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

Transcription

1 Empirical Correlation of Uniaxial Compressive Strength and Primary Wave Velocity of Malaysian Schists 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, Department of Geosciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750, Tronoh, Perak Darul Ridzuan. Ailie Sofyiana Serasa Student, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor, 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 Azimah Hussin Doctor, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor, Malaysia. ABSTRACT The uniaxial compressive strength (UCS) is one of the important mechanical parameters widely used for design, analysis and modeling in geotechnical engineering. Determination of UCS is critical to reducing risk in various applications which include assessment of excavation and cut slopes in rock mass. However, determination of UCS requires extensive laboratory works, which is time consuming, destructive and rather expensive to conduct. This paper presents an empirical equation to estimate UCS from V p for dry schist of Malaysia. Based on a total of 26 ultrasonic and UCS tests that were conducted, an empirical equation to estimate UCS was established. UCS = 3.40 x V p with a coefficient of determination (R 2 ) of This new correlation is non-destructive and an inexpensive method for estimation of UCS of dry Malaysian schist, through measuring the ultrasonic velocity of rock samples in laboratory. KEYWORDS: Schist, uniaxial compressive strength, V p, empirical equation

2 Vol. 20 [2015], Bund INTRODUCTION The uniaxial compressive strength (UCS) is one of the important mechanical parameters widely used for design, analysis and modeling in geotechnical engineering. Since ultrasonic testing is a non-destructive and easy to be conducted, it becomes an attractive approach to be used in estimation of UCS indirectly. Goodman (1989) reported that the UCS value of schist at schistosity inclination of 90 is 55.2 MPa, and Abdul Rahim Samsudin (1990) reported that the value of primary wave velocity of schist ranges from m/s. Goh et al. (2012) reported that the mean compressive strength for fresh and slightly weathered schist in Peninsular Malaysia were ±9.2 MPa and 84.8 ±5.1 MPa respectively, when the load was applied perpendicular to the foliation of schist. There are several correlations established in estimating UCS from V p. McNally (1987) and Horsrud (2001) developed an empirical correlation between UCS and slowness parameter (Δt p ) in sandstones and shales, respectively. Goh (2014) proposed a correlation in estimation of UCS for granite under dry condition. Moos et.al, (1999) developed an empirical correlation for sandstones using V p and density. Godfrey et.al, (2000) have studied the contribution of rock anisotropy to seismic velocities on schist. The study revealed that primary wave velocity is higher when the seismic wave travels 90 perpendicular to foliation of schist, compared to when the seismic wave travels at 0 and 45 to foliation of schist. The results clearly show that the effects of anisotropy must be taken into consideration in interpretation of data. A study by Lama and Vutukuri (1978) shows that saturated rock has higher V p when compared to unsaturated rock. Thus, it is important that these rock characteristics are taken into consideration whenever estimation of UCS is made by utilizing V p. Table 1 summarizes the empirical correlation established by previous researchers in estimating UCS by using ultrasonic test. Table 1: Empirical relationships between UCS and P-wave velocity (V p ) Source: Zoback 2007 Reference UCS (MPa) Lithology Sample Condition McNally (1987) 1200 exp (-0.036Δtp) Sandstones Saturated Moos et.al, (1999) (1.745 x 10-9 ) ρv p 2 Sandstones Saturated Horsrud (2001) 0.77 [304.8 / (1/V p )] 2.93 Shales Saturated Goh et.al, (2014) (2.55 x 10-5 ) V p Granite Dry Units used: V p (m/s), ρ (g/cm 3 ), Δt p (s/m) GEOLOGY Schist samples were collected from Pos Selim to Kg. Raja Road (km 18-km 26), Cameron Highlands Pahang/Perak, Kuala Kubu Bahru Bukit Fraser Road (km 15) Selangor and Ukay Perdana Ulu Klang, Selangor. The coordinate of the study areas are exhibited in Table 2.

3 Vol. 20 [2015], Bund Table 2: Coordinates of study area No. Study Area Longitude Latitude 1 Pos Selim- Kampung Raja Road Cameron Highlands, Pahang/Perak a) km b) km c) km d) km e) km E101 o E101 o E101 o E101 o E101 o N04 o N04 o N04 o N04 o N04 o Kuala Kubu Bahru-Bukit Fraser (km 15) road, Selangor E101 o N03 o Ukay Perdana Ulu Klang, Selangor E101 o N03 o The age of the metamorphic rock along Jalan Pos Selim to Kampung Raja, and Cameron Highlands is Ordovician-Silurian period and is originated by regional metamorphism during igneous intrusion into clastic sediments that include shale and sandstone from the Permian age (Oh 2008). The metamorphic rock includes fine grained phyllite and hornfels. The resulting foliation of quartz schist, quartz mica schist, mica schist is often referred to schistosity. It has coarser grain that results from crystallization of quartz and mica minerals (muscovite and biotite). The quartzite contains very high quartz mineral content having granoblastic texture. Strongly foliated fine to medium-grained amphibole schist forms small isolated outcrop along Jalan Kuala Kubu Bahru Bukit Fraser, Selangor (Hutchison 2009). The age of schist at Ukay Perdana Ulu Klang, Selangor is from early Paleozoic era under Cambrian to Ordovician period (Gobbett 1964) and has been mapped as Dinding schist.

4 Vol. 20 [2015], Bund Figure 1: Location of study area, West Malaysia METHODOLOGY The uniaxial compressive strength (UCS) of intact rock was measured by using apparatus DHR 2000 exhibited in Figure 2. The test is intended to measure the UCS value of rock material based on the recommendation by ISRM (2007). Testing was carried out on regular geometry core specimens with diameter of 54 mm. The height of the specimen was measured to a ratio of 2:1 (height : diameter) with both end of the core surface trimmed to smooth and flat surface. Loading was applied at constant rate of MPa/s by using apparatus shown in Figure 2. UCS value was calculated by using equation (1). UCS = P/A (1)

5 Vol. 20 [2015], Bund Figure 2: Apparatus for uniaxial compressive strength test (DHR 2000). Testing was carried out on regular geometry core specimens with diameter of 54 mm at a loading rate of MPa/s Primary wave velocity (V p ) of cored samples was measured by using PUNDIT Plus (Portable Ultrasonic Non Destructive Digital Indicating Tester) with a frequency of 50 khz (figure 3). The ultrasonic test is intended to measure the velocity of compressional waves that travels through rock sample based on the recommendation by ISRM (2007). This is a common non-destructive test that is conducted in predicting rock material strength whenever destructive testing is not preferable. Testing was carried out on regular geometry core specimens with diameter of 54 mm. The height of the specimen was measured to a ratio of 2:1 (height : diameter) with both end of the core surface trimmed to smooth and flat surface. A single transmitter sends ultrasonic waves through one surface of the rock and a separate single receiver detects the travel time taken for the primary waves to reach the other surface end. The V p of the sample was calculated by using equation (2): V p = L/t (2)

6 Vol. 20 [2015], Bund Figure 3: Portable Ultrasonic Non Destructive Digital Indicating Tester (PUNDIT Plus) for conducting ultrasonic test. The apparatus was used to measure travel time (t) of primary wave from transmitter to receiver RESULT AND DISCUSSION A total of 26 ultrasonic tests and uniaxial compressive strength tests were conducted on dry schist samples. The loading direction of UCS test and wave travelled of ultrasonic test were 90 (perpendicular) to foliation of schist. Figure 4 shows the laboratory results plotted with the proposed empirical correlation for dry schist, and the empirical correlations established by McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) to predict UCS for saturated sandstone and shale. It is revealed that the laboratory results are not in good agreement with the established empirical correlations, as it predicts too low the value of UCS. The new established empirical correlation, UCS = 3.40 x V p with a coefficient of determination (R 2 ) of 0.91 as shown in Figure 5 provides better predictions of UCS from V p as it considers the effect of anisotropy and water condition of rock.

7 Vol. 20 [2015], Bund Figure 4: Comparison of laboratory test results plotted with proposed empirical correlation for dry schist, together with the empirical correlations established by McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) to predict UCS for saturated sandstone and shale. It is revealed that the laboratory results are not in good agreement with the established empirical correlations, as it predicts too low the value of UCS.

8 Vol. 20 [2015], Bund Figure 5: Estimation of UCS from V p for dry schist as established. The new empirical correlation is UCS = 3.40 x V p with a coefficient of determination (R 2 ) of The results of testing were analyzed at 95 % confidence level by using SPSS statistical software version 16 (Table 3). The minimum, maximum, mean and median values of UCS were 2.5 MPa, MPa, MPa and MPa respectively, with a standard deviation of MPa. The minimum, maximum, mean and median values of V p were 1886 m/s, 6038 m/s, 4525 m/s and 4854 m/s respectively, with a standard deviation of 1094 m/s. Table 3: Summary of statistical analysis for dry schist analyzed at 95% confidence level by using SPSS statistical software version 16 Parameter No. of test Min Max Mean Median Standard Deviation Skewness UCS MPa MPa MPa MPa MPa Positive V p m/s 6038 m/s 4525 m/s 4854 m/s m/s Negative Figure 6 and 7 shows the boxplots of UCS test and V p values respectively. The skewness of UCS results is positive skewness. This implies that more test results having lower value of UCS

9 Vol. 20 [2015], Bund compared to the mean value. The skewness of ultrasonic testing results is negative skewness. This implies that more test results having higher value of V p compared to the mean value. Figure 6: (a) Boxplot of uniaxial compressive strength (UCS) result. The skewness of UCS results is positive skew. (b) Histogram of uniaxial compressive strength (UCS) results Figure 7: (a) Boxplot of P-wave velocity (V p ) result. The skewness of V p results is negative skew. (b) Histogram of P-wave velocity results Table 4 exhibits the calculated values of uniaxial compressive strength values based on McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) predictions together with the new correlation established from this study.

10 Vol. 20 [2015], Bund Table 4: Calculated values of uniaxial compressive strength (UCS) based McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) predictions and new empirical equation V p (m/s) New Empirical Equation (MPa) McNally (1987), MPa Moos (1999), MPa Horsrud (2001), MPa Goh (2014), MPa Percentage differences of uniaxial compressive strength predictions between new correlation with the published correlations are illustrated in Table 5. As seen from this table, the percentage differences between the new correlation values and the published correlation values range from % to 3316 %. From this percentage differences, it clearly shows the need and importance in establishing correlation for dry schist, as the published correlations of McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) are not suitable in prediction of UCS for schist, especially when anisotropy and water condition are taken into consideration.

11 Vol. 20 [2015], Bund Table 5: Percentage of differences of uniaxial compressive strength predictions between new correlation with published correlations proposed by McNally (1987), Moos et.al, (1990), Horsrud (2001) and Goh et.al, (2014) V p (m/s) McNally 1987 (%) Moos 1999 (%) Horsrud 2001 (%) Goh 2014 (%) CONCLUSION A new empirical equation was established to estimate the value of UCS from primary wave velocity (V p ) for dry schist. The new equation is UCS = (3.40 x ) Vp with a coefficient of determination of 0.9. Estimation of UCS value from this empirical correlation is a simple and fast method as V p can be measured easily in the laboratory. Assesment of rock strength is crucial during site assessment as it provides engineers and geologists better insight of the mechanical properties of rock. Thus, this equation is expected to be useful for the purpose of rock mass assessment in cut slope and underground excavation especially in the lithological area of schist.

12 Vol. 20 [2015], Bund ACKNOWLEDGEMENT This publication was funded by the Fundamental Research Grant Scheme (FRGS/1/2014/STWN06/UKM/02/1), e-science Fund grant scheme ( SF 1140), Geran Universiti Penyelidikan (GUP ). The authors also acknowledge the support of the staff and facilities at geology program and faculty. REFERENCES 1. Abdul Rahim Samsudin Geofizik Konsep dan Penggunaan. Kuala Lumpur: Dewan Bahasa dan Pustaka. 2. Gobbett, D.J The lower palaeozoic rocks of Kuala Lumpur, Malaysia, Fed. Museums Journal, Vol.9 : pp Godfrey et.al, Anisotropy of schists: Contribution of crustal anisotropy to active source seismic experiments and shear wave splitting observations. Journal of Geophysical Research, Vol. 105, No. B12, pp 27, , 007D. 4. Goh, T. L Classification and quantification of rock mass in rock slope evaluation, Unpublished Ph.D. Thesis, Geology Programme, National University of Malaysia, Bangi. 5. Goodman, R.E Introduction to Rock Mechanics, 2 nd edition. New York: John Wiley & Sons. 6. Horsrud, P Estimating mechanical properties of shale from empirical correlations, SPE Drilling and Completion, Vol. 16, No. 2, pp Hutchison, C.S Geology of The Malay Peninsular. New York:John Wiley & Sons. 8. ISRM, The Complete ISRM Suggested Methods for Characterization, Testing and Monitoring: , Ankara: ISRM Turkish National Group. 9. Lama R D and Vutukuri V S Handbook on mechanical properties of rocks (Germany) Vol McNally, G. H. N Estimation of coal measures rock strength using sonic and neutron logs, Geoexploration Vol. 24, pp Moos, D., M.D. Zoback and L. Bailey, Feasibility study of the stability of openhole multilaterals, Cook Inlet, Alaska. The 1999 SPE Mid-Continent Operations Symposium, Oklahoma City, Oklahoma, March SPE Oh, H.T Pemetaan geologi sepanjang km14 km 27 Jalanraya Kg. Raja, Cameron Highland, Pahang Pos Selim, Perak. Unpublished Bachelors Degree Thesis, Geology Programme, National University of Malaysia, Bangi. 13. T.L. Goh, A.G. Rafek, A.S. Serasa, N. Simon, K.E. Lee Empirical Correlation of Uniaxial Compressive Strength and Primary Wave Velocity of Malaysian Granites. Electronics Journal of Geotechnical Engineering (EJGE) Vol. 19 [2014], Bund. E 14. Zoback, M Reservoir Geomechanics, New York: Cambridge University Press ejge