Empirical Correlation of Uniaxial Compressive Strength and Primary Wave Velocity of Malaysian Granites

Transcription

1 Empirical Correlation of Uniaxial Compressive Strength and Primary Wave Velocity of Malaysian Granites Goh Thian Lai Doctor, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor, Malaysia. Abdul Ghani Rafek Professor, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor, Malaysia. Ailie Sofyiana Serasa Student, Petroleum Engineering Department, Faculty of Engineering, Technology & Built Environment (FETBE), UCSI University, Kuala Lumpur, Malaysia Norbert Simon Doctor, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor, Malaysia. Lee Khai Ern Doctor, Institute for Environment and Development (LESTARI), National University of Malaysia, UKM Bangi, Selangor D. E., Malaysia ABSTRACT Uniaxial compressive strength (UCS) plays a significant role in influencing the stability of structures such as cut slopes and excavation in rock masses. The rock material parameter of UCS also serves as an input parameter for geomechanical modeling in fracture basement studies. However, uniaxial compressive strength test (UCT), requires sample preparation, together with expensive and destructive laboratory testing and thus the limited rock samples has becomes a disadvantage. This article presents an inexpensive laboratory method for estimating the UCS values for Malaysian granites through means of non-destructive ultrasonic test. A total of 77 ultrasonic tests and uniaxial compressive strength tests were conducted to establish an empirical correlation of UCS and primary wave velocity (V p ). The empirical correlation of UCS and V p for granite was UCS = (2.55 x 10-5 ) V p with a coefficient of determination (R 2 ) of This new correlation offers a simple and fast method in estimation of uniaxial compressive strength of Malaysian granites, through measuring the ultrasonic transit time of rock samples in the laboratory. KEYWORDS: Granite, uniaxial compressive strength, primary wave velocity

2 Vol. 19 [2014], Bund. E 1064 INTRODUCTION Uniaxial compressive strength (UCS) plays a significant role in influencing the stability of structures such as cut slopes and excavation within rock masses. Under the limited rock samples condition, uniaxial compressive strength test (UCT), requires sample preparation together with expensive and destructive laboratory testing and therefore has become a disadvantage. There are several non-destructive laboratory tests that can be conducted to determine UCS indirectly such as point load index test, Schmidt hammer rebound test and ultrasonic test. Goodman (1989) reported that the values of UCS and primary wave velocity of granite ranged from MPa MPa and 5500 m/s 6000 m/s, respectively. Goh et al. (2012) reported that the means of compressive strength for fresh and slightly weathered granite in Peninsular Malaysia were 113.6±7.0 MPa and 68.9±3.6 MPa respectively. There are several correlations established from non-destructive testing that can be applied in estimating UCS. Hoek and Bray (1981) suggested that the UCS of rock material is estimated by multiplying the point load index strength value by 24. The UCS can also be estimated based on dry rock density and Schmidt hammer rebound value as established by Deere and Miller (1966). Ramli et al. (2013) suggested an exponential equation to predict UCS of Malaysian limestone based on Schmidt hammer rebound value. McNally (1987), Freyburg (1972), Militzer & Stoll (1973) and Horsrud (2001) recommended several empirical relationships to estimate UCS from the slowness ( t p ) value and primary wave velocity (V p ) for sandstone, limestone, dolomite and shale as exhibited in Table 1. However, none of the empirical correlations are recommended for to be applied for granitic rock. Thus, the present paper demonstrates an inexpensive method for estimating the UCS value from non-destructive ultrasonic testing for Malaysian granite. Table 1: Empirical relationships between UCS and P-wave velocity (V p ) Reference UCS, MPa Lithology McNally (1987) 1200 e tp Fine-grained sandstones (Bowen Basin, Australia) McNally (1987) tp -3 Weak, unconsolidated sandstones (Gulf Coast) Freyburg (1972) 0.035V p 31.5 Sandstones (Thuringia, Germany) Militzer & Stoll (1973) (7682/ tp) 1.82 /145 Limestone and dolomite Horsrud (2001) 0.77(304.8/ tp) 2.93 High porosity tertiary shales (North Sea) Units used: tp (μs/ft) and V p (m/s) Source: Zoback 2007 GEOLOGY Granite samples were collected from four different locations (Figure 1), which are as follows: (a) Kajang Rock Quarry and SILK Highway, Kajang, Selangor, Peninsular Malaysia. Granite samples from this area are of medium to coarse grained and of Triassic age as

3 Vol. 19 [2014], Bund. E 1065 reported by Gobbett and Hutchison (1973). Mineralogical content of the granite samples includes quartz, feldspar and mica (Shu, 1989). (b) Pos Selim to Kg. Raja Road (km 29-30), Cameron Highland Pahang/Perak, Peninsular Malaysia. These granites are also of Triassic age as reported by Bignell and Snelling (1977). Metamorphic rocks such as graphitic mica schist, quartz mica schist as well as mica schists are also exposed along this road. (c) Bukit Penggorak Quarry, Kuantan, Pahang, Peninsular Malaysia. With a Late Permian to Early Triassic age (Bignell and Snelling, 1977). These granite samples are light coloured and have a coarse grain size as reported by Goh (2012). Figure 1: Location of test sites, Peninsular Malaysia METHODOLOGY The uniaxial compressive strength test is used to measure the uniaxial compressive strength (UCS) of intact rock. The uniaxial compressive strength test was conducted based on the recommendation by International Society for Rock Mechanics, ISRM (2007). Testing was conducted on 54 mm diameter cored specimens with applied loading rate of MPa/s by using apparatus shown in Figure 2. The UCS of the core samples was calculated by dividing the maximum load (P) carried by the core sample during the test, by the original cross-sectional area (A) as shown in equation (1).

4 Vol. 19 [2014], Bund. E 1066 UCS = P/A (1) Figure 2: Apparatus for uniaxial compressive strength test (DHR 2000).The uniaxial compressive strength testing was conducted on 54 mm cored granites at a loading rate of MPa/s The ultrasonic test is used to measure the speed of sonic waves that travels through rock materials to predict the rock strength, and it is usually conducted when destructive testing is not preferable. The test was conducted on 54 mm diameter cored samples according to the recommendations of ISRM (2007), by using PUNDIT Plus (Portable Ultrasonic Non Destructive Digital Indicating Tester) with a frequency of 50 khz as shown in Figure 3. The primary wave velocity (V p ) of the core sample was calculated by dividing the length of core sample (L), by travelling time (t) of primary wave from transmitter to receiver as shown in equation (2). V p = L/t (2)

5 Vol. 19 [2014], Bund. E 1067 Figure 3: Apparatus for ultrasonic test (Portable Ultrasonic Non Destructive Digital Indicating Tester). The apparatus was used to measure travel time (t) of primary wave from transmitter to receiver RESULT AND DISCUSSION A total of 77 ultrasonic tests and uniaxial compressive strength tests were conducted on cored granite samples according to the recommendations of the International Society for Rock Mechanics, ISRM (2007). The results of testing were analyzed at 95 % confidence level by using SPSS statistical software version 16 (Table 2). The minimum, maximum, mean and median values of UCS were 5.0 MPa, MPa, 72.0 MPa and 76.8 MPa respectively, with a standard deviation of 27.7 MPa. The minimum, maximum, mean and median values of V p are 1258 m/s, 6142 m/s, 4379 m/s and 4678 m/s respectively, with a standard deviation of 1159 m/s. Boxplots of UCS and V p are shown in Figure 4 and Figure 5 respectively. The skewness for both UCS and V p results were found to be negative, which implies more test results have higher value of UCS or V p compared to the mean value. Positive skewness implies more test results have lower values of UCS or V p compared to the mean value. Table 2: Summary of statistical results of UCS and V p values of granitic rock, Malaysia No. of test Min. Max. Mean Median Standard Deviation Skewness UCS MPa 109.9MPa 72.0MPa 76.8 MPa 27.7 MPa negative V p m/s 6142 m/s 4379 m/s 4678 m/s 1159 m/s negative

6 Vol. 19 [2014], Bund. E 1068 Figure 4: Boxplot of uniaxial compressive strength (UCS) of Malaysian granite Figure 5: Boxplot of primary wave velocity (V p ) of Malaysian granite An empirical correlation, UCS = (2.55 x 10-5 ) Vp with a coefficient of determination (R 2 ) of 0.9 was established for Malaysian granite under dry conditions as illustrated in Figure 6. Comparison of this correlation with published correlations for sandstone (McNally, 1987, Freyburg, 1972), limestone & dolomite (Militzer and Stoll, 1973) and shale (Horsrud, 2001) are illustrated in Figure 7. It is revealed that the laboratory results falls in between the correlation curves of Freyburg (1972) and Militzer and Stoll (1973). Table 3 exhibits the calculated values of uniaxial compressive strengths based on the predictions of McNally (1987), Freyburg (1972), Militzer and Stoll (1973) and Horsrud (2001) together with the new correlation established from this study. Percentage differences of uniaxial compressive strength predictions between new correlation with the published correlations are illustrated in Table 4. As noted from this table, the percentage differences between the new correlation values and the published correlation values range from -100 % to 124 %. These results revealed the need and importance in establishing

7 Vol. 19 [2014], Bund. E 1069 correlation for granite, as the published correlations of McNally (1987), Freyburg (1972), Militzer and Stoll (1973) and Horsrud (2001) are not suitable in prediction of UCS for granitic rock, especially in the Malaysian environment. Figure 6: An empirical correlation, UCS = (2.55 x 10-5 ) Vp with a coefficient of determination (R 2 ) of 0.9 had been established from UCS versus V p for Malaysian granite

8 Vol. 19 [2014], Bund. E 1070 Figure 7: Comparison of new correlation with published correlations for sandstone (McNally, 1987; Freyburg, 1972), limestone & dolomite (Militzer & Stoll, 1973) and shale (Horsrud, 2001). The laboratory results fall in between the correlation curves of Freyburg (1972) and Militzer & Stoll (1973) Table 3: The calculated values of uniaxial compressive strengths based on McNally (1987), Freyburg (1972), Militzer & Stoll (1973) and Horsrud (2001) predictions and new correlation Vp (m/s) New correlation, MPa McNally (1987), Australia, MPa McNally (1987), USA, MPa Militzer & Stoll (1973), MPa Freyburg (1972), MPa Horsrud (2001), MPa

9 Vol. 19 [2014], Bund. E 1071 Table 4: Percentage of differences of uniaxial compressive strength predictions between new correlation with published correlations for sandstone (McNally, 1987; Freyburg, 1972), limestone & dolomite (Militzer & Stoll, 1973) and shales (Horsrud, 2001) Vp (m/s) McNally (1987), Australia, % McNally (1987), USA, % Militzer & Stoll (1973), % Freyburg (1972), % Horsrud (2001), % CONCLUSION An empirical correlation, UCS = (2.55 x 10-5 ) Vp with a coefficient of determination (R 2 ) of 0.9 was established for selected granites in Malaysia. This result offers a simple and fast method in estimating of uniaxial compressive strength of Malaysian granites, by simply measuring the ultrasonic transit time of rock samples in the laboratory. This equation is expected to be useful for the assessment of the rock mass in cut slope and underground excavation as well as the construction of a geomechanical earth model. ACKNOWLEDGEMENT This publication was funded by the Young Researcher Grant (GGPM & GGPM ) under the National University of Malaysia. The authors also acknowledge the support of the staff and facilities at geology program and faculty. REFERENCES 1. Bignell, J.D. & Snelling, N.J Geochronology of Malayan granites, Overseas Geology and Mineral Resources, pp Deere, D. U. & Miller, R. P Engineering classification and index properties for intact rock, Technical Report No. AFNL-TR Air Force Weapons Laboratory. New Mexico.

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