1 USING THE POINT LOAD TEST TO DETERMINE THE UNIAXIAL COMPRESSIVE STRENGTH OF COAL MEASURE ROCK John Rusnak, Director of Geology Peabody Group St. Louis, MO Christopher Mark, Rock Mechanics Team Leader National Institute for Occupational Safety and Health Pittsburgh, PA ABSTRACT Point load testing is used to determine rock strength indexes in geotechnical practice. The point load test apparatus and procedure enables economical testing of core or lump rock samples in either a field or laboratory setting. In order to estimate uniaxial compressive strength, index-to-strength conversion factors are used. These factors have been proposed by various researchers and are dependent upon rock type. This study involved the extensive load frame and point load testing of coal measure rocks in six states. More than 1, individual test results, from 98 distinct rock units, were used in the study. Rock lithologies were classified into general categories and conversion factors were determined for each category. This allows for intact rock strength data to be made available through point load testing for numerical geotechnical analysis and empirical rock mass classification systems such as the Coal Mine Roof Rating (CMRR). INTRODUCTION is sufficient. This is due in part to the high variability of UCS measurements. Moreover, the tests are expensive, primarily because of the need to carefully prepare the specimens to ensure that their ends are perfectly parallel. THE POINT LOAD TEST The PLT is an attractive alternative to the UCS because it can provide similar data at a lower cost. The PLT has been used in geotechnical analysis for over thirty years (ISRM, 1985). The PLT involves the compressing of a rock sample between conical steel platens until failure occurs. The apparatus for this test consists of a rigid frame, two point load platens, a hydraulically activated ram with pressure gauge and a device for measuring the distance between the loading points. The pressure gauge should be of the type in which the failure pressure can be recorded. A state of the art point load testing device with sophisticated pressure reading instrumentation is shown in Figure 1. The point load test (PLT) is an accepted rock mechanics testing procedure used for the calculation of a rock strength index. This index can be used to estimate other rock strength parameters. The focus of this paper is to present the data analysis used to correlate the point load test index (Is 5 ) with the uniaxial compressive strength (UCS), and to propose appropriate Is 5 to UCS conversion factors for different coal measure rocks. The rock strength determined by the PLT, like the load frame strengths that they estimate, are an indication of intact rock strength and not necessarily the strength of the rock mass. THE UNIAXIAL COMPRESSIVE STRENGTH TEST The UCS is undoubtedly the geotechnical property that is most often quoted in rock engineering practice. It is widely understood as a rough index which gives a first approximation of the range of issues that are likely to be encountered in a variety of engineering problems including roof support, pillar design, and excavation technique (Hoek, 1977). For most coal mine design problems, a reasonable approximation of the UCS Figure 1. The Point Load Tester.
2 The International Society of Rock Mechanics (ISRM, 1985) has established the basic procedures for testing and calculation of the point load strength index. There are three basic types of point load tests: axial, diametral, and block or lump. The axial and diametral tests are conducted on rock core samples. In the axial test, the core is loaded parallel to the longitudinal axis of the core, and this test is most comparable to a UCS test. The point load test allows the determination of the uncorrected point load strength index (Is). It must be corrected to the standard equivalent diameter (De) of 5 mm. If the core being tested is "near" 5 mm in diameter (like NX core), the correction is not necessary. The procedure for size correction can be obtained graphically or mathematically as outlined by the ISRM procedures. The value for the Is 5 (in psi) is determined by the following equation. Is 5 = P/De 2 (1) P = Failure Load in lbf (pressure x piston area). De = Equivalent core diameter (in). As Hoek (1977) pointed out, the mechanics of the PLT actually causes the rock to fail in tension. The PLT s accuracy in predicting the UCS therefore depends on the ratio between the UCS and the tensile strength. For most brittle rocks, the ratio is approximately 1. For soft mudstones and claystones, however, the ratio may be closer to 5. This implies that PLT results might have to be interpreted differently for the weakest rocks. Early studies (Bieniawski, 1975; Broch and Franklin, 1972) were conducted on hard, strong rocks, and found that relationship between UCS and the point load strength could be expressed as: UCS = (K) Is 5 = 24 Is 5 (2) Where K is the "conversion factor." Subsequent studies found that K=24 was not as universal as had been hoped, and that instead there appeared to be a broad range of conversion factors. Table 1 summarizes published results obtained for sedimentary rocks. Most of the estimates place the conversion in a range between 16 and 24, with even lower values for some shales and mudstones. In studies comparing the PLT with the UCS, it is generally assumed the UCS test is the standard. In reality, however, UCS tests provide an estimate of the true UCS of the rock. The accuracy of the estimate depends on the natural scatter in the UCS test results (indicated by the standard deviation (SD)) and the number of tests conducted (n). This relationship is captured by the concept of the Confidence Interval (CI). For normally distributed data, the 95% CI of the mean is expressed as: CI 95% = 196. SD n (3) Table 1. Published comparisons between the point load and uniaxial compressive strength tests for sedimentary rock. Reference Rock Type Location Number of tests Conversion Factor Comments Das, 1995 Siltstone Western Canada, bituminous coalfields NG lumps, fresh core, old core Sandstone/siltstone NG 18 Shale/mudstone NG 12.6 Vallejo et al, 1989 Sandstone Eastern KY, VA, WV 42 PLT, 21 UCS 17.4 Freshly blasted rock, irregular lump samples Shale surface coal mines 1,1 PLT, 55 UCS 12.6 Smith, 1997 Dredge material various harbors NG 8 UCS<1 psi Dredge material various harbors NG 15 UCS<35 psi sandstone/limestone unk NG 24 UCS>6 psi Broch and Franklin, 1972 Various UK (?) NG rock types Carter and Sneddon, 1977 Coal measure UK 1, PLT, 68 UCS units tested O'Rourke, 1988 Sedimentary Paradox Basin, US 66 3 samples from one borehole Hassani et al., 198 Sedimentary UK 1, 29 Singh and Singh, 1993 Quartzite India, copper pit Read et al, 198 Sedimentary rocks Melbourne, Australia NG 2 Reference in Choi and Hong, 1998 Bieniawski, 1975 Sandstone South Africa Rusnak, 1998 Coal measure Southern WV Subset of current data Jermy and Bell, 1991 Coal measure South Africa NG 14.1 Mainly sandstones 1 NG=Not given in reference
3 In general, the variability in the PLT-UCS relationship can be attributed to three sources: 1. Inaccuracy in the estimate of the true UCS obtained from UCS tests. 2. Inaccuracy in the estimate of the true PLT obtained from PLT tests. 3. Real differences between the two tests. Many of the studies summarized in Table 1 compared a suite of point load tests to a single UCS test. With such an experimental design, much of the scatter in the results might actually be attributable to the inaccuracy of the UCS tests. PEABODY ROCK MECHANICS DATA Peabody established an in house rock mechanics testing facility in the fall of This facility is located in Freeburg, IL. A full range of equipment was purchased to perform tests including uniaxial compressive strength, indirect tensile strength, point load index, triaxial compressive strength, flexural strength, direct shear strength, long term creep, roof bolt anchorage capacity, slake durability, ultrasonic velocity, swelling strain and Atterberg limits. The diametral point load (DPL) was not initiated until 1996, which resulted from an interest in utilizing of the Coal Mine Roof Rating (CMRR). ASTM and ISRM procedures are followed for all rock mechanics testing. This testing has been done primarily on core samples obtained from exploration drilling to provide data for mine planning and design. The Freeburg facility was eventually sold to Standard Laboratories in 1991 who continue to operate it. The majority of the data analyzed in this paper was from the testing done at Freeburg. After 1997, all West Virginia testing has been carried out at Commerical Testing and Engineering's facility in Beckley, WV. Currently, the data base contains rock mechanics test results from 914 drill holes from the states of THE UCS AND PLT DATA BASE DESCRIPTIVE STATISTICS The methodology used in the selection of core samples for testing was as follows: 1. Within each hole, rock units were identified where a sequence of tests had been performed with an identical geologic description and no major gaps in elevation. 2. Rock units with at least 3 UCS and 3 PLT results were selected for inclusion in the data base. 3. The mean UCS, mean Is 5, the standard deviations, and the CI 95 were calculated for each rock unit. The samples were also categorized into rock type based on the geologic description. These rock types correspond to the Ferm Classification numbers. Ferm and Weisenfluh (1981) developed a number system classification for coal measure rock types using color photographs of rock core in an index guide. It as been widely accepted as a means for consistent rock identification and for use in computer data bases of drilling information. The categories of rock types and their Ferm classification numbers used in this data analysis are as follows: Rock Type Ferm Series Shale and Claystone 1-2 Silty or Sandy Shale 3-4 Sandstone 5-7 Of the original 36, tests, more than 1, from 98 rock units were retained for the analysis. The distribution of the units and representative values are reported in Table 2. The median of the means is reported, rather than the mean of the means, to reduce the influence of outliers. All the statistical analysis was performed using SPSS version 1. Figure 3 compares UCS determined for different rock types in different regions. One striking observation is that the rocks from the Midwest (IN, IL, and western KY) are significantly weaker than their counterparts from WV (a fact confirmed by ANOVA). Figure 4a shows the range of standard deviations for the UCS tests, expressed as a fraction of the mean UCS. The standard deviations are greatest for limestones and shales, with the median SD about 35% of the mean. The median standard deviations for siltstones and sandstones are about 19% of the mean. Figure 2. Location of the drillholes from which the samples were obtained. WV, IL, KY, IN, CO, and OH. Most of the core was NX-size with some 75-mm (3-in) diameter. A map showing the distribution of the drilling is shown below (figure 2). Table 2 also reports the median Is 5 and SD of Is 5. Expressed as a percent of the mean, the median standard deviation for the Is 5 ranges from 2% for sandstone to 35% for shale. As figure 4b confirms, the variability of the PLT is similar to that of the UCS test, as has been reported elsewhere (ISRM, 1985).
4 Count Count Table 2. Summary of the data used in this study. Rock type Location N units N UCS Median Median SD of Median Median SD N PLT tests tests UCS UCS Is 5 of Is 5 All states 289 1, ,664 1, Shale Midwest 29 1,72 4,367 1,314 1, West Virginia ,752 2, All states 296 1,557 6,286 1,166 1, Siltstone Midwest 236 1,275 5,931 1,27 1, West Virginia ,332 2, All states 228 1,591 1,931 2,96 1, Sandstone Midwest ,773 1, West Virginia ,574 2, Limestone Midwest ,752 6, All states All states 98 5,139 7,4 1,796 5, N - Number of tests. UCS - Unconfined compressive strength (psi). SD - Standard deviation (psi) Is 5 - Point Load Index. 35 SHALE SILTSTONE UNIAXIAL COMPRESSIVE STRENGTH ( UCS,psi) SHALE SILTSTONE SANDSTONE LIMESTONE REGION 75 th % Median 25 th % Midwest W.V a SANDSTONE LIMESTONE ROCK TYPE 75 Figure 3. Range of uniaxxial compressive strengths found in the data base Standard Deviation of Is 5 (Compared with the mean) Figure 4b. Histograms of standard deviations, Point Load Test. Figure 4a. Histograms of standard deviations, Uniaxial Compressive Strength. The Is 5 values obtained from this study are compared with data reported by Molinda and Mark (1996) in table 3. Molinda and Mark s data was obtained from throughout the US and includes a high percentage of tests from southern WV. Table 3 reports means of the mean Is 5 values to make the results comparable. It can be seen that the two studies found similar results.
5 Table 3. Comparison between PLT data from this study and that presented by Molinda and Mark (1996). Rock Type Average, this study Is(5) (psi) Midwest, this study WV, this study Molind a & Mark Shale Sandy Shale Sandstone SUMMARY OF THE REGRESSION ANALYSIS A linear regression between the mean Is 5 and mean UCS values determined for all 98 units yielded the following equation: Equation 4 contains an intercept, however, unlike the traditional form of the UCS-PLT relationship (equation 3). Unfortunately, the r 2 obtained from a zero-intercept regression is not comparable to the standard r 2. Therefore a different measure of the validity of the result must be used. For this study, the validity measure was defined as the percent of mean Is 5 values that fall within the 95% CI of the corresponding UCS. In addition, the percent of mean Is 5 values falling 1 and 2 MPa (1,5 and 3, psi) from the 95% CI of the mean UCS were also calculated. The zero-intercept regression equation obtained from the entire data set is: UCS = 21. Is 5 (5) UCS = Is 5 (4) The correlation coefficient (r 2 ) obtained for equation 4 is.68, which is not bad for rock mechanics. The regression equation simply uses the pairs of means, without regard to the associated standard deviations. Therefore, the r 2 for equation 4 implies that the point load test explains two-thirds of the variability in the UCS, with one-third attributable to the three potential sources of scatter listed earlier. With this equation, 5.4% of the predicted UCS values fall within the 95% CI of the measured UCS. Only 8.5% of the predicted values are more than 2 MPa away from the 95% CI (figure 5). For equation 4, the regression equation with an intercept, 49.% of the predicted values were within the 95% CI and 7.6% were more than 2 MPa away. It seems that the zero-intercept equation is just as accurate as the standard regression equation that includes an intercept. 5 ACCURACY OF REGRESSION EQUATIONS 4-1, -8, -6, -4, -2, 2, 4, 6, 8, 1, NUMBER OF UNITS 12, DISTANCE FROM 95% ci (psi) Figure 5. Histogram showing hte difference between UCS predicted by the PLT using equation 5, and the 95% confidence interval of the measured UCS. The zero bar includes all cases that fell withing the 95% CI.
6 Table 4 shows the conversion factors (K) obtained from zero-intercept regression analyses on various subsets of the data. Nearly all the K values lie between 2 and 22, regardless of rock type or geographic origin. Figures 6a-6e shows the regression equation (equation 5) mapped on the different data subsets. Table 4. Conversion factors (K) obtained from zero-intercept regression analysis. Rock type Location K All states 21.8 Shale Midwest 22.4 West Virginia 2.2 All states 2.2 Siltstone Midwest 19.6 West Virginia 2.8 All states 2.6 Sandstone Midwest 2.2 West Virginia 2.4 Limestone Midwest 21.9 All states All states 21. Finally, the relationship between rock strength and K was explored. There was a slight tendency for the UCS/Is 5 ratio (K i ) to decrease for low UCS rocks. The median K i for the entire data set was 22.7, but that decreased to 16.9 for the subset of rocks whose UCS was less than 2 MPa (3, psi). Unfortunately, a similar trend was not evident in the PLT data, so efforts to adjust K for low Is 5 rocks did not improve overall accuracy. DISCUSSION Several factors are relevant in comparing this study with previous ones. First, the present study involves the largest number of tests, nearly 1 times as many as the next largest study. It also includes a wide variety of rock types from several mining regions, and it explicitly addresses the variability associated with the UCS tests. One disadvantage of the study was that the number of PLT tests averages about 5 per unit. Therefore it was not possible to follow the ISRM (1985) suggested method for determining the mean value, which involves deleting the two highest and two lowest Is 5 values from a suite of at least 1 tests. Finally, it should be noted that in these tests the average moisture content varied from.79% for the shale to.49% for the sandstone. Vallejo et al. (1989) found that K values were greater when the samples were saturated. UNIAXIAL COMPRESSIVE STRENGTH (UCS,psi) ROCK TYPE UCS=21 PIV SHALE SILTSTONE SANDSTONE LIMESTONE ALL DATA POINT LOAD INDEX (Is (5), psi) Figure 6a. Regression between uniaxial compressive strength and point load index. All rock types (a random selection of 4% of the data points is shown).
7 SHALE 3 UNIAXIAL COMPRESSIVE STRENGTH (UCS,psi) POINT LOAD INDEX (Is (5), psi) 25 Figure 6b. Regression between uniaxial compressive strength and point load index. SHale. SILTSTONE UNIAXIAL COMPRESSIVE STRENGTH (UCS,PSI) s POINT LOAD INDEX (IS(5),psi) Figure 6c. Regression between uniaxial compressive strength and point load index. Siltstone.
8 3 SANDSTONE UNIAXIAL COMPRESSIVE STRENGTH (UCS,psi) UNIAXIAL COMPRESSIVE STRENGTH (UCS,psi) POINT LOAD INDEX (Is (5), psi) Figure 6d. Regression between uniaxial compressive strength and point load index. Sandstone. LIMESTONE POINT LOAD INDEX (Is (5), psi) Figure 6e. Regression between uniaxial compressive strength and point load index. Limestone.
9 he conversion factors (K) determined in this study fall in the middle of the range of the studies reported in table 1. They are somewhat greater than the K factors currently used in the CMRR (Mark and Molinda, 1996). Those values, 12.5 for shales and 17.4 for sandstones, were originally proposed by Vallejo et al. (1989). Many of the samples that Vallejo tested came from the same geologic formations included in this study. However, Vallejo tested lump samples rather than the core samples used here, and he compared the results from single UCS tests with suites of PLT tests. Like some other researchers, Vallejo et al. (1989) concluded that K should be smaller for shales than for sandstones. While the current study found some evidence that K was less for the weakest rocks (not just shales), it was difficult to identify those rocks from the PLT measurements alone. Therefore, using different K values may not be justified for axial PLT tests. However, diametral tests often give Is 5 values that are much lower than those from axial tests. Converting diametral test results using the same K value is likely to be inaccurate. It is also unnecessary, because diametral tests are used as an indirect measure of bedding plane cohesion, not rock strength (Mark and Molinda, 1996). It is probably more sensible to report Is 5 from diametral tests directly. CONCLUSION The PLT is an efficient method to determine intact rock strength properties from drill core samples. It has become an accepted test in geotechnical evaluations. This study found that a conversion factor K=21 worked well for a variety of rock types and geographic regions. The variability of the PLT, as measured by the standard deviation, was no greater than that of the UCS test. There is some indication that K decreases for lower strength rocks, but the tendency was not very pronounced. Geologic and engineering judgment should be used when converting PLT results to UCS. It must be remembered that both tests can only be used to estimate intact rock strength and not rock mass strength. The point load test provides for full utilization of data that can be gained from exploration drilling programs. Intact rock strength information can be acquired for use in geotechnical evaluation and design work through numerical modeling and rock mass classification systems. The cost of point load testing is minimal when compared to the overall exploration expense. Point load testing of roof and floor rock core of coal seams that are to be mined by underground methods should be standard procedure in any exploration program. ACKNOWLEDGMENTS The authors wish to thank Peabody Group for permission to utilize the data and present this paper. The conclusions contained here are solely those of the authors and not those of Peabody Group. Also, the authors would like to thank Colin Henkes, Geologist for Peabody Group, who oversees exploration drilling and testing programs in West Virginia, and Angela Abruzzino, statistical assistant at NIOSH in Pittsburgh, who helped prepare the database. REFERENCES Bieniawski ZT. The Point Load Test in Geotechnical Practice. Eng. Geol., Sept., 1975, pp Broch E, Franklin JA. The Point Load Strength Test. Int. Journal Rock Mech. Min. Sci 9, 1972, pp Carter PG, Snedden M. Comparison of Schmidt Hammer, Point Load and Unconfined Compression Tests in Carboniferous Strata. Proceeding of a Conference on Rock Engineering. University of New Castle, Tyne, England, 1977, pp Chau KT, Wong RHC. Uniaxial Compressive Strength and Point Load Strength of Rocks. Int. Journal of Rock Mech. Min. Sci and Geomech., 1996, Vol 33, No. 2, pp Das BM. Evaluation of the Point Load Strength for Soft Rock Classification. Proceeding of the 4 th International Conference on Ground Control in Mining. 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