uniaxial strengths for the Cobourg limestone specimens with different fabric orientations. 4.2 Tensile Strength The tensile strength of the Cobourg limestone, obtained from the Brazilian testing of specimens with different layering orientations at various loading angles, ranged between approximately 3. MPa to 1.4 MPa. The tensile strength of 3 specimens with fabric orientation had to be ignored due to the presence of pre-existing fractures in these specimens. The mean distribution of the tensile strengths for various layering orientations and loading angles is shown in Figure 12. Since the rotation of the 9 specimens does not influence the loading scenario therefore the same test results are repeated at the various loading angles for the 9 fabric orientation only (in Figure 12). It is rather interesting to notice that loading angle plays an important role in the measured tensile strength when comparing the tensile strengths of specimens tested at a loading angle (increasing trend with increasing the fabric orientation) with samples tested at a 9 loading angle (bi-modal distribution). Further testing with larger number of samples is required to better understand the effect of loading angle on the failure mechanics of Brazilian samples and consequently the determined tensile strength. Crack initiation and crack propagation thresholds estimated for the Cobourg samples are plotted in Figure 11. These thresholds are calculated from the AE data according to the method described in detail by Ghazvinian et al (212). A minor dependency of and thresholds to the layering orientation can be established, which shows the minimum and to occur when the layers are oriented at 3 with respect to the loading direction (MPa) 4 2 y = -7E-5x x x Figure 12. Mean distribution of the Cobourg limestone tensile strength for various layering orientations and loading angles y = 2E-5x x x Figure 11. and thresholds for the Cobourg limestone specimens with different fabric orientations. Figure 13. Normalized distribution of the mean tensile strengths for the Cobourg limestone.

5 The mean distribution of tensile strengths for different layering orientations and loading angles, normalized to the minimum tensile strength is illustrated in Figure DISCUSSION OF RESULTS Distinguishing between the UCS specimens according to the failure mode shows that and 9 specimens mainly failed in axial splitting, while 3, 45 and specimens failed in mix modes. Pure shear failure only occurred for a few number of 45 and specimens (Fig. 14) Axial splitting 4 Shear 3 Mix mode Figure 14. Failure modes for the UCS samples. UCS (MPa) Investigation of the fabric and apparent bedding present in the Cobourg limestone reveals that the relative scale of the fabric and specimen sizes can lead to a heterogeneous behaviour in some specimens. This can explain the reason for the wide distribution of strengths and crack damage thresholds for specimens in the same orientation group. Therefore it is anticipated that more uniform and consistent results could be obtained from testing larger specimens or a larger number at each orientation. Some other rock types such as Olkiluoto mica gneiss show isotropic behaviour at the stress level and anisotropic behaviour at and peak strength (Hakala et al 25), in comparison to the Cobourg limestone, the anisotropy is weakly evident at all crack damage stress levels (i.e. and ) and the peak strength. 6 FAILURE ENVELOPES To predict the in situ behaviour of an underground opening excavated in Cobourg limestone, it is worthwhile to examine the failure envelopes of suites of specimens with different anisotropy angles (fabric orientation relative to the stress orientation). The data collected from UCS, triaxial and Brazilian tests for the Cobourg limestone specimens with different fabric orientations were used to establish the Hoek-Brown (1997) failure envelopes. Hoek-Brown (1997) envelopes for, and thresholds for each orientation were estimated and are illustrated in Figure 15. The tensile strengths used for calculating the and thresholds are the Brazilian test strengths for each orientation (the effect of loading angle was ignored and only the fabric orientation was considered). The tensile strengths used for deriving the envelopes were calculated as 1/8 of the thresholds based on the Griffith theory (Perras & Diederichs 213) degree 3 degrees 45 degrees degrees 9 degrees Figure 15. Hoek-Brown envelopes for peak, and of the Cobourg limestone with various fabric orientations.

6 Figure 16. Comparing the Hoek-brown envelopes of different fabric orientations for peak, and. Studying the failure envelopes for peak, and thresholds in Figure 15 shows that there is a gap between the and peak envelopes for the and 9 specimens. This gap decreases for the 45 and specimen sets and nearly diminishes for the 3 specimens. This suggests that in specimens where shear failure is the dominant mode of failure, the peak strength and yielding strength of the rock () are in a close range, if not identical. Comparing the peak, and stress envelopes across different orientations in Figure 16 shows that the 9 peak envelope stands drastically higher in comparison to the peak envelope of other orientations. 9 and 45 envelopes are also seen as respectively representing the upper- and lower-bound for the and threshold envelopes. 7 CONCLUSIONS The anisotropy of the Cobourg limestone at different crack damage stress levels was examined in this study. The results show that the peak strength, and thresholds of the Cobourg limestone have a minor dependency to the orientation of the apparent bedding. Further testing is however recommended on larger samples. The in situ behaviour of the Cobourg limestone for different fabric orientations with respect to the direction of the major principal stress as predicted by the Hoek-Brown strength criterion (1997) is more or less similar for all orientations, except for the 9 orientation, which exhibits a higher strength. In general 9 and 45 fabric orientations define the upper- and lower-bounds for and threshold envelopes of the Cobourg limestone. A good understanding of the anisotropic behaviour of crack damage stress levels of rocks in the laboratory helps to improve the prediction of the rock mass behaviour around underground openings. ACKNOWLEDGEMENTS The authors would like to acknowledge the Nuclear Waste Management Organization of Canada (NWMO) for funding this research and providing the samples for testing, and in particular Mark Jensen and Tom Lam for their valuable comments. Drilling, preparation and testing of the Cobourg limestone test specimens were completed at CanmetMINING Laboratories, Natural Resources Canada, Ottawa, Ontario, by Blain Conlon and Gilles Brisson. This work was also supported by the National Science and Engineering Research Council of Canada (NSERC). REFERENCES Amadei, B Lecture Notes in Engineering: Rock Anisotropy and Theory of Stress Measurements, Edited by C.A. Brebbia and S.A. Orszag, Springer- Verlag, Berlin: Amadei, B Importance of anisotropy when estimating and measuring in situ stress in rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 33(3): ASTM. 213a. Standard Practices for Preparing rock core as cylindrical test specimens and verifying conformance to dimensional and shape tolerances. Designation D4543-8, ASTM International, West Conshohocken (PA): 9 p. ASTM. 213b. Standard Test Method for Compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. Designation D712-1, ASTM International, West Conshohocken (PA): 9 p. ASTM. 213c. Standard Test Method for Splitting tensile strength of intact rock core specimens. Designation D3967-8, ASTM International, West Conshohocken (PA): 4 p.

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