1 Introduction

The electrical resistivity method is an easy and economical non-destructive technique in geophysics. Its easily applicability both in the field and laboratory conditions increased its usage in different engineering disciplines (geophysics, geology, mining, geotechnical, hydrology, petroleum, and civil), in recent years. Therefore, it is crucial to find out the relationship between electrical resistivity of rocks and their engineering features. The resistivity of rocks, on the other hand, varies depending on porosity [1,2,3], pore geometry [4, 5], saturation [4,5,6], heat [7,8,9,10,11], and pressure [12, 13].

In recent years, many researchers have investigated the relationship between the electrical resistivity and index-mechanical properties of rocks [4, 14,15,16,17,18,19,20,21]. Kate and Sthapak [14] determined a logarithmic relationship between resistivity and uniaxial compressive strength (UCS) from a study carried out on the Himalayan rocks. On the other hand, Matsui et al. [4] stated in a study of different rock units (conglomerate, sandstone, granite, shale, and tuff) that the electrical resistivity values of rocks decreased as the porosity values of rocks increased. Kahraman et al. [16] and Kahraman and Yeken [17] indicated that there is a linear relationship between strength and resistivity values of magmatic rocks. Kahraman and Alber [15] found a logarithmic relationship among UCS, elastic modulus, and resistivity values in a study conducted on fault breccia and indicated that the resistivity values increase with increasing strength values. Su and Momayez [18], on the other hand, investigated the relationships among index (porosity, water absorption), strength (indirect tensile strength, young modulus), and abrasion (Los Angeles abrasion test) properties and electrical resistivity values using simple regression analysis and stated that resistivity values were susceptible to the index and strength properties of rocks. İnce [19] determined a very high correlation between the porosity, dry density, P-wave velocity, and UCS properties and electrical resistivity values of 12 different pyroclastic rock samples taken from the Cappadocia region. Sertçelik et al. [20] carried out a study to discover the correlation coefficient between porosity and electrical resistivity values on different rock and concrete samples. Renibar and Nasab [21] also found a strong correlation between UCS and electrical resistivity in their study on granitic rocks. Some researchers have numerically investigated the damage effects of rocks by means of electrical resistivity [22,23,24,25,26].

The objective of this study is to determine the index-strength values of 48 igneous rock (plutonic, volcanic, and pyroclastic) samples, by applying electrical resistivity method.

2 Materials and Methods

Forty-eight igneous rock samples collected from the Anatolian region in Turkey were used in this study. The samples locations and rock types are shown in Table 1. The types of the rock samples are plutonic, volcanic, and pyroclastic.

Table 1 The location and type of the rock samples
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2.1 Experimental Procedure

Nearly uniform rock specimens were collected from the quarries for laboratory tests with dimensions of 20 × 30 × 30 cm. Test specimens were prepared in accordance with the pertinent standards and suggested test methods [29, 30] in order to ascertain their relevant engineering properties. Porosity (n), water absorption by weight (Wa), dry density (ρd), and P-wave velocity (Vp) tests were performed according to ISRM [29] on cylindrical rock samples. Porosity and water absorption by weight values of the rocks were found by applying saturation and caliper procedures [29]. To determine the dry density of the samples, the volume of the rock samples was first calculated by averaging several caliper readings. Then, the dry density of the samples was determined as mass of a unit volume of rock sample. P-wave velocity of the rocks was measured over the samples by direct transmission using PUNDIT, which measures the propagation time of ultrasound pulses with an accuracy of 0.1 µs (Fig. 1a). UCS tests were performed on core samples with a diameter of 54 mm and a length of 110 mm according to ASTM D2938 [30] (Fig. 1b). The loading rate within the limits of 1.0 ± 0.5 MPa/s was applied. UCS tests were run five times for each rock sample, and the average UCS value of each specimen was determined.

Fig. 1
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Measurement of some index-mechanical properties: a P-wave velocity, b uniaxial compressive strength

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Thin sections of the samples were prepared in accordance with TS EN-12407 [31] and examined under an optical microscope from Nikon. Volcanic and plutonic rocks and pyroclastic rocks were classified and named according to the Streckeisen [27]’s and Schmid [28]’s classifications, respectively (Table 1).

2.1.1 Electrical Resistivity Measurements

Measurements of electrical resistivity were carried out on the core specimens having 54-mm diameter and approximately 110-mm length. Both surfaces of the core specimens were made flat and parallel to each other. The specimens were completely saturated with distilled water. The saturation of the samples was checked by measuring the increase in weight. In this case, if there was no extra weight increase in the samples, they were considered to be fully saturated. The mechanism depicted in Fig. 2 was used in resistivity measurements. Circular copper electrodes which had the equal diameter same as the specimens were used in the experiments. Twelve-voltage direct current (DC) was exerted across the rock specimen. After exerting the voltage at room temperature, its reaction was measured.

Fig. 2
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The device used in measurements of resistivity: a schematic diagram, b electronic circuit design, c resistivity measurement system (V, voltmeter; A, ampere meter; 12 V, DC voltage source; I, current; R, resistance)

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Utilizing the geometry and the resistance of the specimens, amount of electrical resistivity were computed from the equation below:

$$\rho =\frac{RA}{L}$$
(1)

where ρ is the electrical resistivity and R is the resistance. A and L are the cross-section area and the length of rock sample, respectively.

$$R=\frac{V}{I}$$
(2)

where R, V, and I are called the resistance, the volt, and the current, respectively.

3 Results and Discussion

The index, the UCS, and the electrical resistivity values of the igneous rocks used in this study are given in Table 2. Statistical analyses of these data are presented in Table 3.

Table 2 Some physico-mechanical and electrical resistivity properties of the rock samples (mean value ± standard deviation)
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Table 3 Descriptive statistics of data used in the analysis
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The dry densities of the igneous rocks used in the study vary between 1.23 and 2.68 g/cm3, whereas porosity values vary between 0.86 and 36.83%. According to dry density classification of the NBG [32], the dry density values of the volcanic and plutonic rocks fall into the high-very high class, whereas pyroclastic rocks fall into the very low class. On the other hand, according to porosity classification of the NBG [32], porosity values of the igneous rocks take place in between low to very high class. The water absorption by weight values of these rocks range between 0.32 and 28.27%. The highest P-wave velocity was measured in the basalt sample number 20 as 5.38 km/s, while the lowest P-wave velocity was measured in the pyroclastic sample number 39 as 0.89 km/s. The UCS test results of the rock specimens used in this study vary between 6.87 and 179.39 MPa. According to the ISRM [33] classification, the UCS values of the volcanic and plutonic rocks are classified as medium to high rock class, whereas the pyroclastic rocks classified as low and low-medium class. The measured resistivity values of the samples used in this study vary between 37.97 and 8997.53 Ωm2/m. The lowest resistivity values were measured in the pyroclastic rocks whereas the highest resistivity values were measured in plutonic rocks.

The relationship among the index, the UCS, and the electrical resistivity was investigated using the simple regression analysis. The accuracy of the derived equations was controlled by means of t and F test. If the computed t and F values are greater than those which were arranged, null hypothesis is dismissed. This result shows that r value is important. If the calculated t and F values are less than those of the arranged values, null hypothesis is not dismissed and r value is not significant. The computed values are bigger than the arranged t and F values showing that the models in the study are accurate. For the reliability of the derived equations for 5% significance level (α = 0.05), p value is required to be less than 0.05. In the determination of the best equation within the equations providing this requirement, the equation having the biggest correlation coefficient (r) value was taken into account. The equations derived are given in Table 4. The graphs created for them are presented in Fig. 3. The analyses of variance for the confirmation of equations were implemented and the outcomes are presented in Table 5. In this experimental study, a 95% significance level was preferred. The developed statistical models demonstrated that they could be used reliably in the estimation of strength values for a significance level of 5%.

Table 4 Correlation between electrical resistivity vs. index and strength values of the samples
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Fig. 3
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Correlation between electrical resistivity: a dry density, b P-wave velocity, c porosity, d uniaxial compressive strength

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Table 5 The variance analysis of the models
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There is a logarithmic correlation between density and electrical resistivity values having correlation coefficient (r) value of 0.88 (Fig. 3a). The resistivity values of rocks increase with increasing density values. The correlation coefficient value (r) was found to be 0.80 in the relationship between P-wave velocity and electrical resistivity values (Fig. 3b). When the low value of r compared to other properties was examined, it was found that some points deviated from the matched curve. This situation was connected with the rock properties (e.g., grain size and porosity) influencing the P-wave velocity, as stated by Fener [34]. A power relationship was determined between porosity and electrical resistivity values. The r value of this relationship was 0.91 (Fig. 3c). The porosity values of the rocks increase with decreasing resistivity values. There was a logarithmic relationship between UCS and the resistivity value, and the r value was 0.89. The UCS values of the rocks also increase with increasing resistivity values (Fig. 3d).

Figure 4 shows the comparison between resistivity and index-mechanical (ρd, Vp, n, UCS) data of magmatic rocks from previous studies and this study. This figure indicates that index-mechanical data range in previous studies is quite limited. However, the data range of index-mechanical properties of rocks used in this study is quite wide. This increases the usability and reliability of the equations developed in this study.

Fig. 4
figure 4

The comparison of data obtained from this study with those of other studies: a dry density, b P-wave velocity, c porosity, d uniaxial compressive strength

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4 Conclusions

In this study, the relationship between the index-mechanical properties and electrical resistivity was investigated on 48 different rock samples representing 3 different rock types (plutonic, volcanic, and pyroclastic). Electrical resistivity is influenced by the physico-mechanical properties of igneous rocks such as porosity, dry density, and index-strength. The general conclusions achieved in this study can be summarized as follows:

  • The best connection between electrical resistivity and porosity was found in the power function. On the other hand, the best connection between electrical resistivity and the other properties was defined in the logarithmical function. A very high correlation was identified between electrical resistivity values and index-strength values.

  • The electrical resistivity of rocks increases with increasing the dry density. However, the electrical resistivity of rocks decreases with increasing porosity. The resistivity of rocks increases with increasing UCS value.

Consequently, measurement of electrical resistivity is a relatively fast and cost-effective non-destructive method for determining the engineering properties of rocks. Therefore, this method can be useful in determining mechanical and index properties of rocks where it is difficult and impossible to collect samples either from outcrop or from historical and cultural structures without damaging them.