Correlating P-wave Velocity with the Physico-Mechanical Properties of Different Rocks

MANOJ KHANDELWAL1

Abstract—In mining and civil engineering projects, physico-

mechanical properties of the rock affect both the project design and

the construction operation. Determination of various physico-

mechanical properties of rocks is expensive and time consuming,

and sometimes it is very difficult to get cores to perform direct tests

to evaluate the rock mass. The purpose of this work is to investigate

the relationships between the different physico-mechanical prop-

erties of the various rock types with the P-wave velocity.

Measurement of P-wave velocity is relatively cheap, non-destruc-

tive and easy to carry out. In this study, representative rock mass

samples of igneous, sedimentary, and metamorphic rocks were

collected from the different locations of India to obtain an empir-

ical relation between P-wave velocity and uniaxial compressive

strength, tensile strength, punch shear, density, slake durability

index, Young’s modulus, Poisson’s ratio, impact strength index and

Schmidt hammer rebound number. A very strong correlation

was found between the P-wave velocity and different physico-

mechanical properties of various rock types with very high coef-

ficients of determination. To check the sensitivity of the empirical

equations, Students t test was also performed, which confirmed the

validity of the proposed correlations.

Key words: Physico-mechanical properties, P-wave velocity,

igneous rocks, sedimentary rocks, metamorphic rocks.

1. Introduction

Physico-mechanical properties of intact rocks are

very important in mining and civil engineering works

that interact with rock such as underground struc-

tures, dams, foundations on rock, rock slopes,

tunnels, dams, deep trenches, caverns, etc. They are

also very important for the study of rock bursts and

bumps in underground mines, pillar design, predic-

tion of failure of rock mass, etc. Determination of

physico-mechanical properties in the laboratory as

well as in in situ condition to characterize rock mass

is mostly expensive and requires considerable time

and expertise, especially the preparation of rock

samples for testing (SHALABI et al., 2007).

Measurement of P-wave velocity is an easy and

simple task, and it can be employed in both the site

and laboratory to characterize and determine the

dynamic properties of rocks. It is non-destructive and

easy to apply, which is why it has been used for many

years in geotechnical practice, mining sciences and

petroleum engineering (KHANDELWAL and RANJITH

2010). The P-wave velocity in a solid material

depends on the density and elastic properties of that

material. Because the P-wave velocity depends on

density and elastic properties, there is an infinite

number of value sets resulting for the same P-wave

velocity. Thus, the mechanical laboratory testing of

density and elastic properties of the intact rock

material significantly improves the accuracy of

interpretation of P-wave measurements, especially in

in situ conditions.

A number of researchers (SMORODINOV et al., 1970;

INOUE and OHOMI 1981; GAVIGLIO 1989; BOADU 2000;

KAHRAMAN 2001a, b; OZKAHRAMAN et al., 2004; YASAR

and ERDOGAN 2004; KHANDELWAL and SINGH, 2009;

KHANDELWAL and RANJITH 2010) have studied the

relations between rock properties and P-wave velocity,

and found that it is closely related with the different

rock properties. There are a number of factors that

influence the P-wave velocity in rocks, such as rock

type, density, grain size and shape, porosity, anisot-

ropy, pore-water, confining pressure and temperature,

weathering and alteration zones, bedding planes, and

joint properties (roughness, filling material, water, dip

and strike, etc.) (KAHRAMAN 2001a).

The quality of some materials is sometimes rela-

ted to their elastic stiffness so that measurement of

P-wave velocity in such materials can often be used

1 Department of Mining Engineering, College of Technology

and Engineering, Maharana Pratap University of Agriculture and

Technology, Udaipur 313 001, India. E-mail: mkhandelwal1

@gmail.com

Pure Appl. Geophys. 170 (2013), 507–514

� 2012 Springer Basel AG

DOI 10.1007/s00024-012-0556-7 Pure and Applied Geophysics

to indicate their quality as well as to determine elastic

properties (KAHRAMAN 2002; SHARMA and SINGH

2008). INOUE and OHOMI (1981) investigated the

relation between uniaxial compressive strength and

P-wave velocity of soft rocks and reported very poor

correlation between them. The relation between

density and P- wave velocity was given by GAVIGLIO

(1989). BOADU (2000) predicted the transport prop-

erties of fractured rocks from seismic waves.

KAHRAMAN (2001a) correlated P-wave velocity with

the number of joints and Schmidt rebound number,

and found a strong influence on P-wave velocity with

the number of joints. KAHRAMAN (2001b) evaluated

uniaxial compressive strength using Schmidt rebound

number, point load index, impact strength index, and

P-wave velocity. He used 48 different rocks to

establish the correlation between their physico-

mechanical properties and found a non-linear relation

between the P-wave velocity and uniaxial compres-

sive strength. OZKAHRAMAN et al. (2004) determined

the thermal conductivity of rocks from the P-wave

velocity. YASAR and ERDOGAN (2004) studied car-

bonate rocks of different origin and established a

linear relation among density, Young’s modulus, and

uniaxial compressive strength with P-wave velocity.

They found a higher error between measured and

estimated values of uniaxial compressive strength and

Young’s modulus than in density. KHANDELWAL and

SINGH (2009) correlated the different physico-

mechanical properties of coal measures rocks of India

with the P-wave velocity and found very good results.

KHANDELWAL and RANJITH (2010) correlated the vari-

ous index properties of various rock types with

P-wave velocity with obtained empirical equations

with very high coefficient of determination.

In this article, an attempt was made to correlate

different physico-mechanical properties of various

rock types with the P-wave velocity.

2. Location and Type of Samples Collected

Rock mass samples were collected from different

locations in India to fulfill the aim of this research.

Thirteen rock types were used, two of which were

igneous, eight were sedimentary, and three were

metamorphic (see Table 1).

3. Laboratory Investigation

Core specimens of different rock types were cored

in NX size by a coring machine, and the ends were

trimmed as required and further smoothened by a

lathe in order to avoid end effects. The specimens

were then prepared in the laboratory as per the ISRM

(1981) standards designed to determine different

physico-mechanical properties. Before testing, the

specimens were dried at 105 �C for 24 h to remove

any moisture.

3.1. Determination of P-wave Velocity

The P-wave velocity of rock was determined

using a Portable Ultrasonic Non-destructive Digital

Indicating Tester (PUNDIT) as per ISRM (1978a)

standards. In this, a mechanical pulse is generated on

prepared specimens by piezo-electric transducers. A

high electric voltage pulse of short duration is

generated by piezo-electric transducer, which con-

verts into mechanical pulse. In this system, the pulses

are transmitted from one end and received at another

end of the specimen. The velocity (V) can be

determined by the time elapsed (t) in traveling the

distance (S) by the wave pulse from the emitter to

receiver end transducer in the rock sample using

Eq. (1).

V ¼ S=tðm=sÞ ð1Þ

Table 1

List of rock types with class and location

Rock type Rock class Location (in India)

Quartzite Igneous Rampur (H.P.)

Granite Igneous Jalore (Raj)

Dolomite Sedimentary Jodhpur (Raj)

Sandstone 1 Sedimentary Jodhpur (Raj)

Sandstone 2 Sedimentary Bijoliyan (Raj)

Sandstone 3 Sedimentary Bundi (Raj)

Limestone 1 Sedimentary Satna (M.P.)

Limestone 2 Sedimentary Amreli (Guj)

Shale Sedimentary Jharia (Jharkhand)

Kota stone Sedimentary Ramganjmandi (Raj)

Marble (white) Metamorphic Makrana (Raj)

Marble (pink) Metamorphic Babarmal (Raj)

Marble (green) Metamorphic Kesariyaji (Raj)

508 M. Khandelwal Pure Appl. Geophys.

Table 2 shows the P-wave values determined for

different rock types from various locations based on

the average value of 3–5 samples.

3.2. Determination of Different Physico-mechanical

Properties

In this investigation, determination of uniaxial

compressive strength (UCS) involves the use of an

NX size (54 mm diameter) cylindrical specimen with

a length to diameter ratio of 2.5, loaded axially

between the loading platens of the Universal Testing

Machine (UTM) as per ISRM (1979a) standard. The

stress value at failure is defined as the compressive

strength of the specimen. A uniform stress rate of

1.0 MPa/s was applied till the rock sample failure.

Compressive strength can be calculated with the help

of the following formula:

UCS ¼ P=A ð2Þ

where P is the failure load, and A is the cross-sec-

tional area of the cylindrical specimen.

Tensile strength (TS) is determined in the labo-

ratory by the Brazilian test. It is an indirect and easy

method for determination of tensile strength. This test

is based on the experimental fact that most rocks in

biaxial stress fields fail in tension at their uniaxial

tensile strength when one principal stress is tensile

and the other finite principal stress is compressive

with a magnitude not exceeding three times that of

the tensile principal stress (JAEGER 1967). Rock

specimens of a 2:1 diameter-to-thickness ratio were

prepared for the Brazilian tests. They were loaded

diametrically between the loading platens of UTM as

per ISRM (1978b) standards. Tensile strength can be

calculated with the help of the following formula:

TS ¼ 2P=p � D� T ð3Þ

where P is the failure load, D, the diameter of the

disc, and T is the thickness of the disc.

In the punch shear test (PST), the shear strength of

a rock specimen is evaluated by punching shear. The

sample is taken in the disc form of thickness ‘T.’ The

test equipment consists of a piston-shaped cylindrical

jig having a projected end. This cylindrical jig fits in

a hollow cylindrical block. The disc-shaped sample is

placed at the bottom of the cylindrical block and the

Tab

le2

Ph

ysic

o-m

ech

an

ica

lp

rope

rtie

so

fd

iffe

ren

tro

ckty

pes

S.

no

.R

ock

type

Vp

(m/s

)U

CS

(MP

a)T

ensi

lest

ren

gth

(MP

a)

Pu

nch

shea

r

stre

ngth

(MP

a)

Den

sity

(kg

/m3)

Sla

ke

du

rab

ilit

y

ind

ex

Yo

un

g’s

mo

du

lus

(GP

a)

Po

isso

n’s

rati

o

ISI

SH

RN

1.

Qu

artz

4,6

57

±1

97

13

3.4

8±

10

.21

8.6

9±

0.7

12

5.4

±1

.57

2,7

40

±7

09

9.8

2±

1.0

29

4.7

±5

.74

0.3

±0

.01

09

3.8

±3

.86

4±

3

2.

Gra

nit

e4

,350

±1

53

12

1.4

5±

7.8

49

±0

.72

20

.63

±2

.06

2,6

70

±1

10

99

.26

±1

.56

87

.2±

8.1

50

.29

±0

.01

39

1.8

±5

.36

2±

4

3.

Do

leri

te3

,283

±1

32

89

.45

±6

.34

6.9

3±

.86

13

.29

±1

.43

2,5

80

±8

09

8.3

±1

.47

58

±7

.59

0.2

6±

0.0

14

90

.8±

5.4

49

±7

4.

San

dst

on

e,B

un

di

2,3

84

±1

59

44

.96

±5

.82

4.9

9±

0.7

49

.44

±1

.28

2,3

60

±8

09

7.1

±1

.68

41

.6±

5.5

30

.24

±0

.02

38

7.3

±4

.93

6±

5

5.

Lim

esto

ne

3,1

08

±1

43

59

.92

±1

0.3

56

.35

±0

.77

12

.79

±1

.03

2,3

70

±1

30

97

.8±

1.0

64

7.5

±4

.79

0.2

4±

0.0

21

88

.9±

4.1

45

±3

6.

Lim

esto

ne

23

,016

±1

78

47

.2±

8.2

05

.2±

0.2

41

1.5

5±

1.6

22

,330

±9

09

7.5

±1

.11

44

.08

±6

.38

0.2

5±

0.0

14

86

.7±

5.8

42

±8

7.

Sh

ale

1,6

82

±1

07

32

.51

±7

.17

4.6

4±

0.3

67

.69

±0

.89

2,0

70

±7

09

6.8

±1

.76

18

.5±

2.7

00

.22

±0

.01

68

4.3

±4

.72

8±

6

8.

Ko

tast

on

e4

,375

±1

77

99

.23

±9

.63

9.2

7±

0.8

82

2.5

7±

2.3

42

,580

±6

09

8.7

±1

.74

81

.34

±8

.69

0.2

9±

0.0

22

92

.4±

3.2

56

±4

9.

Mar

ble

(wh

ite)

3,2

39

±1

19

64

.72

±5

.71

7.5

6±

0.7

91

6.6

1±

1.8

92

,560

±1

20

97

.9±

1.9

56

4.8

7±

7.3

40

.23

±0

.01

88

7.3

±3

.74

3±

8

10

.M

arb

le(p

ink

)2

,844

±1

37

46

.69

±4

.68

5.0

1±

0.4

91

4.6

3±

1.5

32

,410

±9

09

7.6

±1

.22

59

.63

±3

.43

0.2

1±

0.0

17

85

.1±

5.3

40

±7

11

.M

arb

le(g

reen

)2

,370

±1

41

42

.27

±3

.89

4.7

3±

0.6

01

0.2

9±

2.0

72

,280

±1

00

97

.3±

1.6

75

5.5

7±

5.2

30

.21

±0

.01

18

5.2

±2

.13

7±

4

12

.S

andst

on

e,Jo

dh

pu

r2

,146

±9

94

8.3

4±

8.4

04

.4±

0.5

11

1.4

1±

0.9

42

,160

±6

09

6.8

±1

.19

51

.39

±7

.06

0.2

±0

.01

58

6.2

±4

.43

1±

6

Vol. 170, (2013) Correlating P-wave Velocity 509

piston is put over the sample. Then the whole

arrangement is put between the platens of a loading

machine and the load applied. The load ‘P’ to punch

the sample is noted. The punch shear test was carried

out by following the IS: 1121 (Part-IV) (1974) and

ULUSAY et al. (2001) method.

The punching shear strength ‘s’ is calculated with

the following equation:

s ¼ P=A ¼ P=p � D� T ð4Þ

where P is the failure load, A, the circumferential

shear area, T, the thickness of the disc, and D, the

diameter of the puncher.

Density (q) is defined as the mass per volume. In

rocks, it is a function of the densities of the individual

grains, the porosity, and the fluid filling the voids.

There are three types of density in rocks: dry density,

wet density, and grain density. Here, dry densities of

different rock types were determined.

The main purpose of the slake-durability index

(SDI) is to evaluate the water resistance of rock

samples. The slake durability of rocks is closely

related to their mineralogical composition and its

relation with water. This test measures the resistance

of a rock sample to weakening and disintegration

resulting from a standard cycle of drying and wetting.

The test was carried out according to standards

suggested by the International Society for Rock

Mechanics (ISRM 1979b). A sample comprising ten

rock lumps of a particular rock of roughly spherical

in shape, each 50 ± 10 g for a total mass of

500 ± 50 g, had been taken and placed in a perfo-

rated drum to dry until a constant mass was obtained

in an oven at 105 �C for a duration of 4–5 h. For the

slake durability test, the drum was mounted on the

trough and was coupled to the motor. The trough was

then filled with water to a level of 20 mm below the

drum axis and the temperature maintained at 25 �C.

The drum had been rotated at 20 rpm for a period of

10 min, and the drum was removed from the trough,

placed in an oven, and dried out at a temperature of

105 �C for 4 h to drain out the remaining moisture in

the samples. During the test, the finer products of

slaking pass through the mesh and into the water

bath. The slake-durability index (SDI) is the percent-

age ratio of final to initial dry mass of rock in the

drum.

Slake durability index SDIð Þ¼ C � Eð Þ= A� Eð Þ � 100 % ð5Þ

where A is the initial mass of sample and drum; C is

the mass of the sample and drum after the second

cycle of rotation; E is the mass of the empty drum.

Young’s modulus (YM) is an extremely important

characteristic of rock. It is the numerical evaluation

of Hooke’s Law, namely the ratio of stress to strain

(the measure of resistance to elastic deformation). To

calculate, Young’s modulus, stress (at any point)

below the proportional limit is divided by corre-

sponding strain. It can also be calculated as the slope

of the straight line portion of the stress–strain curve.

The Young’s modulus of the rock was determined

with the help of the stress-strain curve obtained by

the UTM as per the ISRM (1979a) standard. Here,

tangent Young’s modulus was determined at a stress

level equal to 50 % of ultimate uniaxial compressive

strength with the help of the stress-strain curve.

The Poisson’s ratio (PR) of the rock under

compression was also determined using strain gauges,

which were pasted in lateral and longitudinal direc-

tions to measure the strain in respective directions.

The impact strength test was first developed by

Protodyakonov, and then it was used by EVANS and

POMEROY (1966) for the classification of coal seams in the

former USSR and in the UK. The test was then modified

by PAONE et al. (1969), TANDANAND and UNGER (1975),

and RABIA and BROOK (1980). TANDANAND and UNGER

(1975) obtained a simple relation between the strength

coefficient and compressive strength. RABIA and BROOK

(1980) used the modified test apparatus to determine the

rock impact hardness number and developed an empir-

ical equation for predicting drilling rates for both DTH

and drifter drills. HOBBS (1964) applied this test to various

rocks and established the following equation:

UCS ¼ 53� ISI� 2; 509ð Þ � 0:0981 ð6Þ

where UCS is the uniaxial compressive strength (MPa)

and ISI is the impact strength index. To carry out the

impact strength test (ISI), fragments of rocks were

impacted 20 times by a 1.81-kg plunger falling from

30 cm height. The number of fines below 0.3175 cm is

used as the strength index. The results of the impact

strength test of different rocks are given in Table 2.

Schmidt hammer tests (SHRN) were performed

on intact rock mass to determine the rebound

510 M. Khandelwal Pure Appl. Geophys.

numbers. Representative rock mass samples were

collected from the site to carry out other tests in the

laboratory. During sample collection, each block was

inspected for macroscopic defects so that it would

provide test specimens free from fractures and joints.

Tests were performed with an N-type hammer having

an impact energy of 2.207 J. All tests were performed

with the hammer held vertically downwards and at

right angles to the horizontal rock faces. To get the

Schmidt hammer rebound number, initially ten

readings were taken, and then the mean of five

higher values were used for the analysis. Schmidt

hammer rebound numbers were determined as per

GOKTAN and AYDAY (1993).

Table 2 shows the values of the P-wave, uniaxial

compressive strength, tensile strength, punch shear

strength, density, slake durability index, Young’s

modulus, Poisson’s ratio, impact strength index, and

Schmidt hammer rebound number.

4. Statistical Analysis of Test Results

The P-wave velocity values of the rocks tested

were correlated with the uniaxial compressive

strength, tensile strength, punch shear strength, den-

sity, slake durability index, Young’s modulus,

Poisson’s ratio, impact strength index, and Schmidt

hammer rebound number using the method of least

squares. The equation of the best-fit line and the

coefficient of determination (R2) were determined for

each regression. In all of the cases, linear relations

were seen between different physico-mechanical

properties and the P-wave velocities of the rocks,

except in Poisson’s ratio, where a higher coefficient

of determination was obtained by polynomial rela-

tion. Good relations were found between P-wave

velocity and different physico-mechanical properties

of the rocks. The results of regression equations and

the coefficients of determination are given in Table 3.

The graphs of the mean values of the test results

between P-wave velocity values and uniaxial com-

pressive strength, tensile strength, punch shear

strength, density, slake durability index, Young’s

modulus, Poisson’s ratio, impact strength index, and

Schmidt hammer rebound number of different rocks

are shown in Figs. 1, 2, 3, 4, 5, 6, 7, 8, and 9.

5. Student’s t test

The significance of R values can be determined by

the t test, assuming that both variables are normally

distributed and the observations are chosen randomly.

The test compares the computed t value with a tab-

ulated t value using the null hypothesis. It is done for

comparing the means of two variables, even if they

Table 3

Regression analysis results

S. no. Parameters

to be related

Regression equation R2

value

1. UCS (in MPa)–Vp

(in m/s)

UCS = 0.033 9 Vp - 34.83 0.871

2. Tensile strength

(in MPa)–Vp

(in m/s)

TS = 0.001 9 Vp ? 0.662 0.882

3. Punch shear strength

(in MPa)–Vp

(in m/s)

PST = 0.005 9 Vp - 2.83 0.904

4. Slake durability

index–Vp

(in m/s)

SDI = 0.001 9 Vp ? 94.84 0.931

5. Density (in kg/m3)

– Vp (in m/s)

q = 0.202 9 Vp ? 1,794.7 0.863

6. Young’s modulus

(in GPa)–Vp

(in m/s)

YM = 0.020 9 Vp - 5.881 0.835

7. Poisson’s ratio–Vp

(in m/s)

PR = 8 9 10-09 9 (Vp)2

– 2 9 10-05 9 (Vp)

? 0.222

0.849

8. Impact strength

index–Vp

(in m/s)

ISI = 0.003 9 Vp ? 78.63 0.843

9. Schmidt hammer

rebound number–

Vp (in m/s)

SHRN = 0.012 9 Vp

? 6.849

0.968

Figure 1Correlation between P-wave velocity and uniaxial compressive

strength

Vol. 170, (2013) Correlating P-wave Velocity 511

have different numbers of replicates. In simple terms,

the t test compares the actual difference between two

means in relation to the variation in the data

(expressed as the standard deviation of the difference

between the means).

The formula for the t test is a ratio in which the

numerator is just the difference between the two

means or averages and the denominator is a measure

of the variability or dispersion of the scores. The

numerator of the formula is easy to compute: just find

Figure 2Correlation between P-wave velocity and tensile strength

Figure 3Correlation between P-wave velocity and punch shear strength

Figure 4Correlation between P-wave velocity and density

Figure 5Correlation between P-wave velocity and slake durability index

Figure 6Correlation between P-wave velocity and Young’s modulus

Figure 7Correlation between P-wave velocity and Poisson’s ratio

512 M. Khandelwal Pure Appl. Geophys.

the difference between the means. The denominator

is called the standard error of the difference. To

compute it, the variance for each group has been

taken and divided by the population number in that

group. These two values are then added, and their

square root is taken. The formula for the t test is

t ¼ _€xT � _€xCffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

VarT

nTþ VarC

nC

� �

r ð7Þ

where _€xT and _€xC are the tabulated and computed

mean, respectively, VarT and VarC are the tabulated

and computed variance, respectively, and n is the

number of samples.

Once the t value is computed, it is then compared

with the tabulated value. If the computed value is larger

than the tabulated one, then it indicates a strong and

significant correlation. To test the significance, one

needs to set a risk level, also called the alpha level. In

most cases, the ‘‘rule of thumb’’ is to set it at 0.05,

i.e., the 95 % confidence interval. Since a 95 % con-

fidence level was chosen in this test, a corresponding

critical t value of 2.18 was obtained. As is seen in

Table 4, the two computed t values remain in the upper

critical region. Therefore, it is concluded that there is a

real correlation between the P-wave velocity and uni-

axial compressive strength, tensile strength, shear

strength, density, Young’s modulus, and Poisson’s

ratio, supporting the engineering use of correlations.

In all the above ten cases, the calculated value of

the t test is much higher than the tabulated value;

hence, they all have significantly strong correlation

among themselves, and this can be used for the pre-

diction of these parameters using P-wave velocity.

6. Conclusions

This study indicates that the uniaxial compressive

strength, tensile strength, punch shear strength, density,

slake durability index, Young’s modulus, Poisson’s

ratio, impact strength index, and Schmidt hammer

rebound number of various rock types can be estimated

from their P-wave velocity values by using simple

empirical equations under the specified limits without

extrapolation. All these properties showed a linear

relationship with the P-wave velocity except Poisson’s

ratio where a higher coefficient of determination was

obtained by the polynomial relation. It can be inferred

Figure 8Correlation between P-wave velocity and impact strength index

Figure 9Correlation between P-wave velocity and Schmidt hammer

rebound number

Table 4

Tabulated results of the t test

Rock tests t test

Calculated

value

Tabulated

value

1. Uniaxial compressive strength and

P-wave velocity

11.3 2.18

2. Tensile strength and P-wave velocity 11.5 2.18

3. Punch shear strength and P-wave

velocity

11.5 2.18

4. Density and P-wave velocity 11.5 2.18

5. Slake durability index and P-wave

velocity

11.2 2.18

6. Young’s modulus and P-wave velocity 11.3 2.18

7. Poisson’s ratio and P-wave velocity 11.5 2.18

8. Impact strength index and P-wave

velocity

11.2 2.18

9. Schmidt hammer rebound number and

P-wave velocity

11.3 2.18

Vol. 170, (2013) Correlating P-wave Velocity 513

that P-wave velocity shows a good statistical relation-

ship in the range of 1,682–4,657 m/s with the different

physico-mechanical properties of rocks. This implies

that rocks having the above range of P-wave velocities

could be ideal sources for the determination of the

index properties of those mentioned above.

A strong coefficient of determination was found

between P-wave velocity and different physico-

mechanical properties of the tested rocks. This was also

verified by Student’s t test, which showed higher cal-

culated values for each relation rather than tabulated

values. These equations are practical, simple, and

accurate enough to apply for the use in general practice

to obtain important static physico-mechanical proper-

ties of the different rocks for the design and planning of

excavation with greater safety and stability.

The P-wave velocity measurements cannot com-

pletely replace the mechanical testing of rock

specimens in demanding applications. For delineating

the volume of rock mass where one can interpolate or

extrapolate the measured rock properties, using the

laboratory and field measurements of P-wave veloc-

ities is a fast and cost effective tool.

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(Received November 15, 2010, revised July 9, 2012, accepted July 10, 2012, Published online July 29, 2012)

514 M. Khandelwal Pure Appl. Geophys.