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

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, Unive

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,

43600 UKM Bangi, Selangor, Malaysia

e-mail: gdsbgoh@gmail.com

Abdul Ghani Rafek

Professor, School of Environment and Natural Resources Sciences, Faculty of

Science and Technology, Universiti Kebangsaan Malaysia,

43600 UKM Bangi, Selangor, Malaysia

e-mail: aghani@ukm.my

Ailie Sofyiana Serasa

Student, Petroleum Engineering Department, Faculty of Engineering, Technology & Built Environment (FETBE),

UCSI University, Kuala Lumpur, Malaysia e-mail: ailie.serasa@gmail.com

Norbert Simon

Doctor, School of Environment and Natural Resources Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,

43600 UKM Bangi, Selangor, Malaysia

e-mail: norbsn@yahoo.com

Lee Khai Ern

Doctor, Institute for Environment and Development (LESTARI), National University of Malaysia, 43600 UKM Bangi,

Selangor D E., Malaysia e-mail: khaiernlee@ukm.my

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 withexpensive and destructive laboratory testingand thus the limited rock sampleshas becomes adisadvantage 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 (Vp) The empirical correlation of UCS and Vp for granite was UCS = (2.55 x 10-5) ∙ Vp1.7658 with a coefficient of determination (R2) of 0.90 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

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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 141.1 MPa – 226.0 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 (Vp) 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 (Vp)

Reference UCS, MPa Lithology

McNally (1987) 1200∙e -0.036∆tp Fine-grained sandstones (Bowen Basin,

Australia) McNally (1987) 1.4138∙107 ∆tp-3 Weak, unconsolidated sandstones (Gulf Coast) Freyburg (1972) 0.035Vp – 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 Vp (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

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 0.5 – 1.0 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)

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 0.5 – 1.0 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 (Vp) 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)

Vp = L/t (2)

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, 109.9 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 Vp 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 Vp are shown in Figure 4 and Figure 5 respectively The skewness for both UCS and Vp results were found to be negative, which implies more test results have higher value of UCS or Vp compared to the mean value Positive skewness implies more test results have lower values of UCS or Vp compared to the mean value

Table 2: Summary of statistical results of UCS and Vp values of granitic rock, Malaysia

No of

test Min Max Mean Median Deviation Standard Skewness UCS 77 5.0MPa 109.9MPa 72.0MPa 76.8 MPa 27.7 MPa negative

Vp 77 1258 m/s 6142 m/s 4379 m/s 4678 m/s 1159 m/s negative

Figure 4: Boxplot of uniaxial compressive strength (UCS) of Malaysian granite

Figure 5: Boxplot of primary wave velocity (Vp) of Malaysian granite

An empirical correlation, UCS = (2.55 x 10-5) ∙ Vp1.7658 with a coefficient of determination (R2) 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 ofFreyburg (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

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) ∙ Vp1.7658with a coefficient of

determination (R2) of 0.9 had been established from UCS versus Vp for Malaysian granite

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

1000 5.1 0.0 0.5 2.4 3.5 0.8

1500 10.3 0.8 1.7 5.1 21 2.5

2000 17.2 5.0 4.0 8.6 38.5 5.9

2500 25.5 14.9 7.8 13.0 56 11.3

3000 35.2 30.9 13.5 18.1 73.5 19.2

3500 46.2 52.2 21.4 23.9 91 30.2

4000 58.5 77.2 31.9 30.5 108.5 44.7

4500 72.0 104.7 45.5 37.8 126 63.1

5000 86.7 133.6 62.4 45.8 143.5 85.9

5500 102.6 163.1 83.0 54.5 161 113.6

6000 119.7 192.6 107.8 63.9 178.5 146.6

6500 137.8 221.7 137.0 73.9 196 185.4

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), %

1000 -100 -90 -52 -31 -85

1500 -92 -84 -50 103 -76

2000 -71 -77 -50 124 -66

2500 -42 -69 -49 120 -56

3000 -12 -62 -49 109 -45

3500 13 -54 -48 97 -35

4000 32 -45 -48 86 -24

4500 45 -37 -47 75 -12

CONCLUSION

An empirical correlation, UCS = (2.55 x 10-5) ∙ Vp1.7658 with a coefficient of determination (R2) 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 (025 & GGPM-2013-082) under the National University of Malaysia The authors also acknowledge the support of the staff and facilities at geology program and faculty

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