1 Introduction

Construction of projects such as foundation on rocks, underground structures, infrastructure works, tunnels, dams etc. is substantially influenced by physical and mechanical properties of rocks. The reason of the most of the hazards is the inaccurate evaluation of these rock properties. Especially specimen preparation for laboratory testing to determine the mechanical properties are expensive, difficult to be carried out and time consuming. In addition, the accuracy is mostly dependent on the specimen dimension, human errors, instrument calibration and internal factors. For these difficulties, indirect methods are often applied for preliminary studies. Indirect methods are simple do not require specimen preparation. The physico-mechanical properties of rocks are determined according to both the American Society for Testing and Materials ASTM (1986a) and International Society for Rock Mechanics ISRM (1987) and other common standards.

The P-wave velocity which depends on density and elastic properties of rocks has been used for many years to determine the physico-mechanical properties of different rocks by various authors. Many authors have studied the relations between physico-mechanical properties and P-wave velocity of rocks. Smorodinov et al. (1970) established empirical relation between uniaxial compressive strength (UCS) and density/porosity. Inoue and Ohomi (1981) determined the relations between UCS and P-wave velocity of soft rocks. Gaviglio (1989) investigated the relation between P-wave velocity and density. Boadu (2000) found the transport properties of fractured rocks from seismic waves. Kahraman (2001a) made correlations between P-wave velocity and number of joints and Schmidt rebound number (RN). Kahraman (2001b) evaluated the correlations between UCS, point load index (Is(50)), RN, P-wave velocity and impact strength index. Kahraman (2002) estimated the P-wave velocity of intact rock from indirect laboratory measurements. Ozkahraman et al. (2004) obtained the thermal conductivity of rocks from P-wave velocity. Yasar and Erdogan (2004) correlated P-wave velocity with density, Young’s modulus and UCS of carbonate rocks. Sharma and Singh (2008) studied on the correlations between the P-wave velocity, impact strength index, slake durability index and UCS. Khandelwal and Singh (2009) correlated the P-wave velocity with different physico-mechanical properties of coal measure rocks. Khandelwal and Ranjith (2010) made correlations of P-wave velocity with index properties of different rock types. Kurtulus et al. (2010) evaluated the physical and mechanical properties of Gokceada: Imbroz (NE AegeanSea) Island andesites. Kurtulus et al. (2011a) studied the physical and mechanical properties of serpentinized ultra basic rocks in NW Turkey. Kurtulus et al. (2011b) studied the seismic anisotropy of Devonian limestone. Empirical relationships proposed in literature between P-wave velocity and uniaxial compressive strength (UCS), point load index Is(50), porosity (Φ), Brazilian tensile strength (TS) and Schmidt rebound number (RN) are shown in Table 1. The differences determined could be related to the mineralogical composition and texture of the rock materials or the different methods used for sampling and performing the tests.

Table 1 Equations correlating the UCS, Is(50), Φ, and RN to P-wave velocity for several areas in the world and references
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This paper aims to evaluate the physico-mechanical properties of intact rocks and the correlation of P-wave velocity with the dry unit weight, uniaxial compressive strength (UCS), Point Load Index (Is(50)), Brazilian Tensile Strength (TS), porosity (Φ) and Schmidt Rebound Number (RN), with the intention of providing detailed documentation about intact rocks.

2 Research methodology

2.1 Sample collection

The rock samples were collected from five areas in Kocaeli area (Fig. 1).

Fig. 1
figure 1

Geology map of the research area (TUBITAK 2010). Kızderbent Volcanic, Sopalı Arkose, Körfez Sandstone, Derince Sandstone and Akveren Limestone specimens are shown by the star, circle, rectangle, triangle and square, respectively

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Laboratory tests were performed on 96 rock specimens, including 10 of which are volcanic and 86 of them are sedimentary rocks (Table 2).

Table 2 List of rock types with class and location
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2.2 Laboratory investigation

Core specimens of rock samples collected from five different rock types were cored in NX size (54 mm diameter) by coring machine. The both ends of the specimens were trimmed as 110–115 cm (ISRM 1981) and smoothed using a lathe to avoid end effects. The specimens were dried at 105 °C for 24 h to remove moisture because drying of the specimens are particularly important not to damage or alter the rock fabric. In addition, dry weights are absolutely crucial and must be well defined, stable and controlled throughout handling before, during and after analysis.

2.3 Determination of P-wave velocity

The P-wave velocity of rock specimens was determined using Pundit Plus with the transducers having a 54.0 KHZ frequency as per the ISRM (ASTM 2001; ISRM 2007). Figure 2 shows ultrasonic pulse testers used in this study. A mechanical pulses generated by this instrument are transmitted from one end received at another end of the specimens by piezo–electric transducers. The velocity is determined by dividing the traveling the distance (d) to travel time elapsed (t) in traveling the distance by the wave pulse from the emitter to receiver placed both ends of the specimens, Table 3.

Fig. 2
figure 2

Ultrasonic pulse tester instruments

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Table 3 Vp, DUW, UCS, Is(50), TS, Φ, and RN test results
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As seen from Table 3, the velocity of Kızderbent volcanite specimens ranges from 5800.0 to 6340.0 m/s with the mean 6370.0 m/s, whereas that of Sopalı arkose specimens vary between 2544.0 and 3300.0 m/s with the mean 2922.0 m/s. The velocity of Körfez sandstone specimens change between 2968.0 and 6010.0 m/s with the mean 4489.0 m/s and that of Akveren limestone specimens ranges from 4300.0 and 5800.0 m/s with the mean 5050.0 m/s. The velocity of Derince sandstone specimens vary between 1890.0 and 3300.0 m/s with the mean 2595.0 m/s.

2.4 Determination of different physico-mechanical properties

The effective porosity of rock specimens were determined using saturation method. Dry unit weights and effective porosity of the rock specimens were determined in accordance with ISRM (2007). The uniaxial compressive strength (UCS) were obtained by subjecting each specimen to H incremental loading at about constant rate using a hydraulic testing machine of 150.0 KN capacity in accordance with ASTM (1986b). The Is (50) of the specimens was determined by mounting each specimen between two platens of a point load tester of 50.0 KN capacities in accordance with ASTM (2005). Schmidt hardness of the specimens was determined according to ASTM D5873 (2014) standard recommendations on cylindrical specimens using a Schmidt hammer type NR of impact energy of 2.207 Nm. The Brazilian tensile strength of the specimens of NX diameter were determined using Brazilian test apparatus equipped with digital display unit for displaying maximum load. Rock specimens were loaded diametrically between the loading platens of the apparatus as per ISRM (1978) standards.

2.5 Geophysical survey

The seismic refraction surveys were conducted at Kızderbent volcanites, Sopalı Arkose, Körfez sandstone, Akveren limestone and Derince sandstone in the investigation area to correlate the ultrasonic pulse velocities of rock specimens with dynamic P-wave velocities. The seismic refraction data were recorded using a 12 channel Geometrics Seismic Enhancement (Smart Seis) seismograph. The first arrival phases assumed to be refracted from the same interface, the P-wave velocities were calculated from the slope of the line connecting the first arrival phases using GeoSeis computer program. The determined average P-velocities are given in Table 4.

Table 4 Average P-wave velocities of rocks obtained from seismic refraction surveys in the investigation areas
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The discrepancy increases notably when comparing Vp in situ values with laboratory results. The large reductions in Vp in situ values are clearly the functions of fractures and natural joints. P-wave velocity depends on mineralogical composition, micro cracks and pores of the rocks and on the physical parameters, such as absorption by weight, density or porosity.

2.6 Result and discussion

Results of laboratory tests on 96 specimens are listed in Table 3. As can be seen in this table, volcanic rocks give higher uniaxial compressive strength (UCS) values (172–202 MPa) and point load index Is(50) compared to sedimentary rocks.

The previous literatures show that our results are in acceptable ranges (Cobanglu and Celik 2008; Entwisle et al. 2005; Kahraman 2001a; Khandelwal and Singh 2009; Kurtulus et al. 2010; Kurtulus et al. 2011a; Kurtulus et al. 2011b; Moradian and Behnia 2009; Sharma and Singh 2008).

In order to describe the relationships between P-wave velocity and physico-mechanical properties of rocks a regression analysis was carried out. The equation of the best fit line and the coefficient of determination (R2) were determined for each test result (Figs. 3, 4, 5, 6, 7, 8). It can be seen from the figures that, in all cases, the best fit relationships were found to be the best.

Fig. 3
figure 3

Graph of dry unit weight (DUW) and P-wave velocity (Vp)

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Fig. 4
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Graph of uniaxial compressive strength (UCS) and P-wave velocity (Vp)

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Fig. 5
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Graph of point load index (Is(50)) and P-wave velocity (Vp)

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Fig. 6
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Graph of tensile strength (TS) and P-wave velocity (Vp)

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Fig. 7
figure 7

Graph of effective porosity (Φ) and P-wave velocity (Vp)

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Fig. 8
figure 8

Graph of Schmidt rebound number (RN) and P-wave velocity (Vp)

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There is an exponential relation between P-wave velocity and dry unit weight with a strong correlation of (R2 = 0.795) (Fig. 3). The equation of this relation is given as;

$$ {\text{DUW}} = 0.52{\text{V}}_{\text{p}}^{0.45} \quad \left( {{{\text{R}}^2} = 0.795} \right) $$
(1)

Polynomial relations have been observed between P-wave velocity and UCS and Is(50) (Figs. 4, 5). The equations are given below:

$$ {\text{UCS}} = {8.10^{ - 6}}{\text{V}}{{\text{p}}^2} - \,0.024{\text{Vp}} + 31.92 \quad \left( {{{\text{R}}^2} = \, 0.89} \right) $$
(2)
$$ {{\text{I}}_{\text{s}}}\left( { 5 0} \right)\,{ = 7} . 1{ 0^{ - 7}}{\text{V}}_{\text{p}}^ 2 - 0 . 0 0 2{{\text{V}}_{\text{p}}} + 2 . 8 3 9 \quad \left( {{{\text{R}}^ 2}\,{ = 0} . 8 8} \right) $$
(3)

A very good correlation (R2 = 0.89) was found between Vp and UCS, and also (R2 = 0.88) between Vp and Is(50) for P-wave velocity and the tensile strength, effective porosity and Schmidt rebound number show linear relationships (Figs. 6, 7, 8).

$$ {\text{TS}}\;{ = }\; 0. 0 0 8{{\text{V}}_{\text{p}}} + 3. 8 4 \quad \left( {{{\text{R}}^ 2}\;{ = }\; 0. 7 8} \right) $$
(4)
$$ {\text{\O}} = - 6\text{E}\,{-}\,05{{\text{V}}_{\text{p}}} + 0.383\quad\left( {{{\text{R}}^2} = 0.85} \right) $$
(5)
$$ {\text{RN}}\; = \;0.006{{\text{V}}_{\text{p}}} + 9.52 \quad \left( {{{\text{R}}^2} = 0.80} \right) $$
(6)

A good correlation (R2 = 0.78) was found between P-wave velocity and Brazilian tensile strength, (R2 = 0.85) between Vp and Ø, and (R2 = 0.80) between Vp and RN.

From Fig. 7, it may be seen that when, the P- wave velocity increases the porosity decreases. However, from Figs. 3, 4, 5, 6, and 8 it can be observed that when the P- wave velocity increases, dry unit weight, uniaxial compressive strength, point load index, tensile strength and Schmidt rebound number increase. Kızderbent volcanites have the highest P-wave velocities range between 5800.0 and 6340.0 m/s with the mean 6370.0 m/s and for physico-mechanical properties wherein dry unit weights (DUW) vary between 2.68 and 2.95 gr/cm3 with the mean 2.815 gr/cm3, uniaxial compressive strengths (UCS) range from 172.0 to 202.0 MPa with the mean 187.0 MPa, Point load index (Is (50)) change between 13.6 and 16.32 MPa with the mean 14.96 MPa, Brazilian tensile strengths range between 53.0 and 65.0 MPa with the mean 59.0 MPa and Schmidt rebound numbers vary from 51.0 to 60.0 with the mean 55.5. Kızderbent volcanites have the lowest effective porosity values (Φ) vary between 0.032 and 0.048 % with the mean 0.04 %. Sopalı Arkoses have the lowest P-wave velocities ranging from 2544.0 to 3300.0 m/s with the mean 2922.0 m/s. Their (DUW) vary between 2.18 and 2.46 gr/cm3 with the mean 2.32 gr/cm3, (UCS) range between 11.6 and 28 MPa with the mean 19.8 MPa, (Is (50)) change between 0.93 and 2.24 MPa with the mean 1.585 MPa, (TS) range from 25.0 to 38.0 MPa with the mean 31.5 MPa, (RN) change between 24.0 and 32.0 with the mean 28.0. Sopalı arkoses have the highest effective porosities (Φ) vary between 0.23 and 0.278 % with the mean 0.254 %. P-wave velocities and physico-mechanical properties of Körfez sandstone, Akveren limestone and Derince sandstone follow the Kızderbent volcanites respectively. In general, the correlation coefficients (R2) were lower for the DUW and TS than for the UCS, Is (50), Φ and RN (Figs. 3, 4, 5, 6, 7, 8) in this study.

The relation between DUW and Vp is similar to relationship given by Kurtulus et al. (2011b), but its correlation coefficient (R2 = 0.795) higher than proposed by Kurtulus et al. (2011b). The proposed relationship between UCS and Vp is similar to suggested relationships given by Cobanglu and Celik (2008) and Kurtulus et al. (2010), but correlation coefficient is 0.89 which is relatively higher than their suggested correlation coefficients. However, it is relatively lower than correlation coefficients given by Khandelwal and Singh (2009), Kurtulus et al. (2011a), Sharma and Singh (2008). Our relationship between Is (50) and Vp is similar to relationships given by Kurtulus et al. (2010), Kurtulus et al. (2011a), Kurtulus et al. (2011b), but its correlation coefficient (R2 = 0.88) is lower than that given by Kurtulus et al. (2010), very close to that of others. Relation between RN and Vp is similar to relationship proposed by Kurtulus et al. (2010), however, its correlation (R2 = 0.80) is higher than their suggested correlation.

3 Conclusions

In this study, the physico-mechanical properties including P-wave velocity, dry unit weight, uniaxial compressive strength, point load index, indirect tensile strength, effective porosity, and Schmidt hardness of the intact rocks were determined in the laboratory. The test results were interpreted statistically and reasonable good relationships were determined with P-wave velocity (ranging between 1890.0 and 6340.0 m/s) to the physico-mechanical properties. This result denotes that P-wave velocities could be used in determination of the physico-mechanical properties of intact rocks.