Arab J Geosci DOI 10.1007/s12517-013-1235-4

ORIGINAL PAPER

Empirical correlation of physical and mechanical properties of marly rocks with P wave velocity Abdolazim Azimian & Rassoul Ajalloeian

Received: 25 May 2013 / Accepted: 11 December 2013 # Saudi Society for Geosciences 2014

Abstract The geomechanical strength of rock mass plays a key role in planning and design of mining and civil construction projects. The main aim of this study was to develop empirical relations between P wave velocity and physical and mechanical properties such as slake durability index (SDI), uniaxial compressive strength (UCS), modulus of elasticity (E), porosity, water absorption, and density for marly rocks extracted from the southwest Iran. Determination of geomechanical properties in the field as well as laboratory is a time consuming, tedious, and costly process. In this study, an attempt was made to determine these index properties in the laboratory and then each index property was correlated with P wave velocity values. Empirical equations were developed using P wave velocity values to predict SDI, UCS, modulus of elasticity (E), porosity, water absorption, and density where the results were in good agreement. To examine the sensitivity of empirical relationships, Student’s t test was performed to verify the correlation between P wave velocity values and other rock index properties. Keywords Empirical relations . Marly rocks . P wave velocity . Empirical equations . t test

Introduction Elastic properties of rocks play a major and crucial role for the design of any engineering structure (Khandelwal and Singh 2011). Studying the mechanical characteristics of weak A. Azimian (*) Department of Environmental Engineering, Science and Research Branch, Islamic Azad University, Bushehr, Iran e-mail: [email protected] A. Azimian e-mail: [email protected] R. Ajalloeian Department of Geology, Faculty of Science, The University of Isfahan, Isfahan, Iran

sedimentary rocks such as marl is a burning issue in civil and mining engineering designs and analysis since obtaining rock mechanical properties of these rocks has always faced lots of problems and uncertainties due to the structural weaknesses (Minaeian and Ahangari 2011; Ozcelik et al. 2012; Mikaeil et al. 2013; Azadan and Ahangari 2013). Marls are among the geomaterials (soil or rock) which are generally composed of clay minerals and carbonate with different proportions, normally between 35 and 65 % (Pettijohn 1975). One of the main problems reported for marls is their high deformation and settlement since they have some clay contents. Despite the efficient design of the structure and foundation, many buildings and structures constructed on these types of materials are damaged in various countries, since their strength and deformation values are difficult to be precisely determined (Johnes and Holtz 1973; Akili and Torrance 1981; Ruwaih 1987; Chen 1988; Trenter 1989; Sanad and Bader 1990; Mohamed et al. 1991; Nelson and Miller 1992; Yong et al. 1996; Alber and Heiland 2001; Vishal et al. 2011). Therefore, measuring the engineering properties of these materials is necessary for safe design and construction of engineering structures such as dam, tunnel, and building. The aim of this study is to apply correlation analysis to investigate the relationships between P wave velocities and physical and mechanical properties of marly rocks. Seismic techniques are increasingly used in various fields such as mining, geotechnical, civil, and underground engineering (Kahraman and Yeken 2008; Singh et al. 2012a; b). These techniques are applied in the field of geophysical researches and in the laboratory for the determination of the dynamic properties of rocks. Since ultrasonic techniques are nondestructive and easy to apply, for both site and laboratory conditions, they are increasingly being applied in geotechnical applications (Fener 2011). The P wave velocity of a rock is closely related to the intact rock properties and measuring the velocity in rock media interrogates the rock structure and texture (Khandelwal and Ranjith 2010). The factors influencing P wave velocity in

Arab J Geosci Table 1 Some empirical relationships between physical and mechanical properties and P wave velocity from previous studies

Rock properties

Empirical relation

Coefficient of determination (R2)

Researchers

Density (gr/cm3)

VP=2.76ρ−0.98 VP=2.33+0.08 ρ3.63

– –

VP=3.66ρ−4.46 VP=2.61ρ−1.0±0.4 VP=5.00ρ−8.65 VP=4.32ρ−7.51 ρ=0.213VP+1.256 ρ=0.0011VP−0.0847 ρ=0.19+1.61 ρ=0.0027VP+12.02 ρ=0.0002VP+1.7752

– – 0.55 0.81 0.82 0.97 0.58 0.83 0.87

Birch (1961) Christensen and Salisbury (1975) Gaviglio (1989) Henkel et al. (1990) Starzec (1999) Yasar and Erdogan (2004) Kahraman and Yeken (2008) Khandelwal and Singh (2009) Yagiz (2011b) Diamantis et al. (2011) Kurtulus et al. (2011)

ρ=0.0001VP+1.7937 ρ=0.00028VP+1.59 ρ=0.202VP+1.794 ρ=0.0002VP+1.94 VP=6.32n−0.016 VP=6.52−0.36n VP=4.08n−0.42 n=−4.733VP+29.377 n=−0.0002VP+1.70 n=−0.0031VP+16.736

0.83 0.93 0.86 0.89 0.76 0.66 0.79 0.88 0.84 0.87

Sarkar et al. (2011) Khandelwal (2013) Current study Al-Harthi et al. (1999) Turgrul and Zarif (1999) Sousa et al. (2005) Kahraman and Yeken (2008) Diamantis et al. (2011) Kurtulus et al. (2011)

n=−0.0029VP+16.373 n=−5.19VP+27.1 n=−0.008VP+39.55 Wa=−2.248VP+13.76 Wa=−2.23VP+11.6 Wa=−0.0049VP+20.39 Id=0.0069VP+78.577 Id4 =1.131VP+93.26 Id2 =0.71VP+95.7 Id=0.0014VP+92.970 Id=0.001VP+94.84 Id1 =0.002VP+87.60

0.83 0.86 0.84 0.90 0.85 0.83 0.78 0.73 0.69 0.90 0.93 0.91

Yagiz (2011b) Current study Kahraman and Yeken (2008) Yagiz (Yagiz 2011a; b) Current study Sharma &Singh (2008) Yagiz (2011a) Yagiz (2011; b) Sarkar et al. (2011) Khandelwal (2013) Current study

Id2 =0.0021VP+82.80 E=19.87VP−27813 E=4.9718VP−7151 E=0.0015VP−2.516 E=0.041VP−264.15 E=20.1VP−53 E=0.919VP1.9122 E=0.008VP−5.619 UCS=35.0VP−31.5 UCS=2.45VP1.92 logUCS=0.358VP−0.283

0.90 0.84 0.97 0.74 0.81 0.95 0.79 0.89 – – –

UCS ¼ 1277e−117=Vp UCS=36.0VP−31.2 UCS=35.54VP−55

– – 0.64

Porosity (%)

Water absorption (%)

Slake durability index (%)

Modulus of elasticity (GPa)

Uniaxial compressive strength (Mpa)

Vasconcelos et al. (2007) Khandelwal and Singh (2009) Kurtulus et al. (2011) Diamantis et al. (2011) Yagiz (Yagiz 2011a; b) Altindag (2012) Current study Freyburg (1972) Militzer and Stoll (1973) Golubev and Rabinovich (1976) McNally (1987) Goktan (1988) Tugrul & Zarif (1999)

Arab J Geosci Table 1 (continued) Rock properties

Empirical relation

Coefficient of determination (R2)

Researchers

Uniaxial compressive strength (Mpa)

UCS=9.95VP1.21 UCS=31.5VP−63.7 UCS=22.032VP1.247 UCS=2.304VP2.4315 UCS=64.2VP−117.99 UCS=56.71VP−192.93 UCS=110VP−515.56 UCS=133.3VP−227.19

0.69 0.80 0.72 0.94 0.90 0.67 0.81 0.96

Kahraman (2001) Yasar and Erdogan (2004) Sousa et al. (2005) Kılıç and Teymen (2008) Sharma &Singh (2008) Cobanoglu and Celik (2008) Diamatis et al. (2009) Khandelwal and Singh (2009)

UCS=36VP−45.37 UCS=0.14VP−899.33 UCS=0.0675VP−245.13

0.93 0.83 0.92

Sharma and Singh (2010) Diamantis et al. (2011) Kurtulus et al. (2011)

UCS=0.0188VP−71.054 UCS=49.4VP−167

0.83 0.89

Yagiz (2011b)

UCS=12.746VP3.543 UCS=0.038VP−50 UCS=0.258VP1.194 UCS=0.033VP−34.83 UCS=0.026VP−20.47

0.92 0.93 0.79 0.87 0.91

Sarkar et al. (2011) Altindag (2012) Khandelwal (2013) Current study

rocks include mineral compositions and textures, density, porosity, pore water, confining pressure, temperature, weathering and alteration, bedding planes, joint properties (roughness, filling material, water, attitude, etc.), and anisotropy (Sharma and Singh 2008). A number of researchers have attempted to evaluate grouting, rock bolt reinforcement, and blasting efficiencies in the rocks by the seismic velocity (Young et al. 1985). The prediction of stress, rock mass deformation, and extent of damage zones (EDZ) developed around underground openings is one of the applications of the seismic techniques (Hudson et al. 1980). Many researchers have found that sound velocity is strongly correlated with different physical and mechanical properties of rocks (Deere and Miller 1966; Saito et al. 1974; Gardner et al. 1974; Lama et al. 1978; Inoue and Ohomi 1981; Gaviglio 1989; Kahraman 2001; Yasar and Erdogan 2004; Sharma and Singh 2008; Kahraman and Yeken 2008; Kahraman et al. 2009; Khandelwal and Ranjith 2010; Yagiz 2011a, b; Sarkar et al. 2011; Sharma et al. 2011 and Martínez-Martínez et al. 2012; Altindag 2012). Some of the empirical relationships between P wave velocity and physical and mechanical properties for different rock types found in the literature are summarized in Table 1. Many attempts have been made to correlate the wave velocity with the rock characteristics, but only few studies have been concentrated on marly rocks. In this work, the studied marly rocks were subject to detailed petrographic investigations. Mineralogy of the analyzed samples was carried out using the X-ray diffraction (XRD) method. Based on the obtained XRD results, the marl samples were mainly composed of clay minerals (illite, chlorite), quartz, plagioclase, and carbonate minerals (calcite and

dolomite). The studied rock samples were collected from the Southwestern part of Iran. Linear regression analysis was performed to determine statistic relationship among the P wave velocities and the other properties. Besides, the determination coefficients (R2) and the fitted line equations were obtained for the studied parameters.

Sample preparation and test procedures In this work, 40 samples of big rock blocks were extracted from southwest part of Shiraz, Iran. In order to reduce the uncertainty, regarding the influence of the sample size on the measured properties and especially on strength (Hoek and Brown 1980; Hawkins 1998), cylindrical specimens with length between 110 and 115 mm and a diameter of 54 mm (ASTM 2001, 2010; ISRM 2007) were prepared. The two ends of the specimens were ground and lapped parallel to accomplish an accuracy of ±0.2 mm and both end surfaces were polished. The cylindrical sides were made straight with an accuracy of ±0.3 mm over the full length of each specimen. The physical properties of the specimens such as porosity, water absorption and density were determined in accordance with ISRM (2007). The porosity of rock specimens was determined using saturation and buoyancy techniques. All samples were saturated by water immersion for a period of 48 h with periodic agitation to remove trapped air. Next, the samples were submerged basket into an immersion bath and their saturated submerged weights were measured with a scale having accuracy of 0.01 g. Then, the surface of the specimens

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was dried with a moist cloth and their saturated-surface-dry weights were measured outside the water. Bulk sample volumes were found from weight differences between saturated-surface-dry weight and saturated-submerged weight. The dry mass of specimens was determined after oven drying at a temperature of 105 °C for a period of at least 24 h. The porosity volumes were determined from weight difference between saturatedsurface-dry weight and dry sample weight. The density values were obtained from the ratio of the specimen mass to the specimen volume. The uniaxial compressive strength of the marly rock was determined using a uniaxial compression testing machine in accordance with ASTM (1986) standards, on the prepared core samples, while the deformation was determined by the respective strain gauges. The modulus of elasticity was derived from the slope of the stress–strain curves by tangent method. The main purpose of ‘slake durability test’ is to evaluate the water resistance of rock samples. The slake durability of rocks is closely related to their mineralogical composition and its relation to water. This test measures the resistance of a rock sample to weakening and disintegration resulting from a standard cycle of drying and wetting. Test was carried out according to the standards suggested by International Society for Rock Mechanics (ISRM 1979). A sample, comprising ten rock lumps of a particular marly rock roughly spherical in shape, each weighing 50 ± 10 g for a total weight of 500± 50 g, had been taken and placed in a perforated drum to dry until a constant weight was obtained in an oven at 105 °C for 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 to maintain the temperature at 20 °C. The drum had been rotated at 20 rpm for a period of 10 min and the drum was removed from the trough and placed in an oven and dried out at a temperature of 105 °C for 4 h to drain out there 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 percentage ratio of final to initial dry weights of rock in the drum (Singh et al. 2004). Slake Durability Index ðIdÞ ¼ ðC − E Þ=ðA − EÞ  100 where the initial weight of sample+drum (kilogram) C: eight of sample +drum after second cycle of rotation (kilogram); and E: weight of empty drum. The velocity of ultrasonic pulses traveling in a solid material is controlled by its density and elastic properties. Besides,

the quality of some materials may vary with their elastic stiffness; as such measurement of ultrasonic pulse velocity can be used to indicate their quality as well as the determination of their elastic properties. The PUNDIT 6 Pulse Generator Unit controls and two transducer (with diameter of 50 mm) having a frequency of

Table 2 Physical properties of marly rocks Sample no.

Density (gr/cm3)

Water absorption (%)

Porosity (%)

M-1 M-2 M-3 M-4 M-5 M-6

2.23 2.25 2.50 2.54 2.46 2.22

11.7 12.8 6.3 4.2 7.8 10.9

24.1 25.3 10.3 10.2 15.8 25.8

M-7 M-8 M-9 M-10 M-11 M-12 M-13 M-14 M-15 M-16 M-17 M-18 M-19 M-20 M-21 M-22 M-23 M-24 M-25

2.51 2.41 2.38 2.46 2.36 2.50 2.54 2.39 2.45 2.50 2.36 2.53 2.45 2.48 2.41 2.40 2.51 2.48 2.62

4.7 6.9 5.3 6.8 7.9 5.9 4.2 8.0 6.2 5.1 5.9 4.7 6.6 5.4 6.2 7.5 4.9 4.5 2.4

11. 3 15.5 15.3 14.2 17.3 14.0 10.3 17.7 13.9 11.7 13.1 9.2 15.2 12.7 15.1 16.9 11.6 7.5 6.3

M-26 M-27 M-28 M-29 M-30 M-31 M-32 M-33 M-34 M-35 M-36 M-37 M-38 M-39 M-40

2.39 2.28 2.28 2.24 2.33 2.35 2.20 2.57 2.09 2.15 2.34 2.24 2.27 2.47 2.18

8.5 11.3 12.6 13.5 6.2 6.0 16.9 2.2 15.8 14.5 8.3 11.3 10.6 5.8 14.4

18.7 23.2 25.4 27.6 17.0 13.8 27.4 9.6 33.7 32.5 17.3 20.6 21.3 14.2 26.3

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the measurements, the tests were conducted for several times on each sample. In this regard, the average of two ultrasonic pulse velocity (UPV) obtained from two instruments was used for the analyses. Each specimen was inspected for macroscopic defects as such it would provide isotropic, homogeneous, and unweathered (or

0.5 MHz were used in this study. The frequency of 0.5 MHz corresponds to a 0.3 mm wave length. To establish a good coupling, the ends of the core specimens were polished and covered with stiffer grease measurements were applied along the axis of the core samples using two instruments. To ensure accuracy of Table 3 P wave velocities and mechanical properties

Sample no.

Slake durability index (SDI) Id1 (%)

Slake durability index (SDI) Id2 (%)

Modulus of elasticity (GPa)

Uniaxial compressive strength (MPa)

Compression wave velocity, VP (m/s)

M-1 M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M-10 M-11 M-12 M-13 M-14

91.7 92.3 94.9 95.2 93.3 92.3 94.6 93.7 93.3 93.2 92.5 94.5 94.7 93.2

87.0 86.4 90.3 90.6 88.4 87.4 90.3 89.7 87.8 88.3 87.8 90.7 90.8 88.9

6.3 7.2 17.5 23.4 14.4 7.2 19.8 17.3 15.3 15.3 12.7 21.4 20.4 16.8

26.0 29.7 59.6 75.4 56.2 28.0 56.3 56.7 45.3 40.7 47.5 63.7 69.5 33.1

1,960.8 2,054.1 3,335.7 3,761.3 2,601.5 1,990.3 3,241.4 2,828.4 2,630.0 2,601.6 2,369.9 3,095.2 3,283.8 2,565.1

M-15 M-16 M-17 M-18 M-19 M-20 M-21 M-22 M-23 M-24 M-25 M-26 M-27 M-28 M-29 M-30 M-31 M-32

94.5 94.9 92.2 92.9 94.7 93.2 93.7 93.3 95.3 94.8 95.5 92.7 91.7 91.3 91.1 93.3 93.4 89.7

89.7 90.5 88.2 89.4 89.8 89.4 89.2 88.9 90.3 89.3 91.7 88.5 86.8 86.7 86.8 87.5 88.8 85.6

21.4 30.7 16.3 19.2 19.8 15.8 18.9 13.2 27.2 25.3 30.1 12.3 11.9 9.2 10.5 12.5 12.6 8.5

72.5 88.9 51.4 62.1 65.2 52.9 48.6 43.0 71.1 64.6 83.4 54.1 35.1 21.4 17.7 36.7 51.8 22.7

3,319.6 3,959.2 2,514.5 3,115.9 3,169.6 2,665.4 2,882.2 2,687.6 3,636.4 3,149.2 3,839.2 2,417.7 1,844.0 1,787.0 1,826.8 2,492.4 2,568.9 1,666.7

M-33 M-34 M-35 M-36 M-37 M-38 M-39 M-40

95.5 90.2 90.6 93.5 91.7 91.8 93.8 90.3

90.8 85.4 85.7 89.6 87.5 87.3 89.3 85.4

24.5 5.6 7.2 18.8 13.2 8.9 19.5 7.8

71.8 15.3 16.8 50.3 27.3 28.3 53.3 19.8

3,679.0 1,145.7 1,203.6 2,567.9 2,056.8 2,065.4 2,890.4 1,376.4

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slightly weathered) specimens free from fractures, partings, or alteration zones.

Physical and mechanical properties Physical properties of marly rocks were determined by a variety of laboratory tests (ISRM 2007) where their mean values are listed in Table 2. Density, water absorption and porosity varied between 2.09 and 2.62 gr/ cm3, 2.23 and 19.92 %, and 6.3 and 27.49 %, respectively. The P wave velocities (Vp) were determined from the measured travel time and the distance between transmitter and receiver in accordance with ASTM test designations (1983). The results are given in Table 3. The compressional wave velocity (Vp) values were between 1,145.67 and 3,959.18 m/s, while their mean value was 2,621.16 m/s. The mechanical properties such as SDI, UCS, and E were obtained from laboratory tests (Table 3). The slake durability tests were conducted according to ISRM (1979). The slake durability index (Id1 and Id2) values fluctuate from 89.77 to 95.56 % and 84.44 to 90.89 %, respectively. The UCS values were in the range of 15.34 to 88.9 MPa, exhibiting a

great fluctuation of UCS which can be attributed to the weathering degree, moisture content, and calcium carbonate content of the samples. The modulus of elasticity varies between 5.67 and 30.78 GPa, with a mean value of 15.94.

Correlation analysis Simple regression analyses were performed to develop relationships between dependent and independent parameters by considering linear functions. Regression analysis was applied in order to describe the relationships among the P wave velocities and physical–mechanical properties.

Correlation between P wave velocity and physical properties Many researchers (D’Andrea et al. 1965; Irfan and Dearman 1978; Lama et al. 1978; Koumantakis 1982; Gaviglio 1989; Koukis et al. 1998; Escartin et al. 2001; Sabatakakis et al. 2002; Yasar and Erdogan 2004; Christensen 2004; Sharma

Fig. 1 P wave velocity versus physical properties. Density (a), porosity (b), water absorption (c)

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and Singh 2008; Diamantis et al. 2009; Kurtulus et al. 2011; Yagiz 2011a, b; Sharma et al. 2011 and MartínezMartínez et al. 2012; Altindag 2012) have studied the relationship between wave velocities and physical characteristics of rocks and have concluded that these rock parameters are closely related with wave velocities. Wave velocities increase, with an increase in the density (decrease of porosity, and water absorption). All physical rock properties adopted in this study were strongly correlated with P wave velocity (Fig. 1). The relations follow a linear function. The regression equations are given as follows:

Relationships between P wave velocity and mechanical properties It is known that the mechanical properties increase with an increase in wave velocities. In order to describe the relationships between P wave velocities and slake durability index (SDI), uniaxial compressive strength (UCS), and modulus of elasticity (E) of the tested rocks, regression analysis was performed. The equation of the best-fit line and the coefficient of determination (R2) was determined for each test result. The plots of the P wave velocity as a function of SDI (Id1 and Id2) are shown in Fig. 2. There is a linear relation between P wave velocity and slake durability index. Moreover, a strong coefficient of determination was found between P wave velocity and the Id1 and Id2. The equation obtained for this relation is as follows:

ρ ¼ 0:0002VP þ 1:94 0:89

ð1Þ

n ¼ − 0:008VP þ 39:55 0:84

ð2Þ

Id1 ¼ 0:002VP þ 87:60 0:91

ð4Þ

W a ¼ − 0:0049VP þ 20:39 0:83

ð3Þ

Id2 ¼ 0:0021VP þ 82:80 0:90

ð5Þ

where, VP=P wave velocity (meter per second); ρ=density (gram per cubic centimeter); n= porosity (percent); and Wa=weight percentage water absorption (percent).

where, Id is the slake durability index (percent). Similarly, linear relationship was also observed between P wave velocity and modulus of elasticity (Fig. 2).

Fig. 2 P wave velocity versus mechanical properties. Slake durability index (SDI) Id1 (a), slake durability index (SDI) Id2 (b), modulus of elasticity (c), uniaxial compressive strength (d)

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Statistical analysis of the t test

The equation of this relation is as follows: E ¼ 0:008V p −5:619 0:89

ð6Þ

where E is the modulus of elasticity (gigapascal). The relation between P wave velocity and uniaxial compressive strength also shows a linear curve (Fig. 2). A significantly higher coefficient of determination was obtained between uniaxial compressive strength and P wave velocity for all samples. The equation of relation is given as: UCS ¼ 0:026VP −20:47 0:91

ð7Þ

where UCS is the uniaxial compressive strength (megapascal). The empirical methods used in this study were evaluated by comparing their obtained results. Data from each test were used in the respective empirical equation to calculate the other properties. The predicted values of SDI, UCS, E, n, Wa, and ρ were then plotted against the measured values for all tested rocks using a 1:1 slope line (Figs. 3 and 4). A point locating on the 1:1 slope line indicates an exact correlation. The figures indicate that P wave velocity is a reliable method for estimating SDI, UCS, E, n, Wa, and ρ avoiding other cumbersome and time consuming test procedures.

The relationship between P wave velocity values with other tests including SDI, UCS, E, n, Wa, and ρ of the tested rock samples, was determined using the Student’s t test. 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 by finding the difference between the means. The denominator is called the standard error of the difference which is computed by calculating the variance for each group and dividing it by the number of people in that group. These two values are then added and their square root is taken. The final formula for the t test is as follows: …

…

XT − XC t ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi VarT VarC þ nT nC The t value is positive if the first mean is greater than the second and negative if it is lower. Once the t

Fig. 3 Observed versus predicted of physical properties obtained from P wave velocity. Density (a), porosity (b), water absorption (c)

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Fig. 4 The values observed versus predicted of mechanical properties obtained from P wave velocity. Slake durability index (SDI) Id1 (a), slake durability index (SDI) Id2 (b), modulus of elasticity (c), uniaxial compressive strength

value is computed, it is then compared with the tabulated value. If the computed value is greater than the tabulated one, then it indicates strong and significant correlation. To test the significance, one needs to set a risk level (called the alpha level). In most cases, the “rule of thumb” is to set the alpha level at 0.05, i.e., 95 % confidence interval. Table 4 shows the calculated and tabulated values of t test. In all seven cases, calculated value is much higher than the tabulated value; hence, they all have significantly strong correlation among themselves and this may be used for the prediction of these parameters using P wave velocity for other rock types also.

Conclusions Density, porosity, weight percentage water absorption, slake durability index, modulus of elasticity, UCS, and P wave velocity tests were carried out on 40 marl samples to compare P wave velocity values and the physical and mechanical properties of the rocks. The results indicated significant correlations between ρ, n, Wa, SDI, E, and UCS with P wave velocity and the following empirical equations have been developed.

ρ ¼ 0:0002 VP þ 1:94 n ¼ − 0:008 VP þ 39:55 W a ¼ − 0:0049VP þ 20:39 Id1 ¼ 0:002 VP þ 87:60 Id2 ¼ 0:0021 VP þ 82:80 E ¼ 0:008 VP − 5:619 UCS ¼ 0:026 VP −20:47

0:89 0:84 0:83 0:91 0:90 0:89 0:91

The test results were interpreted statistically and significant linear relationships. These equations are practical, simple, and Table 4 Student’s t test Rock test

P wave velocity and density P wave velocity and porosity P wave velocity and water absorption P wave velocity and SDI (Id1) P wave velocity and SDI (Id2) P wave velocity and modulus of elasticity P wave velocity and UCS

t test Calculated value

Tabulated value

22.96 22.83 22.91 22.16 22.20 22.84

2.02 2.02 2.02 2.02 2.02 2.02

22.55

2.02

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accurate enough for general applications for obtaining important index properties of the marly rocks. A strong coefficient of determination was found between P wave velocity with slake durability index (SDI), uniaxial compressive strength (UCS), modulus of elasticity (E), porosity, water absorption, and density of the tested rocks. The results were also verified by Student’s t test, which showed higher calculated values for each relationship, rather than tabulated values. Hence, the proposed correlation equations can be used for the determination of SDI, UCS, E, n, W%, and ρ by P wave velocity. Furthermore, this study showed that the physical and mechanical properties of marly rocks can be predicted using ultrasonic testing at least for preliminary investigations. Further research is necessary to check the validity of the derived equations for the other marly rocks. In addition, the effect of petrography and bedding planes on the developed correlations must be investigated. However, these equations can help researchers have a good estimation of physical and mechanical properties of marl.

References Akili W, Torrance JK (1981) The development and geotechnical problems of sabkha, with preliminary experiments on the static penetration resistance of cemented sands. Q J Eng Geol 14(2):59–73 Alber M, Heiland J (2001) Investigation of a limestone pillar failure: part 1; geology, laboratory testing and numerical modeling. Rock Mech Rock Eng 34(3):167–186 Al-Harthi AA, AI-Amri RM, Shehata WM (1999) The porosity and engineering properties of vesicular basalt in Saudi Arabia. Eng Geol 54:313–320 Altindag R (2012) Correlation between P-wave velocity and some mechanical properties for sedimentary rocks. J South Afr Inst Min Metall 112:229–237 ASTM (1983) Test methods for ultra violet velocities determination. D2845 ASTM (1986) Standard test method of unconfined compressive strength of intact rock core specimens. D2938 ASTM (2001) Standard practice for preparing rock core specimens and determining dimensional and shape tolerances. American Society for Testing and Materials. D4543 ASTM (2010) Standard test method for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. ASTM D7012–10 Azadan P, Ahangari K (2013) Evaluation of the new dynamic needle penetrometer in estimating uniaxial compressive strength of weak rocks. Arab J Geosci. doi:10.1007/s12517-013-0921-6 Birch F (1961) The velocity of compressional waves in rocks to 10 kilobars (part II). J Geophys Res 66:2199–2224 Chen FH (1988) Foundations on expansive soils. Developments in soils geotechnical engineering. Elsevier, New York Christensen NI (2004) Serpentinites, peridotites and seismology. Int Geol Rev 46:795–816 Christensen NJ, Salisbury UH (1975) Structure and constitution of the lower oceanic crust. Rev Geophys Space Phys 13:57086 Cobanoglu I, Celik SB (2008) Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bull Eng Geol Environ 67:491–498

D’Andrea DV, Fischer RL, Fogelson DE (1965) Prediction of compressive strength from other rock properties. US B M Report of Investigations 6702 Deere DU, Miller RP (1966) Engineering classification and index properties for intact rock. Air Force Weapons Lab. Technical Report, AFWL-TR 65–116, Kirtland Base, New Mexico Diamantis K, Gartzos E, Migiros G (2009) Study on uniaxial compressive strength point load strength index, dynamic and physical properties of serpentinites from Central Greece: test results and empirical relations. Eng Geol 108:199–207 Diamantis K, Bellas S, Migiros G, Gartzos E (2011) Correlating wave velocities with physical, mechanical properties and petrographic characteristics of peridotites from the Central Greece. Geotech Geol Eng 29(6):1049–1062 Escartin J, Hirth G, Evans B (2001) Strength of slightly serpentinized peridotites: implications for the tectonics of oceanic lithosphere. Geol Soc Am 29(11):1023–1026 Fener M (2011) The effect of rock sample dimension on the P-wave velocity. J Nondestruct Eval 30:99–105. doi:10.1007/s10921011-0095-7 Freyburg E (1972) Der untere trod mittlere Buntsandstein SW-Thuringen in seinen gesteinstechnischen Eigenschatten. Ber Dtsch Ges Geol Wiss 17:911–919 Gardner GHF, Gardner LW, Gregory AR (1974) Formation velocity and density—the diagnostic basis for stratigraphic traps. Geophysics 39: 770–780 Gaviglio P (1989) Longitudinal wave propagation in a limestone: the relationship between velocity and density. Rock Mech Rock Eng 22: 299–306 Goktan RM (1988) Theoretical and practical analysis of rock rippability. Ph.D. thesis, Istanbul Technical University Golubev A, Rabinovich GJ (1976) Resultaty primenenia apparatury akusticeskogo karotasa dlja predelenia procnostych svoistv gornych porod na mestorosdeniach tverdych iskopaemych. Prikl Geofiz Moskva 73:109–116 Hawkins AB (1998) Aspects of rock strength. Bull Eng Geol Environ 57:17–30 Henkel H, Lee MK, Lund CE (1990) An integrated geophysical interpretation of the 200 km FENNOLORA section of the Baltic Shield. In: Freeman R, Giese P, Mueller S (eds) The European Geotraverse: integrative studies. European Science Foundation, Strasbourg, pp 1–47 Hoek E, Brown ET (1980) Underground excavations in rock. Inst Min Metal, London Hudson JA, Jones EJW, New BM (1980) P-wave velocity measurements in a machine bored chalk tunnel. Q J Eng Geol 13:33–43 Inoue M, Ohomi M (1981) Relation between uniaxial compressive strength and elastic wave velocity of soft rock. In: Proceedings of the international symposium on weak rock, Tokyo, 9–13 Irfan TY, Dearman WR (1978) The engineering petrography of a weathered granite in Cornwall, England. Q J Eng Geol 11:233–244 ISRM (1979) Suggested method for determining water content, porosity, density, absorption and related properties and swelling and slake durability index properties. Int J Rock Mech Min Sci 16:141–156 ISRM (2007) In: Ulusay and Hudson (eds) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. Suggested methods prepared by the commission on testing methods, International Society for Rock Mechanics Johnes DE, Holtz WG (1973) Expansive soils: the hidden disaster. ASCE Civil Eng 43(8):49 Kahraman S (2001) Evaluation of simple methods for assessing the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 38:981–994 Kahraman S, Yeken T (2008) Determination of physical properties of carbonate rocks from P-wave velocity. Bull Eng Geol Environ 67: 277–281

Arab J Geosci Kahraman S, Gunaydin O, Fener M (2009) Predicting the uniaxial compressive strength of pyroclastic rocks from the P-wave velocity. In: Sixth International Symposium on Geophysics, Tanta, Egypt, 11–12 November, 27p Khandelwal M (2013) Correlating P-wave velocity with the physicomechanical properties of different rocks. Pure Appl Geophys 170: 507–514. doi:10.1007/s00024-012-0556-7 Khandelwal M, Ranjith PG (2010) Correlating index properties of rocks with P-wave measurements. J Appl Geophys 71:1–5 Khandelwal M, Singh TN (2009) Correlating static properties of coal measures rocks with p-wave velocity. Int J Coal Geol 79:55–60 Khandelwal M, Singh TN (2011) Predicting elastic properties of schistose rocks from unconfined strength using intelligent approach. Arab J Geosci 4(3–4):435–442. doi:10.1007/s12517-009-0093-6 Kılıç A, Teymen A (2008) Determination of mechanical properties of rocks using simple methods. Bull Eng Geol Environ 67:237–244. doi:10.1007/s10064-008-0128-3 Koukis G, Sabatakakis N, Tsiambaos G (1998) Geotechnical properties of Greek limestones. Proceedings of the 8th IAEG congress. Vancouver, Balkema, pp 2883–2888 Koumantakis J (1982) Comportement des peridotitesetserpentinites de la Grece en travaux public. Leurpropretes physiques etmechaniques. Bull Eng Geol Environ 25:53–60 Kurtulus C, Bozkurt A, Endes H (2011) Physical and Mechanical Properties of Serpentinized Ultrabasic Rocks in NW Turkey. Pure Appl Geophys. doi:10.1007/s00024-011-0394-z Lama RD, Vutukuri VS, Saluja SS (1978) Handbook on mechanical properties of rocks, 2nd edn. Trans Tech Publications, Germany Martínez-Martínez J, Benavente D, García-del-Cura MA (2012) Comparison of the static and dynamic elastic modulus in carbonate rocks. Bull Eng Geol Environ 71:263–268 McNally GH (1987) Estimation of coal measures rock strength using sonic and neutron logs. Geoexploration 24:381–395 Mikaeil R, Ataei M, Yousefi R (2013) Correlation of production rate of ornamental stone with rock brittleness indexes. Arab J Geosci 6(1): 115–121. doi:10.1007/s12517-011-0311-x Militzer H, Stoll R (1973) Einige Beitraige der Geophysik zur primadatenerfassung im Bergbau. Neue Bergbautechnik 3:21–25 Minaeian B, Ahangari K (2011) Estimation of uniaxial compressive strength based on P-wave and Schmidt hammer rebound using statistical method. Arab J Geosci (6):1925–1931. doi: 10.1007/ s12517-011-0460-y Mohamed AMO, Yong RN, Mohammed LF (1991) Soil improvement using chemical treatment. In: Proceedings of the first geotechnical engineering conference, Cairo University, Egypt, pp 1–10 Nelson JD, Miller DJ (1992) Expansive soils problems and practice in foundation and pavement engineering. Wiley, New York Ozcelik Y, Bayram F, Yasitli NE (2012) Prediction of engineering properties of rocks from microscopic data. Arab J Geosci. doi:10.1007/ s12517-012-0625-3 Pettijohn FJ (1975) Sedimentary rocks, 3rd edn. Harper and Row, New York Ruwaih IA (1987) Experiences with expansive soils in Saudi Arabia. In: Proceedings of the sixth international conference on expansive soils, New Delhi, India, International Society for Soil Mechanics and Foundation Engineering (ISSMFE), 317–322 Sabatakakis N, Tsiambaos G, Gerochristodoulou D (2002) Estimation of physical and mechanical parameters of rock material. Bull. of the Public Works Central Laboratory of Greece (KEDE), special edition, pp 3–8

Saito T, Mamoru ABE, Kundri S (1974) Study on weathering of igneous rocks. Rock Mech Jpn 2:28–30 Sanad H, Bader B (1990) Laboratory study on leaching of calcareous soil from Kuwait. J Geotech Eng-ASCE 116(12):1797–1809 Sarkar K, Vishal V, Singh TN (2011) An empirical correlation of index geomechanical parameters with the compressional wave velocity. Geotech Geol Eng. doi:10.1007/s10706-011-9481-2 Sharma PK, Singh TN (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Environ 67:17–22 Sharma PK, Singh TN (2010) Reply to discussion by N Arıoglu, G. Kurt and E. Arıoglu (DOI: 10.1007/s10064-0100261-7) on the paper entitled “A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength” by P. K. Sharma and T. N Singh, Bull Eng Geol Environ Sharma PK, Khandelwal M, Singh TN (2011) A correlation between Schmidt hammer rebound numbers with impact strength index, slake durability index and P-wave velocity. Int J Earth Sci (Geol Rundsch) 100:189–195 Singh TN, Verma AK, Singh V, Sahu A (2004) Slake durability study of shaly rock and its predictions. Environ Geol 47:246–252 Singh R, Vishal V, Singh TN, Ranjith PG (2012a) A comparative study of generalized regression neural network approach and adaptive neurofuzzy inference systems for prediction of unconfined compressive strength of rocks. Neural Comput Appl. doi:10.1007/s00521-012-0944-z Singh R, Vishal V, Singh TN (2012b) Soft computing method for assessment of compressional wave velocity. Sci Iran Trans Civil Eng 19(4):1018–1024 Sousa LMO, Del Rio LMS, Calleja L, ArgandonaVGR D, Rey A (2005) Influence of microfractures and porosity on the physicomechanical properties and weathering of ornamental granites. Eng Geol 77:153–168 Starzec P (1999) Dynamic elastic properties of crystalline rocks from south-west Sweden. Int J Rock Mech Min Sci 36:265–272 Trenter NA (1989) Some geotechnical problems in the Middle East. In: Proceedings of the 1st regional congress on civil engineering, University of Bahrain, Bahrain, pp 1–22 Turgrul A, Zarif IH (1999) Correlation of mineralogical and textural characteristics with engineering properties of selected granitic rocks from Turkey. Eng Geol 51:303–317 Vasconcelos G, Lourenço PB, Alves CSA, Pamplona J (2007) Predication of the mechanical properties of granites by ultrasonic pulse velocity and Schmidt hummer hardness. Tenth North American Masonry Conference, Missouri, SA Vishal V, Pradhan SP, Singh TN (2011) Tensile strength of rock under elevated temperature. Geotech Geol Eng 29:1127–1133 Yagiz S (2011a) Correlation between slake durability and rock properties for some carbonate rocks. Bull Eng Geol Environ 70:377–383 Yagiz S (2011b) P-wave velocity test for assessment of geotechnical properties of some rock materials. Bull Mater Sci 34(4): 947–953 Yasar E, Erdogan Y (2004) Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Mining Sci 41:871–875 Yong RN, Ouhadi VR, Mohamed AMO (1996) Physico chemical evaluation of failure of stabilized marl soil. In: Proceedings of the 49th Canadian geotechnical conference frontiers in geotechnology 2: 769–776 Young RP, Hill TT, Bryan IR, Middleton R (1985) Seismic spectroscopy in fracture characterization. Q J Eng Geol 18:459–479