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RELATION BETWEEN UNIAXIAL COMPRESSIVE STRENGTH POINT LOAD INDEX AND SONIC WAVE VELOCITY FOR DOLERITE.

Byline: A. M. Sheraz M. Z. Emad M. Shahzad and S. M. Arshad

ABSTRACT: Uniaxial compressive strength (UCS) of intact rocks is a major consideration in rock mechanics study for civil and mining projects. UCS direct testing is expensive time consuming and it involves preparation of rock samples. Indirect tests are relatively cheaper faster and are convenient to perform in the laboratory and at site. This work presents the development of possible empirical relations between UCS values determined by direct and indirect testing methods including Point Load Index and Sonic Velocity for dolerite. A review of various correlations established for UCS versus point load index and UCS versus sonic wave velocity for different rocks by various researchers have also been presented.

Key words: Uniaxial compressive strength Sonic velocity Point load index Dolerite Hadda formation

INTRODUCTION

A complete site characterization for mining and geotechnical engineering applications require extensive database of geo-mechanical engineering properties of rocks. Initial assessment of site portrayal requires quick information of rockmass properties. Various constraints including economics remote locations and time limitations restrict rock engineers to directly attain the explicit design parameters of interest. Therefore alternative ways based on empirical or theoretical relations for estimating various geo-mechanical and physical properties of rocks are required. Geo-mechanical characteristics of rocks are crucial for geotechnical design of subsurface structures. In mines uniaxial compressive strength (UCS) of rock mass is a key design aspect for stope and pillar roof support excavations in rock burst prone ground squeezing and swelling ground etc. Determination of UCS for different rocks in laboratory is a common practice.

Standard testing procedures have been established by the American Society for Testing and Materials (ASTM) and the International Society of Rock Mechanics (ISRM). However these methods are expensive time consuming and involve high quality sample preparation (Fener et al; 2005). On the other hand indirect testing techniques such as point load test and sonic pulse velocity for the estimation of UCS of rocks require little or no sample preparation very less testing time and can be easily performed on-site. This study aims at to establish possible correlations between the UCS values determined by direct and indirect methods for the dolerite rock samples from Hadda Formation of Sillanwali area in Punjab province of Pakistan. The Sillanwali region is expected to host a few civil works and mining projects in future. Point Load Index: The point load index (PLI) is extensively used for the indirect estimation of UCS. It can furnish similar data at a lower cost. The testing apparatus is portable and can be used on-site. The rock sample is compressed between conical points until failure occurs. Failure pressure is recorded and point load index Is(50) is determined by relation given as (1):

Is(50) = P/De2 ------ (1)

Where P = failure load in lbs

De = equivalent core diameter (inches)

Several researchers have recommended a variety of empirical relations for the calculation of UCS from IS(50).

D'Andrea et al; (1964) proposed the following linear

correlation equation for estimating UCS from IS(50):

qu = 16.3 + 15.3 Is (50) ------ (2)

where

qu = Uniaxial compressive strength of the rock.

Is (50) = Point load index for rock core diameter of 50 mm.

Broch and Franklin (1972) disclosed that UCS of rock

core of NX size is roughly about 24 times its point load index and suggested following relationship between UCS and IS(50):

UCS = 24 Is (50) ------ (3)

Bieniawski (1975) recommended the following

relationship amongst UCS PLI (Is (50)) and rock core diameter (D):

UCS = (14 + 0.175 D) Is (50) ------ (4)

Cargill and Shakoor (1990) conducted standard UCS and

point load tests on fourteen rock types including Sandstone Limestone Dolomite Marble and Syenitic Gneiss to determine possible correlation between UCS and PLI and established following linear relationship:

qu = 13 + 23 ls(50) ------ (5)

Sonic Wave Velocity: Ultrasonic techniques being non- destructive and easy to apply are widely utilized for indirect estimation of mechanical and geo-physical properties of rocks. Sonic wave velocity has a direct relationship with strength of material. Various researchers have determined a close relationship between sonic wave velocity of a rock mass and rock compressive strength.

Inoue and Ohomi (1981) reported the following correlation among UCS sonic velocity and rock density: UCS = k V 2 + 31.18 ------ (19)

Where

k= Empirical coefficient

= Density of rock

The testing program of Grasso et al; (1992) on calcareous mudstone core samples collected from five boreholes drilled for geotechnical investigations of a road tunnel in Central Italy produced following correlation linking UCS and compression wave velocity: -3

Equation

MATERIALS AND METHODS

Sampling Source: The core samples of dolerite rock were collected as a result of exploratory drilling by the Geological Survey of Pakistan near the boundary of Jhang and Sargodha districts in Punjab province of Pakistan. The drill hole site was located 1.5 kilometers north of Chak 142 and 12 kilometers southwest of Sillanwali area at a Latitude of 31o45'30 and a Longitude of 72o29'50. The hole was drilled to a depth of 550 meters divided into upper non-coring alluvium cover of 192.6 meters and below that dolerite coring run of 357.4 meters.

The GSP logged the cores and handed over the samples to the rock mechanics laboratory for further analysis. Six core boxes with a total length of 120 meters were received. Majority of the samples were damaged and were discarded. After sorting and visual examination the flawless samples were cut trimmed and lapped to standard sizes. Preparation of core samples and testing was conducted in accordance to standard methods adopted by ISRM and ASTM.

Laboratory Testing Procedure: A total of twenty three (23) sets of rock core samples were tested for direct UCS point load index (IS(50)) and sonic velocity (Vp). Direct UCS test was executed on rock cores with approximate length to diameter ratio 2.5:1 (Figure 1). The cores were pressed to fracture at a very slow rate (to avoid dynamic loading) using a 200 ton Universal Testing Machine. Point load test was performed by loading cores on two pointed platens until failure occured (Figure 2). Core diameters with 54 mm 42 mm and 30 mm were used to perform point load test. Corrections were applied for diameters other than 54 mm to calculate equivalent diameter and Is(50) was computed. The sonic velocity was measured by means of Portable Ultrasonic Non- destructive Index Tester (PUNDIT). The time taken by sound waves to pass through rock cores was recorded and sound velocities were computed.

RESULTS AND DISCUSSION

The test results of experiments performed for uniaxial compressive strength point load index and sonic velocity on dolerite samples revealed that UCS of dolerite varied from 31.27 to 388.74 MPa with an average value of 189.61 MPa. The average values of point load index and sonic velocity were found to be 0.91 MPa and 7.33 km/s. The point load test values and sonic velocities computed ranged from 0.11 to 2.63 MPa and 6.62 to 7.85 km/s respectively.

The results were statistically scrutinized by using regression analysis and six statistical significant equations were found.

Correlations between UCS and Is (50): The various relationships between UCS and Point Load Index (PLI) and their correlation coefficients were found through statistical regression analysis. All the three functions (linear exponential and power) showed increase in UCS with increase in PLI values thus representing a positive correlation between the two parameters. Figures 3 4 and 5 present the results for linear exponential and power function respectively. Among the results power function was the more reliable with greater coefficient of correlation thus it provided a better estimation of UCS for a wide range of Is (50) values. It can be seen that the power function was the most suitable with the data obtained. Although linear-fit curve was not an ideal one but it provided better prediction of UCS for lower values of Is(50).

Correlations between UCS and Vp: Various correlation relationships (linear exponential and power) between Uniaxial Compressive Strength (UCS) and Sonic Wave Velocity (Vp) are presented in Figures 6 7 and 8 respectively. All three relationships depict positive correlations between UCS and Vp. In this case linear function exhibited statistically more realistic correlation with correlation coefficient of 79%.

The relationship was not applicable for smaller values of Vp as the equation had a negative intercept of 1413. The range of Vp for prediction of UCS may be 7.40 km/s to 8.00 km/s or above. It can be seen that exponential function gave a better estimation at lower values of Vp but it overestimated UCS at higher values. It can be observed from Figure 6 that power function was best-fit curve for the correlation between UCS and Vp. Although its correlation coefficient was slightly less than that of linear function but it better estimated UCS values over a wider range of Vp values.

Significance of derived equations: The statistical analysis of test results produced the following six prediction equations for UCS versus Is (50) and UCS versus Vp:Equation

Correlations between UCS and Vp: Various correlation relationships (linear exponential and power) between Uniaxial Compressive Strength (UCS) and Sonic Wave Velocity (Vp) are presented in Figures 6 7 and 8 respectively. All three relationships depict positive correlations between UCS and Vp. In this case linear

The statistical significance of all the six correlations was determined by the standard test wherein the computed t value [t = r (n-2)1\2 / (1-r2)] was checked against a critical t value. If the t value from computation was more than the critical t value the correlation coefficient was considered to be statistically lesser or greater than zero which means the relationship can be used for the prediction of the dependent variable from the independent variable. All the six relationships were found to have statistical significance

To check the estimation accuracy of these equations the concept of Confidence Interval" (CI) was used. For a normal distribution the 95% confidence interval of mean is expressed as:

The standard deviation mean and 95% confidence interval values of the uniaxial compressive strength are given in Table 1 whereas Table 2 and Table 3 shows estimated values of UCS computed from derived prediction equations against measured UCS values. It can be observed that 95% of the predicted UCS values from UCS versus Is (50) equations fall within 95% CI range. Whereas all the predicted UCS values from UCS versus Vp equations fall within 95% CI range.

Table 1 - Mean UCS and Standard Deviation of tested rocks

Mean UCS###Standard Deviation###UCS Range

T###SD###T + 1.96 (SD)

(MPa)###(MPa)###(MPa)

189.61###89.55###14.10 to 365.13

Table 2 - Validation of predicted equations of UCS from Point Load Index values

Sr.###Estimated values

###Sample title###UCS (MPa)###Is (50)

No.###UCS = 110.1Is + 89.87###UCS = 85.52e0.718Is###UCS = 202.71Is0.633

1###S-1###331.38###2.63###379.43###565.15###373.86

2###S-2###46.12###0.20###111.89###98.73###73.19

3###S-3###233.71###0.71###168.04###142.38###163.20

4###S-6###71.23###0.48###142.72###120.71###127.38

5###S-8###31.27###0.11###101.98###92.55###50.13

6###S-10###214.26###1.63###269.33###275.64###276.18

7###S-11###140.00###1.01###201.07###176.61###203.99

8###S-12###250.45###1.16###217.59###196.69###222.68

9###S-13###179.49###1.25###227.50###209.82###233.46

10###S-14###156.71###0.40###133.91###113.97###113.50

11###S-19###245.49###0.90###188.96###163.20###189.63

12###S-20###312.21###1.10###210.98###188.40###215.32

13###S-21###388.74###1.58###263.83###265.92###270.79

14###S-22###258.09###1.16###217.59###196.69###222.68

15###S-23###83.15###0.31###124.00###106.84###96.58

16###S-24###126.70###0.18###109.69###97.32###68.46

17###S-27###225.91###0.51###146.02###123.34###132.36

18###S-28###139.81###0.90###188.96###163.20###189.63

19###S-29###199.77###0.86###184.56###158.58###184.25

20###S-31###234.08###0.49###143.82###121.58###129.05

21###S-32###154.63###1.06###206.58###183.06###210.33

22###S-34###191.40###1.36###239.61###227.06###246.27

23###S-35###146.52###0.84###182.35###156.31###181.53

Table 3 - Validation of predicted equations of UCS from P-wave velocity

Sr.###Estimated values

###Sample title###UCS (MPa)###Vp (Km/s)

No.###UCS = 218.8Vp - 1413###UCS = 0.003e1.455Vp###UCS = Vp10.6 x 10-7

1###S-1###331.38###7.85###304.58###273.86###305.93

2###S-2###46.12###6.94###105.47###72.86###82.87

3###S-3###233.71###7.69###269.57###216.98###245.93

4###S-6###71.23###7.12###144.86###94.68###108.71

5###S-8###31.27###6.88###92.34###66.77###75.59

6###S-10###214.26###7.62###254.26###195.97###223.21

7###S-11###140.00###7.49###225.81###162.20###186.00

8###S-12###250.45###7.49###225.81###162.20###186.00

9###S-13###179.49###7.21###164.55###107.92###124.20

10###S-14###156.71###7.28###179.86###119.49###137.59

11###S-19###245.49###7.55###238.94###176.99###202.41

12###S-20###312.21###7.50###228.00###164.57###188.65

13###S-21###388.74###7.60###249.88###190.35###217.08

14###S-22###258.09###7.76###284.89###240.24###270.73

15###S-23###83.15###6.62###35.46###45.74###50.25

16###S-24###126.70###7.27###177.68###117.77###135.60

17###S-27###225.91###7.67###265.20###210.76###239.24

18###S-28###139.81###7.05###129.54###85.51###97.90

19###S-29###199.77###7.04###127.35###84.27###96.44

20###S-31###234.08###7.57###243.32###182.22###208.17

21###S-32###154.63###7.07###133.92###88.03###100.89

22###S-34###191.40###7.11###142.67###93.31###107.11

23###S-35###146.52###7.12###144.86###94.68###108.71

Direct UCS prediction equations from indirect UCS tests have been developed. The empirical relations so developed in this study were also found to be statistically significant. Among these relationships power functions both for point load test and p-wave velocity can be employed reliably for prediction of UCS. It was found that linear and exponential relationships could also predict UCS for the same rock type but were less reliable. The results presented are appreciable for the rock type studied.

Conclusions: A critical review of literature revealed that there had been significant work done in establishing statistical significant relationships. In the present work it was established that dolerite rock provided an indirect fast assessment of one of the important rock strength parameters.

REFERENCES

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ASTM. Standard test method for unconfined compressive strength of intact rock core specimens. (1984). Bieniawski Z.T. Point load test in geotechnical practice. Engineering Geology 9(1): 111 (1975). Broch E. and J.A. Franklin. Point-load strength test.

International Journal of Rock Mechanics and Mining Sciences 9(6): 66997 (1972). Cargill J.S. and A. Shakoor. Evaluation of empirical methods for measuring the UCS of rock. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 27: 495-503 (1990).

Chary K.B. L.P. Sarma K.J. Prasanna Lakshmi N.A. Vijaya kumar V. Naga Lakshmi and M.V.M.S. Rao. Evaluation of engineering properties of rock using Ultrasonic Pulse Velocity and Uniaxial Compressive Strength. Proceedings National Seminar on Non- Destructive Evaluation 379-385 (2006).

D'Andrea D.V. R.L. Fisher and D.E. Fogelson. Prediction of Compression strength from other rock properties. Colorado School of Mines 59(4B): 62340 (1964).

Entwisle D.C. P.R.N. Hobbs L.D. Jones D. Gunn and M.G. Raines. The Relationships between Effective Porosity Uniaxial Compressive Strength and Sonic Velocity of intact Borrowdale Volcanic Group core samples from Sellafield. Geotechnical and Geological Engineering 23: 793809 (2005).

Fener M. S. Kahraman A. Bilgil and O. Gunayadin. A comparative evaluation of indirect methods to estimate the compressive strength of rocks. Rock Mechanics and Rock Engineering 38(4): 329-343 (2005).

Grasso P. S. Xu and A. Mahtab. Problems and promises of index testing of rocks. Proceedings of the 33rd U.S. Symposium on Rock Mechanics Balkema Rotterdam 879 888 (1992).

Hakan E. and K. Darya. Multicriteria decision making analysis based methodology for predicting carbonate rocks Uniaxial Compressive Strength. Earth Sciences Research Journal 16: 65-74 (2012).

Inoue M. and M. Ohomi. Relation between Uniaxial

Compressive Strength and Elastic Wave Velocity of soft rock. Proceedings of the International Symposium on Weak Rock Tokyo 913 (1981).

ISRM. Rock characterization testing and monitoring.

ISRM suggested methods (ed. E.T. Brown) Pergamon Oxford 211 (1981).

Jabbar M.A. Correlations of Point Load Index and Pulse Velocity with the Uniaxial Compressive Strength for rocks. Journal of Engineering 17(4): 992-1006 (2011).

Kahraman S. Evaluation of simple methods for assessing the Uniaxial Compressive Strength of rock. International Journal of Rock Mechanics and Mining Sciences 38(7): 981- 994 (2001).

Kurtulus C. A. Bozkurt and H. Endes. Physical and mechanical properties of serpentinized ultrabasic rocks in NW Turkey. Pure and Applied Geophysics 10: (2011).

Palchik V. and Y. H. Hatzor. The influence of porosity on tensile and compressive strength of porous chalk. Rock Mechanics Rock Engineering 37(4): 331341 (2004).Quane S. L. and J. K. Russel. Rock strength as a metric of welding intensity in pyroclastic deposits. Eur. J. Mineral 15: 855864 (2003).

Rusnak J. and C. Mark. Using the point load test to determine the uniaxial compressive strength of coal. 19th Ground Control Conference in Mining West Virginia University 362-371 (2000).

Sharma P.K. and T.N. Singh. A correlation between P- Wave velocity impact strength index slake durability and Uniaxial Compressive Strength. Bull Eng. Environ 67: 17-22 (2008).

Yagiz S. P-Wave velocity test for assessment of geotechnical properties of some rock materials. Bull Mater Science. 34(4): 947-953 (2011).

Yasar E. Y. Erdogan. Correlating sound velocity with the density compressive strength and Young's Modulus of carbonate rocks. International Journal of Rock Mechanics and Mining Sciences 41: 871-87 (2004).

ZCZC

EFFICIENT VQ-BASED SPEAKER IDENTIFICATION THROUGH ELIMINATION OF ANOMALOUS VECTORS DURING MFCC FEATURE EXTRACTION

By: M. Afzal T. Ahmad M. F. Hayat H.M. S. Asif and K. H. Asif

_: ABSTRACT: Floating Point (FP) numbers are ubiquitous to manipulate real number in digital computations. Mel-Frequency Cepstral Coefficients (MFCC) feature vectors of real values are extracted from speech to represent a large number of phonetic variations pertaining to speaker and spoken text. The MFCC vectors require log sine cosine and etc for their computation. However multilevel rounding that occurs in FP arithmetic operation requires extra care for computing MFCC vectors. Computing log of FP zero gives FP which is carried along till last step in extracting MFCC vectors. We propose elimination of anomalous vectors in MFCC features vectors extraction process. Vector Quantization (VQ) compresses MFCC vectors into a small set of mean vectors called codebook to efficiently represent phonetic classes thus making them more feasible to process speech for speaker verification and identification etc. Average taking in clustering algorithms of FP numbers

containing FP computes to FP that give false codebook. Removal of vectors containing FP element is proposed for speaker identification and other VQ-based classification systems in general for higher accuracy. Accuracy was increased by 2% 3% and 2% in our VQ based speaker identification experiments on TIMIT 16 kHz down sampled TIMIT 8 kHz and CSLU speaker recognition data respectively.

Keywords: Speaker identification vector quantization MFCC feature vectors floating point rounding

INTRODUCTION

Automatic Speaker Identification (ASI) systems identify a test speaker as one from its registered speakers (Quatieri 2000). Three major units constituting ASI systems are Feature Extraction (FE) Model Training (MT) and Pattern Matching (PM). FE unit serves as front processor to both MT and PM units. Input digital speech signal to FE unit is converted to a sequence of vectors of real value elements of speaker specific features. In digital computers real numbers are only feasibly represented stored and processed as FP numbers according to IEEE- 754 standards laid down by (Floating-Point Working Group 2008). The use of FP numbers require extra care in extraction of Mel-Frequency Cepstral Coefficients (MFCC) feature vectors. Mostly MFCC vectors having 12 to 20 elements of FP numbers are used (Kinnunen et al. 2006). The conversion process starts by dividing the speech signal into generally 30 millisecond frames overlapping by 30% to 50%. Pre-emphasis filtration of original speech signal is variably practiced.

Silence removal is performed using threshold frame energy to ignore less energy frames as silence frames. Discrete Fourier Transform (DFT) is used to generate magnitude frequency spectrum of each non-silence frame. For the fixed sampling frequency of a speech signal the frequency resolution of the spectrum depends on the frame size. The magnitude spectrums have B /2 number of frequencies where B is number of samples in each frame. Efficient characterization of speaker emphasizes on using less number of frequencies. Mel-Frequency scale is one that corresponds to human auditory system's frequency reception (Quatieri 2000). Usually 15 to 50 frequencies are selected on Mel scale to define a triangular filterbank (Quatieri 2000). Weighted sums of triangular filters are then compressed by taking log. MFCC vectors and are finally formed from sum vectors by taking Discrete Cosine Transform (DCT).

MATERIALS AND METHODS

Weighted sum computation of products of small frequency magnitudes and triangular filter weights can give FP zero because of rounding. FP computation starts degrading unfeasibly at this step. Log compression of an FP zero results into a FP . DCT of such log compressed vector transfer FP to the corresponding MFCC vector. In such case a clustering algorithm like Linde Buzo Gray (LBG) while taking average of clustering vectors will create codebook of mean vectors containing FP . Such impaired codebook increases error in minimum distortion based identification process.

This paper proposes improved MFCC vector extraction sequence as shown in Figure 1. Anomalous vector elimination step is introduced before taking log of Mel-frequency spectral coefficient vectors that discards out vectors containing any FP zero element. This step is depicted by the decision diamond in the log compression process rectangle in Figure 1.

RESULTS AND DISCUSSION

Real number manipulation in digital computers is an intricately involved concept because of conflicting targets to be achieved. Floating point representation of real numbers and their arithmetic involvement multilevel rounding is imposed by sparse representation of real numbers between a minimum and a maximum value because of limited number of bits allocated to store bit- string values as explained in IEEE Standard 754 Floating Point Arithmetic (Floating-Point Working Group 2008).

We experimented on TIMIT (Garofolo 1993) and CSLU (Cole 1998) speech data containing 630 and 91 speakers respectively. MFCC feature vectors generated had 12 elements from output of 19 triangular filters. VQ codebooks trained were of 32 64 128 256 and 512 sizes for the three speech data types. However for CSLU data codebooks of sizes 1024 2048 were also evaluated. We compared VQ based speaker identification performance both with and without discarding the anomalous vectors testing for all target speakers in the data bases as shown in Table 1.

Table###1:###Identification Accuracy###improved###with removal of Anomalous vectors

###Maximum Achieved

###% Accuracy

###CSLU

###TIMIT Data 16 KHz###TIMIT Data###Data

###Linear PCM###8khz###8khz

###Linear PCM

Not###99.0###97.0###97.8

removed

Removed###100###99.5###100

This discovery was possible only because the values of codebook vectors written in text files were personally inspected. The codebook vectors showed INF for each element. INF means infinity FP number (Floating-Point Working Group 2008). The cause of this observation was then traced back to locate the origin of the problem. Hence we located the problematic step in MFCC feature vector extraction to be the one as the log taking of triangular filter output.

Conclusions: It was observed that removal of feature vectors that contain FP elements from feature vector sequence before training VQ codebooks and before minimum distortion computation has increased accuracy of speaker identification. Such anomalous vectors are created when an element of a vector from triangular filters is zero. This element results in FP member when log is taken in the next step of MFCC feature vector extraction. We increased accuracy in speaker identification on TIMIT 16 kHz down sampled TIMIT 8 kHz and CSLU speaker recognition data from 99% to 100% 97 to 99.5% and 97.8 to 100% respectively for codebook sizes larger than 256 through removals of anomalous vectors.

REFERENCES

Cole R. M. Noel and V. Noel The CSLU Speaker Recognition Corpus. Proc. 5th Int. Conference on Spoken Language Processing (ICSLP) Sydney Australia pp.3167-3170 (1998)

Floating-Point Working Group IEEE Standard for Floating-Point Arithmetic: IEEE Std 754- 2008 Microprocessor Standards Committee IEEE Computer Society (2008).

Garofolo J. L. Lamel W. Fisher J. Fiscus D. Pallett N. Dahlgren and V. Zue TIMIT Acoustic- Phonetic Continuous Speech Corpus (1993)

Kinnunen T. E. Karpove and P. Franti Real-Time Speaker Identification and Verification IEEE Transactions on Audio and Language Processing 14 (1): 277-288 (2006)

Quatieri T. Discrete-time Speech Signal Processing Principles and Practice Pearson Education (2000).
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