Lab Testing for Empirical Design D. Beneteau, D. Milne and Z. Szczepanik University of Saskatchewan
ABSTRACT: Ideally data for rock mass characterization is obtained through measurement. In all but weak rock masses and high stress conditions, joint strength and spacing may be more important to the response of the rock mass to mining than basic intact properties of the rock. However, laboratory testing should be performed in all cases as it serves as one element of an overall rock mass description. This paper is a practical guide for mining personnel for requesting laboratory investigations of rock. It addresses questions often received by industry regarding typical testing options such as the number of tests required, recognizing that properties of intact rock are often highly variable. It also provides suggestions regarding sample selection. A variety of both destructive and non-destructive test options are considered as rock testing programs should concentrate on the properties which most influence the site specific requirements requirements of any given operation. operation. 1 INTRODUCTION 1.1 Back to Basics The basic procedures for rock testing have been around for decades. Since the mass marketing of computers in the late 1970’s, analytical methods such as numerical modelling have been growing in complexity and designers have been advancing the theories and methods of calculations now possible with powerful computers. Great effort has been placed on improving measurement methods such as through stress cells, extensometers, LiDAR, borehole cameras, seismic systems, etc. The Rocscience (https://www.rocscience.com) programs are an excellent example of computer programs commonly used to manipulate the basic rock data retrieved for mine design. This paper supports these initiatives, but serves to remind that basic experimentation is still the root of rock engineering design. The lab experiments for obtaining basic rock properties are well written in literature, but questions by clients highlight that there is a gap in knowledge between those requesting the information and those performing the testing. This paper helps to guide those requiring rock properties in how to communicate with their rock mechanics lab and possibly, their design specialists. 1.2 The Specialists Lab testing of rock is generally requested directly by a mining operation, or indirectly by a consultant such as a numerical modeller that needs rock properties for calibration purposes. Regardless, it is generally mine
personnel that assemble the samples for the facility that will perform the lab testing. This paper is aimed at helping those middle people. It is very important that industry accepted testing protocols are explicitly explicitly followed followed by experienced experienced technicians/technologists. If there is one thing for certain about lab testing of rock, it is that rock is never predictable. Proper protocols must be adhered to so that the variability in results can at least be related to the rock itself and not to non-standard methodologies may have affected the results. Goodman (1989) is an excellent reference that provides background information on the fundamentals of lab testing for rock mechanics. 1.3 Choosing Testing Methodologies The most common procedures for consideration in North America are the American A merican Society for Testing and Materials International (ASTM) and the International Society for Rock Mechanics (ISRM). The ASTM standards are developed by consensus and define the way that tests are performed, and describe the precision of results. These are developed to represent the ASTM members, producers, users, consumers, government and academia (ASTM, 2014). The ISRM standards (ISRM, 2007) are similarly developed by consensus. However, these are recommended procedures and not standards (ISRM, 2014). There can be slight differences in methodologies between these organizations which is why it is so im portant to reference the actual one used. For instance, ASTM and ISRM test specimens for UCS have
height-to-diameter ratios of 2.0 to 2.5, and 2.5 to 3.0, respectively. As both ASTM and ISRM procedures are well accepted, it is most important to be consistent over time in choosing procedures so that data can be properly compared. For any tests being performed, it is advised to follow an existing method, if available. It is then possi ble to back compare results to published information. However, there are cases when new procedures must be devised. If new testing is successful, it is beneficial to industry to allow for publication of the work so that duplication of effort is avoided. In publishing that procedure, be very specific to suppliers of components and dimensions of equipment as this can save the people trying to reproduce the work hours of frustration. Most recently, we spent hours trying to find a supplier of a 50 mm diamond saw blade in order to conduct fracture toughness testing. 1.4 Selecting the Testing Facility Different consulting companies and universities provide rock testing services in Canada. It is common for perspective clients to request a lab that is ISO certified as this provides confidence in quality assurance. ISO certification is a very onerous process for laboratories, especially university laboratories where there may be insufficient staff and budget to perform the work required of certification. The reality is that not all labs with acceptable test equipment and qualified staff are certified. Furthermore, clients may question relying on testing done by graduate students. Students can learn from witnessing/performing testing with various rock types rather than relying on data provided by external sources. Testing results, however, can suffer if experienced personnel are not conducting the work. The following are typical questions that can be asked by the client to gain confidence in the quality of testing results by any lab: 1. Is the work being performed or directly supervised by an experienced technician/technologist specializing in rock mechanics? 2. Is the lab adhering to ASTM/ISRM rock standards, and if so, which ones? 3. What type of equipment is used to ensure the ends of samples are properly prepared? 4. Can the lab provide calibration curves for equipment? 5. Will the lab allow the client to watch testing being done? Of those questions, ensuring the work is performed by, or under the direct supervision of a qualified personnel is extremely important. Due to variability in rock types and the complexity of equipment, it can take many years to master rock mechanics testing. Even after many years of experience there are often new surprises to deal with. It may be something as
seemingly insignificant as a small change in chemistry that will affect the transmission of waves through a sample. 1.5 Variability between Laboratories It is reasonable, though not desired, to expect different results between labs. One way to remove this uncertainty is to make use of only one lab, but this may not be in the client’s best interests. Therefore, it is im portant to be aware that variability can arise even while adhering to the standards. Pincus (1993) reported on an interlaboratory testing program using 8 different laboratories. Testing was performed on granite, sandstone, limestone and marble. For the four different ASTM procedures that were used (unconfined compressive strength (UCS), velocities, tensile strength, and elastic modulus from UCS) , it was shown that samples sent to these different laboratories showed variable results. There are many different reasons for variability between laboratories including: 1. End effects. In a paper by Szczepanik et al. (2007), end preparation alone caused variability in strength by as much as 50%. The standards only specify that ends are to be parallel, with a maximum degree of roughness (surface flatness). They do not state the actual equipment to be used to prepare the ends. Many options exist from grinding to polishing and these all meet end preparation requirements of perpendicularity to sides and end surface flatness. Testing has shown significant variability in strength, even when following the standards. 2. The samples themselves. Two samples obtained side-by-side from a core box can vary significantly in strength just due to microfractures and rock fabric. 3. Loading rates. The ASTM and ISRM procedures only state that the UCS samples must be broken in a certain time frame. For example, in 2 to 15 minutes for ASTM. Testing, such as that done by Peng (1975) has shown that rock will break at a higher compressive strength when loaded at higher strain rates. Even an ex perienced technician can be surprised at how weak/strong different core samples are so even setting a loading rate relies on experience. 1.6 Rock or Soils Laboratory In the context of this document, a rock mechanics la boratory is equipped to test solid rock specimens. One notable difference between these two materials is that the strength of soils is generally in KPa’s while that of rock is in MPa’s. While it is very important that the
natural moisture content of soils be preserved for testing as effective stress is highly dependent upon the water content, most rock mechanics tests for mining are done once rock is air dry. Difficulty arises for highly weathered rock for which strength properties are required. For those rocks, strength may be highly dependent upon the moisture content so the client must preserve the core. End preparation for UCS testing may not be feasible in some cases as the samples will crumble during sawing. Or if cutting is successful, it may not be possible to grind the ends to be perfectly parallel or apply an end cap. With these considerations in mind, some deviations from proper ASTM/ISRM procedures may occur merely due to the nature of the samples. All deviations should be noted with results. 1.7 Program Design Clients do occasionally ask for recommendations on test program design. They may have been advised by their numerical modelling consultant to provide rock properties and would like guidance on what they should do. The main objective of the testing is to get the properties required by those specialists so they should be included in the discussion. But rock mechanics testing is a specialty too and there may be times when all parties should be brought into the discussion. Each testing program will have its own requirements. We typically see programs that include uniaxial, tensile strength and occasionally triaxial testing. On occasion, clients may request shear testing. Nondestructive rock characterization tests are also routinely performed such as density and velocity. 1.8 Number of Tests It is very common for clients to ask for three repetitions for each rock type/test type. This could have evolved from concrete testing, in which it is common to test 3 cylinders at each cure time. ASTM and ISRM actually recommend many more tests, typically as many as 10 samples for each rock/test type. The reality is that for routine rock testing, clients typically do not follow the recommendations of the standards. The quantity of testing is actually dictated by the client’s budget and design requirements. A lab should respect the request of the client as their duty is not to analyze the data but to provide quality results. Also, it may not be physically possible to get a large num ber of samples due to the availability of the rock being tested. Samples may be from a narrow seam or the RQD may be so poor that only a few intact samples can actually be selected. Gill et al. (2005) emphasize that “the precision index, testing procedures, test selection, sampling locations, specimen preparation are up to the engineer’s judgement” and those authors do
provide guidance on sampling theories from the perspective of the requirements of the standards. It is unrealistic in rock testing to have a constraint on the number of rock samples. However, the paper by Ruffolo and Shakoor (2009) does support that 10 core samples is the minimum number required for estimating the mean unconfined compressive strength. Regardless of the number, we recommend that the clients aim to get the greatest visual homogeneity between samples of a given group. Clients can opt to do non- destructive testing of those samples as a further indication of homogeneity, as described in Section 3. According to Hoek in Practical Rock Engineering (2007), “10 percent of a well-balanced rock mechanics program should be allocated to laboratory testing”. From the laboratories point of view, we do not want our clients to be upset when they get inconsistent results. However, the client should always consider the sensitivity of the design to the es timated lab test data. The unconfined compressive strength of the rock is a key input in many rock mass classification systems, but some of the strength categories have a range of 100 MPa. For this application, inconsistent lab results may not be a concern. Triaxial testing for numerical modelling is more sensitive to sample variability. A failure envelope for Hoek-Brown failure criteria can be estimated from 3 triaxial tests, however, the results will be very sensitive to rock varia bility. Rock can have hugely variability properties between specimens, while adhering to given procedures. In a recent test, we had two samples that were cut side by side and had a similar appearance. The UCS results were 27.1 MPa and 92.6 MPa versus another set of side-by-side cores from the same shipment that were 84.5 MPa and 116.8 MPa. We do not reject results due to scatter. We encourage clients to look at before/after photographs of samples so that they can get clues as to why there may be such deviation. 1.9 Core Diameter Literature in general tends to support a 50mm core diameter as the standard testing size. As core size is often dictated by geology and drill availability, the engineering department may not have any control over this. It is important to document core diameter with results. We have tested rock as small as 1” diameter, to several inches in diameter, while adhering to the general principles of sample preparation of the specified test procedures. A testing facility will likely have the capability of preparing cores from blocks of rock. In this case, the client should consult with the lab in regards to a practical size block that the lab can handle. What is most important in sample dimensions is to ask your laboratory the capacity of their load frames and triaxial cells prior to shipping samples. As core
size increases, so does the effective load required for failure. Especially under confinement in triaxial testing, a very strong rock may not be able to be broken if the core diameter is too large. Also with respect to triaxial testing, there will be a limitation for sample dimensions based on the dimensions of the cell itself. Sometimes oversized samples can be cored down using a drill press in the lab, but not always. The client should always be aware that added sample disturbance will result from re-coring samples to a smaller size. 1.10 Core Selection Ideally, all samples for a similar rock type are collected side by side so that the composition and stress environment of groupings of samples are as close as possible. But the reality of needing to preserve and/or assay core, and of sampling from thin seams and low RQD dictates that core of similar rock type may be sampled from across many holes. This can be one ex planation for variable results. This variability should not be treated as sampling or testing error, it is providing further information about the properties of the rock. Ideally the core for a given test program should also be of comparable diameter. But it is also common that multiple core sizes are drilled in a given mine. At a minimum, all triaxial testing should be on similar size core if possible. It is preferable if the client provides an Excel spreadsheet in which each piece of core is identified, along with the test required. The nomenclature used for naming core can often be unusual and difficult to decipher when written with markers on samples. There is less chance for error if this is done in advance by the client. In addition, a geologist should ensure that groups of similar rock type are identified properly. If the rock is weak and may deteriorate with exposure to air and water evaporation, it should be individually encased in wax or sealed in tight plastic bags. All core should be packed carefully into core boxes, plastic pails or cardboard boxes in such a way that the core will not slide. Each core piece should be individually labeled and listed in a table of samples that is printed. If the core is silty, the label may wear off with time so those samples should also be placed in la belled plastic bags. Core lengths should be sent at least 3 times the diameter for each triaxial and UCS test so that the final specimen is sufficiently long once trimmed. It is advised to send additional core as pieces do arrive that have split on healed fractures during shipment. In addition, sometimes samples breaks on fractures during sample preparation. Those samples must be discarded and highlight how sample selection alone biases the results of laboratory testing.
It is recognized that, especially in weak rock, the samples selected are the samples that have survived drilling, transport and possibly storage. The bias towards stronger rock is recognized, and is built into our empirical design methods.
2 STRENGTH TESTING RESULTS 2.1 Presenting results In acknowledgement of the variation between strengths of samples, we recommend a simplified graphical presentation of results as shown in Figure 1. Simple charts as shown can be created in Excel by inserting “High-Low-Close” stock chart. This particular chart illustrates UCS results for dolomite samples tested for an undergraduate rock mechanics class. Over the years, different core boxes of dolomite from a drill program in Saskatchewan have been used in teaching. A qualified technologist has prepared sam ples and demonstrated UCS testing to groups of 3 or 4 students. In looking at this chart, it can quickly be observed that there were 5 samples tested in 2012, 4 in 2013, and 9 in 2014. The standard deviation was variable between years, and greatest in 2014. With the 18 sam ples combined, the standard deviation was similar to that of 2013 and overall, the average strength across the years was consistent. Depending upon the rock mass classification for which strength testing is being performed, the strength categories for the classification system can be overlain on this chart. Figure 1 illustrates the seven ISRM (2007) “R” categories. Each classification system provides a different rating for the strength of intact rock material. The Bieniawski (1989) rock mass rating (RMR) provides a strength rating that is between 0 and 15 for the allowable 100 points required. This uses the seven ISRM categories. Another common system for mining, the Q system (Barton et al., 1974) indirectly incorporates strength through the stress reduction factor (SRF). In addition to plotting results,it is also important to note the type of failure associated with each specimen. This could possibly be used to explain the variability in some of the results. Typical failures are identified in Figure 2. 2.2 UCS Testing Figure 3 shows a graphical representations of the UCS data by Pincus (1993). Each point represents five replications of a rock type by each of seven different labs. ASTM procedures for UCS were followed. These five rock types were selected to represent a range of values of rock properties, and were of uniform composition. The granite and marble are mostly in the ISRM R5 strength category and the Sandsotone
and Limesone are generally R3 (Figure 3). Typical rock from mining operations may not be as homogeneous as these rock types. These simplistic plots in Figure 3 highlight the uniformity of these rocks versus the limestone in Figure 1 through narrower standard deviations. As per the comment in Section 1.5, they also confirm that varia bility exists between laboratories.
from UCS testing. This is as expected from the varia ble UCS results of Figure 3. From a budgeting point of view, it is typically less expensive to get moduli (both Young’s Modulus and Poisson’s ratio) from UCS testing. Due to variability with all testing, the results from UCS testing may be adequate in most instances. .
Figure 1. This square symbols on this chart represent the mean strength in MPa of dolomite rock t ests, and the vertical lines represent one standard deviation of mean values determined from 5 to 9 samples per group. ISRM rock classifications overlain on Figure 1 as >250 MPa (R6:Extremely strong), 100-250 MPa (R5:Very strong), 50-100 MPa (R4:Strong), 25-50 (R3: Medium Strong), 5-25 (R2:Weak), 1-5 MPa (R1:Weak) and 0.25 – 1 MPa (R0: 0.25-1 MPa).
Figure 2. Types of failures that can be observed in UCS testing include (a) failure along features (b) shear failure (c) vertical tensile failure (c) complete destruction
2.3 Young’s Modulus Clients have questioned if they should collect Young’s modulus from UCS and/or triaxial testing. The Pincus Round 2 interlaboratory study (1994) found that “E increases with confining pressure for Barre Granite and Berea Sandstone, but decreases for Tennessee Marble”. Logically, the specimens should become stiffer with confinement and have an increase in Young’s modulus. However, the results from the Tennessee Marble highlight that there is nothing predictable about lab test results from rock. As shown in Figure 4, there is variability in Young’s modulus between labs if collecting data
Figure 3. The square symbols on this chart represent the mean UCS in MPa of 4 rock types in an interlaboratory study (Pincus, 1993), and the vertical lines represent one standard deviation of mean values determined from 5 samples per group.
Figure 4. Elastic moduli results. The square symbols represent the average modulus for a given lab in GPa (Pincus, 1993). The lines represent one standard deviation.
Figure 5. Tensile strength results. The square symbols on this chart represent the mean tensile strength in MPa of 4 rock types in an interlaboratory study (Pincus, 1993), and the vertical lines represent one standard deviation of mean values determined from 5 samples per group.
2.4 Tensile Strength Testing (Brazilian) The other most commonly requested test from industry is tensile strength or Brazilian. This is also one of the least expensive tests to perform. Pincus (1993) data is plotted in Figure 5. The standard deviation is up to 1.9 MPa which is less than that for their UCS testing. The ratio average UCS to average Brazilian strength for each of these labs is as follows: 14.7 for Tennessee Marble 11.8 for Salem Limestone 17.1 for Barre Granite 15.7 for Berea Sandstone These results highlight that a rock is weaker in tension than compression and that the ratio is dependent on rock type
2.5 Shear Strength Some projects may require shear test results. Figure 6 presents results from tensile, shear and UCS testing of potash (Neely, 2014). The results are plotted on a Mohr-Coulomb diagram to illustrate the comparison between the three tests. The average Brazilian strength was 1.75 MPa, shear strength was 7 MPa and UCS was 25.4 MPa. Standard deviations were 0.2 MPa, 1.8 MPa and 2.4 MPa respectively. For this potash, the ratio of average UCS to average Brazilian was 14.5. A trend line was sketched in by eye as an approximation of a failure envelope. When asked if UCS and triaxial tests should be included on the same plot, all we can suggest is that the client tests if a failure envelope can be fit to the data. Unfortunately, there were no triaxial results with this dataset.
Ʈ = c + ơ tan φ
Where, Ʈ = shear stressss acting on failure plane (MPa) ơ = normal stress acting on failure plane (MPa) c = cohesive strength of rock (MPa) φ = angle of internal friction There are other failure criteria commonly used in mining such as the Hoek and Brown failure criteria (1980), but for simplicity and a lack of space, only the Mohr-Coulomb was selected. When it comes to triaxial data, the more samples to create the curves the better. Figure 7 shows three examples of triaxial results using only three samples. The goal was to sketch in a linear envelope to the circles, by eye. The upper chart can easily be represented by a linear failure curve and as expected, strength increases with increasing confinement. With the middle curve, an approximate line of best fit can be estimated but results are not as ideal. Finally, the bottom curve presents results that are opposite to that expected. The rock cores actually gave lower failure strengths as confinement increased. Variability in sample strengths was though to be the cause. When selecting intact rock samples, discontinuities and bedding can affect material strength and behavior. Three samples may not be sufficient for determining failure criteria parameters for rock mass characterization. We suggest that a minimum of five samples may improve the interpretation of results. The client needs to know the application for this data to help determine the sensitivity of the design to an accurate estimate of the lab test values. 3 NON-DESTRUCTIVE TESTING 3.1 The purpose
Figure 6. UCS, tensile and shear strength results from Potash testing.
2.6 Triaxial Data The purpose of this paper is not to interpret lab data through failure criteria but instead to give practical guidance on approaching lab testing. The standard Mohr-Coulomb failure criterion is used to demonstrate the types of results that may be obtained with only 3 samples, as follows:
Certain borehole logging tests can be simulated on rock core without causing damage to the cores. This is typically done on prepared UCS and triaxial cores.The advantage of non-destructive testing is that it provides additional properties to help identify the differences between similar looking rock cores. These non-destructive rock characteristics can be compared to results from destructive test properties. Depending on how sampling was done, software is available to plot the results similar to how data is plotted in borehole logs. In Figure 8, density and porosity are plotted alongside representative photographs of the cores. Similar plots could be added to this figure including those from other destructive tests including UCS, Young’s modulus, Poisson’s ratio, tensile strength, shear strength, etc.
more heterogeneous due to fractures, large grain size, increased porosity, etc., this technique becomes more difficult to apply due to wave attenuation. However in general, the technique is fairly reliable and P-wave velocity at a minimum can usually be determined. The frequency range of the ultrasonic vibrations used in laboratory testing is dependent upon rock type. Typical range is 200 kHz to 1 MHz. Again this test highlights why it is important to have qualified personnel running the test. Sensors are selected based on sample size and sample composition. It is not just a matter of turning on an instrument and running the test.
Figure 7. Examples of triaxial results using three samples. Top chart shows ideal Mohr Coulomb relation, middle requires some estimating, and bottom is the reverse of that expected.
3.2 Density The most basic non-destructive test for characterizing rock is density. If porosities and/or natural water content are required, it is important to note the test method used. The porosity can be done by the water saturation method, or using porosimeters that inject gas into the samples. Each method may produce different results so it is important to know how the tests were performed. 3.3 P-wave and S-wave Velocities To measure P-wave and S-wave velocity, ultrasonic pulses are passed through rock core samples. The velocity that those pulses travel in the core depends on the density and elastic properties of the rock. The nature of the rock specimen determines how well the technique can be applied. As the sample becomes
Figure 8. Example of plotting laboratory data and photos on a depth log for a borehole. In this case, average results were plotted when multiple sub-core results were available at the same depth (Hawkes et al, 2013).
Sample dimensions are important to note as this determines the distance which the pulses travel as pulse velocity is calculated by dividing path length by transit time. Ideally this test is done on saturated sam ples as the water content can increase pulse velocity. By having all samples saturated, at least this variable is removed. Again, this should be noted in test records. This test is a good example of the need to keep up with evolving equipment. Recently, our laboratory purchased a new oscilloscope at a cost of approximately $8,000. This is just one small piece of equipment in our laboratory. A rock mechanics laboratory can easily exceed the million dollar range for routine equipment, and equipment should be updated as com puter technology evolves. Not only is it important to have a skilled technologist who is qualified to do the testing, but also it is important that they are technically competent to operate and maintain an inventory of continually upgraded equipment.
requirements for specialized testing that may not be available from ASTM/ISRM and these should be documented and ideally published so that methods can be improved and standardized with time. Rock test results at the laboratory scale are affected by discontinuities and grain structure as in the field, sometimes even when samples appear homogenous. A rock will fail the way it wants so a saying in our lab it that “it is what it is”. RMR allows for 15 of 100 points to be obtained from laboratory testing. As much care should be placed into that 15% as is placed in the remaining 85% collected from field mapping.
3.4 Resistivity It is sometimes possible to perform geophysical tests at the core scale. One such test routinely done at the University of Saskatchewan is resistivity. Figure 10 shows the absolute resistivity measurements made on a two sections of a core cut side by side. Sample A was 25 mm long and Sample B was 77 mm long. Both samples were oven dried, and then saturated together in distilled water. This example highlights the variability in results between adjacent samples of core. The absolute values of resistivity of these two sub-segments are very different with Samples A and B having resistivities of 250,000 Ωm and 350,000 Ωm at 0.1 Hz. Fortunately when these results are normalized as shown in Figure 11, the results are almost identical. ASTM/ISRM procedures are not available for geo physical properties. When required, the client will need to find a qualified lab.
4 CONCLUSIONS Laboratory testing is one component of a program to characterize a rock mass. This must be done by a specialized testing facility with proper equipment. Though the basics behind the testing seem simple, the actual mechanics of carrying our rock mechanics testing is not. It is important that this testing is done by qualified personnel, that test procedures are strictly followed, and that test methods are noted with results. Rock results are usually highly variable and test design should aim for a number of samples that will meet the requirements of the project. There may be
Figure 9. Resistivity results for two adjacent samples. Top chart shows absolute results and bottom chart shows normalized results.
5 REFERENCES Rocscience, 2014. https://www.rocscience.com (Last accessed April 8, 2014) ISRM, 2014. International Society for Rock Mechanics, http://www.isrm.net (Last accessed April 8, 2014) ASTM International, 2014. http://www.astm.org (Last accessed April 8, 2014) Goodman, R.E., 1989. Introduction to Rock Mechanics Second Edition, John Wiley & Sons, 562 p.
ISRM, 2007. The complete ISRM suggested methods for rock characterizations, testing and monitoring: 1974-2006. Editors: R. Ulusay&J.A.Hudson, 628 p. Pincus, H.J., 1993. Interlaboratory testing program for rock properties (ITP/RP), Round 1 – longitudinal and transverse pulse velocities, unconfined compressive strength, uniaxial elastic modulus and splitting tensile strength. Geotechnical Testing Journal GTJODJ, Vol. 16. No. 1, March 1993, pp. 138-163. Szczepanik, Z., Milne, D. & Hawkes, C., 2007. The confining effect of end roughness on unconfined compressive strength. In proceedings of the 1st Canada-US Rock Mechanics Sym posium, Vancouver, Canada, pp. 191-198. Peng, S.S., 1975. A note on the fracture propagation and timedependent behavior of rocks in uniaxial tension. Int. J. rock Mech. Min. Sci. 12, 125-127 Gill, D. E., Corthesy, R.,& Leite, M. H., 2005. Determining the miniumal number of specimens for laboratory testing of rock properties. Engineering Geology 78, pp. 29-51. Ruffolo, R.M. & Shakoor, A., 2009. Variability of unconfined compressive strength in relation to number of test samples. Engineering Geology 108 (2009) pp. 16-23. Hoek, E., 2007. Practical Rock Engineering. Notes downloaded from https://www.rocscience.com , Last accessed April 8, 2014, 237 p. Bieniawski, Z.T., 1989. Engineering rock mass classifications, New York: Wiley Barton, N.R., Lien, R. and Lunde, J. 1974. Engineering classification of rock masses for the sesign of tunnel support. Rock Mechan. 6(4), pp. 189-239. Pincus, H.J., 1994, Interlaboratory testing program for rock properties (ITP/RP), Round 2 – confined compression: elastic modulus and ultimate strength, Institute for Standards Research Report PCN: 33-000010-38, 80 p. Neely, D., 2014, Failure mechanism of resin anchored rebar in potash, MSc. Thesis Draft, Department of Civil and Geological Engineering, University of Saskatchewan. Hoek, E. and Brown, E.T., 1980. Underground excavations in rock, the Institution of Mining and Metallurgy, 527 p. Hawkes, C., Beneteau, D., and Szczepanik, Z., 2013. Geological and geomechanical controls on hydraulic fracturing in the Bakken formation Part 2-Geomechanics, PTRC Report No. L0-UOS-00001-2011, Petrolieum Technology Research Centre STEPS Research Program, 49 p., December 2013
