Introduction

Estimating geotechnical properties of rocks is considered to be the most important components in different engineering projects such as tunnels, dams, rock foundations, rock slopes, underground structures, selection of construction materials [32] and damage to historical buildings [22]. Many researchers indicated that the mechanical and physical properties of different rocks are under the influence of their lithological and textural characteristics [1, 11, 17, 21, 23, 37, 45, 53]. So, the characteristics have particular importance for predicting mechanical and physical properties of rocks. The most important lithological and textural characteristics that may affect the physical and mechanical properties of various rocks are grain shape, grain size, grain interlocking, type of contacts, packing density, packing proximity, mineralogical composition, amount and type of cement and matrix. These properties can be easily measured in laboratory and they are commonly determined during routine thin section studies [34]. On the other hand, determining geotechnical parameters are generally difficult, destructive, expensive and requires considerable amount of time [4, 30], although can be indirectly measured using their relationships by petrographic characteristics and some index test of rocks [8, 38, 46]. Indirect methods have several advantages, including little or no specimen preparation, easy operation and low cost [33, 44].

Howarth and Rowlands [23] developed the theory of texture coefficient (TC), which made it possible to understand the variety of physical and mechanical properties of rocks with rock textural properties. In this research, they investigated the relations between the mechanical properties and TC for ten different rock types including sandstones, marbles and igneous rocks and found that there are close relationships between rock mechanical properties and TC with high correlation coefficients. Numerous researchers such as Howarth and Rowlands [24], Ulusay et al. [49], Azzoni et al. [6], Jeng et al. [28], Prikiryl [42], Tandon and Gupta [48], Ajalloeian et al. [2], Yalcinalp et al. [52], Kolay and Baser [36], Kamani and Ajalloeian [31], Garia et al. [18], Wang et al. [50], Koken [35], Cheshomi et al. [10], Cueto et al. [12] and Rahimi et al. [43] have investigated the correlations between textural characteristics, physical and mechanical properties of various rocks, by using statistical analyses and soft computing methods (e.g., Jensen et al. [29]; Singh and Verma [47]; Esamaldeen and Guang [16]; Chen et al. [9]; Germinario et al. [19]) and found strong relations between the parameters.

Dogan et al. [13] presented classifications for carbonate hardground based on petrographic characteristics and engineering geological properties including uniaxial compressive strength (UCS), triaxial compressive strength (TCS), modulus ratio and elastic constant ratio. Alber and Kahraman [3], by texture coefficient (TC) and regression analyses, predicted the elastic modulus (E) and UCS of breccia. They believed that the UCS can be easily estimated from texture coefficient. Jensen et al. [29] stated that many parameters including crystal size, porosity, cleavage planes and micro-cracks control the strength behavior of limestone. Manouchehrian et al. [39] based on textural characteristics estimated UCS by using artificial neural network (ANN) and multiple regression analysis (MRA). Ozcelic et al. [40] predicted the geotechnical properties of marble and limestone samples from microscopic data by regression analyses. Bandini and Berry [7] studied the effect of marble samples’ textures on their mechanical behaviors. Pappalardo et al. [41] showed that the mechanical characteristics of migmatite are influenced by porosity and mineral composition. Ersoy and Acar [15] studied the influences of petrographic and textural properties on strength of very strong granitic rocks and concluded that the mineral size has a greater effect on strength than mineral type. Ajalloeian et al. [1] studied the impacts of petrographic properties on the ultrasonic wave velocity including dynamic elastic constants and P and S wave velocity of granitic rocks. The results showed that mineral grain size and ratio of quartz/feldspar have good accuracy for estimating the VP and VS.

The above-mentioned researches show that petrographic and textural characteristics have effect on the engineering properties of different rocks. Therefore, in the present research, geotechnical properties, petrography and textural characteristics of nine rock samples including limestone and travertine were determined and an attempt has been made to extract equations between textural characteristics and geotechnical properties of the rocks using regression analysis technique.

Sampling locations and geological setting

Northern and northwestern parts of Damghan are selected as the study area which has a typical continental climate and an irregular morphology that is related to its geological history, tectonics and lithology. From a geological point of view, the area is located on the Alborz-Azarbayejan structural zone and fairly complete succession of Paleozoic to Neogene rocks exist in this area. Suitable locations for sampling were selected using the 1:100,000 geological map prepared by the Geological Society of Iran [20]. The limestone samples were collected from Bahram formation of the middle Devonian outcropped in northern parts of a ballast mine in 10th Km of Cheshmeh-Ali road. These samples have a light brown color with dolomitic and silicone veins in their texture. Atari fault were passing from near the sampling locations which put together the Bahram limestones and Karaj formation tuffs. The travertine samples were collected from Baba-Hafez quarry located near the Astaneh village in 27th Km of Cheshmeh-Ali road. The studied travertine, along the Astaneh fault, was occurred by chemical activities of springs with dolomite and limestone of Elika formation. They were deposited between the Pishsarkoh and Anbehkoh mountains. The quarry covers small area and has porous travertines with light colors namely white, gray, cream and light brown. The elevation of study area is between 1380 and 1445 m above sea level. Figure 1 depicts the geological properties of area and shows the sampling locations.

Fig. 1
figure 1

Geological map of the study area indicating sampling locations and its situation on the general map of Iran [20]

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Methodology

This research was based on laboratory testing and field investigations. During the field investigations, lithological characteristics of nine block samples of two rock types including travertine and limestone were determined and suitable block samples were collected from mines, quarries and road cuttings of the study region and transferred to the engineering geology laboratory. To identify mineral composition, petrographic properties, textural characteristic and texture coefficient (TC) of the rock samples, XRD analyses and optical microscopy studies on polished thin sections were performed based on ISRM [27]. A comprehensive laboratory test program was carried out on the prepared rock specimens to assess specific gravity, dry and saturated unit weights, apparent porosity, water absorption, Schmidt rebound hardness, P-wave velocity, slake-durability index, uniaxial compressive strength, point load index, Brazilian tensile strength and block punch strength based on ISRM [27]. Required specimens were prepared in three shapes: irregular or lump, disk and cylinder in the laboratory. The irregular specimens were used in the slake-durability test. The disk specimens were prepared for performing the Brazilian and punch tests. The cylindrical specimens were used for measuring physical properties, ultrasonic P wave velocity, point load index and uniaxial compressive strength. The required cores were prepared from the selected rock blocks using a radial coring machine. Finally, empirical equations between the geotechnical properties and texture coefficient (TC) were extracted using regression analyses and the results have been discussed. Figure 2 presents test plan for mineralogical, physical, index and mechanical tests in this study.

Fig. 2
figure 2

Test plan for mineralogical, physical, index and mechanical test

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Results

Mineralogical and petrographic studies

Thin section studies and X-ray diffraction (XRD) analyses were performed to determine mineralogical, petrographic and textural characteristics of the rock samples based on ISRM [27] standard procedure. The results indicated that the limestone samples as dolomitic limestone are composed of calcite, dolomite and quartz. The presence of breccia structure and dolomitic vain with fossils fragments is textural properties of the samples. The travertine samples were commonly composed of calcite, aragonite and quartz. The samples are porous, and they have a layered texture due to succession of crystalized aragonite and calcite and micritic layers. The aragonite with especial extinction is obviously visible in the thin sections. The XRD analyses in the 2θ ranges from 4° to 72° were conducted on the rock samples which confirmed quartz, calcite and aragonite are the most important minerals of the studied rocks. The average modal abundance of minerals in the samples are presented in Table 1. Microscopic images of the samples of LS1 and TS1 as representative samples in normal and polarized lights are presented in Fig. 3, and XRD diffractograms are shown in Fig. 4.

Table 1 Type and mineral composition of the rocks
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Fig. 3
figure 3

Microscopic images of the representative rock samples in normal and polarized lights

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Fig. 4
figure 4

Diffractograms of the representative rock samples

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Geotechnical properties

Geotechnical parameters including physical, mechanical and index properties were determined for the rocks based on ISRM [27] suggested methods. The properties including specific gravity (GS), dry unit weight (γdry), saturated unit weight (γsat), water absorption (Wa), apparent porosity (n), Schmidt rebound hardness (HS), P-wave velocity (VP), elasticity modulus (E), slake-durability index (Id), uniaxial compressive strength (UCS), point load strength index (IS(50)), Brazilian tensile strength (BTS) and block punch strength (BPS). A total of 252 core specimens were prepared and used for various destructive and nondestructive tests. The prepared NX cylindrical core specimens were tested in different length/diameter ratio to determine physical and mechanical properties that some of them are presented in Fig. 5. The number of tests or tested specimens of each sample for determining physical properties was five cylinder specimens, for Schmidt rebound hardness was twenty impacts on each rock block sample, for P-wave velocity and UCS was five cylinder specimens, for slake-durability index was ten irregular lumps and for IS(50), BTS and BPS was ten cylinder, ten disc and ten thin disc specimens, respectively.

Fig. 5
figure 5

Prepared specimens of the studied rocks a limestone samples, b travertine samples

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The slake-durability test is performed on the samples up to three cycles in natural water. The Schmidt hammer test was performed by N type Schmidt hammer with 2.207 N/m energies on rock blocks of samples. The axial point load test was applied to determine point load strength index (IS(50)) of the rock samples. The Brazilian tensile test was carried out on rock specimens with lengths to diameter ratios from 0.5 to 0.75. In order to assess shear strength of the samples, thin disks core specimens with thicknesses ranging between 5 and 15 mm were tested under block punch. Prepared NX core specimens with a 2:2 length/diameter ratio were tested for each rock sample to determine the values of UCS. Average values of the obtained geotechnical parameters including physical, index and mechanical properties for the rock samples are outlined in Tables 2, 3 and 4, respectively.

Table 2 Physical properties of the studied rocks
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Table 3 Index properties of the studied rocks
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Table 4 Mechanical properties of the studied rocks
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Texture coefficient (TC)

Williams et al. [51] defined rock texture as "the degree of crystallinity, grain size or granularity, and the fabric or geometrical relationships between the constituents of a rock." Affective textural characteristics on rock strength are grain size and shape, density, degree of interlocking, porosity, grain orientation, quartz content, the nature of grain boundaries and texture model. Compositional features requiring investigations are strength properties, and percentages of component grains and cementing materials [24]. The innovation of texture coefficient by Howard and Rowlands [23] is the most exclusive technique when applying petrography techniques to quantitatively express the concept of rock texture. These researchers developed a dimensionless quantitative measure of rock texture. The procedure can be formulated as follow:

$${\text{TC}} = {\text{AW}}\left[ {\left( {\frac{{N_{0} }}{{N_{0} + N_{1} }} \times \frac{1}{{{\text{FF}}_{0} }}} \right) + \left( {\frac{{N_{1} }}{{N_{0} + N_{1} }} \times {\text{AR}}_{1} \times {\text{AF}}_{1} } \right)} \right]$$
(1)

where, TC is the texture coefficient, AW is the grain packing weighting, N0 is the number of grains whose aspect ratio is below a pre-set discrimination level, N1 is the number of grains whose aspect ratio is above a pre-set discrimination level, FF0 is the arithmetic mean of discriminated form-factors, AR1 is the arithmetic mean of discriminated aspect ratios, and AF1 is the angle factor, quantifying grain orientation [3, 4]. The grain packing weighting (AW), the arithmetic mean of discriminated aspect ratios (AR) and form factor (FF) were calculated based on following formula in Eqs. 2, 3 and 4, respectively:

$${\text{AW}} =\Sigma { }\frac{{\left( {\text{grain areas within the reference area boundary}} \right)}}{{\left( {\text{area boundary by the reference area boundary}} \right)}}$$
(2)
$${\text{AR}} = \frac{L}{W}$$
(3)
$${\text{FF}} = \frac{4\pi A}{{P^{2} }}$$
(4)

where, L is length, W is width, P is perimeter and A is area. The angle factor (AF) is calculated by summing the products of the class weightings and the fractions of the total number of angular differences in each class from equation below:

$${\text{AF}} = \sum\limits_{i = 1}^{9} {\left( {\frac{{x_{i} }}{{\frac{N(N - 1)}{2}}}} \right)} \times i$$
(5)

where, N is the total number of elongated particles, Xi is the number of angular differences in each class and i is the weighting factor and class number [14].

Calculating the texture coefficient (TC) on obtained TIFF format images of thin sections was performed by JMicroVision (v1.27) software. The program, containing most of the common image processing operations, has an efficient visualization system and innovative features. This software has been developed to analyze high definition images of thin sections and is a powerful software for object analyses such as determining size, shape, orientation and texture of different rocks. After calibrating the images and drawing grains boundary, related parameters including length (L), width (W), perimeter (P), area (A) and orientation of grains were determined by the software (Fig. 6). Requirement parameters such as AW, AR, FF and AF were determined after calculations, and the texture coefficient derivations are summarized in Table 5. Also, the comparative diagrams of the values of texture coefficient for the studied rock samples are presented in Fig. 7a. According to the histograms, the average value of TC is 0.55 and standard deviation (Std. Dev.) value equal to 0.25 which is presented in Fig. 7b. The standard deviation values in all samples are very low, that shows the dispersion in the values of TC is low (Fig. 7b). As can be seen from Table 5 and Fig. 7, the values of TC for limestone samples are higher than travertine samples. The samples of LS3 and TS6 have maximum and minimum values of TC, equal to 0.98 and 0.30, respectively. Also, results show when AW and AR1 increase, the values of TC will increase too.

Fig. 6
figure 6

Calculation procedure of TC parameter in JMicroVision (v1.27) setting

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Table 5 Values of texture coefficient derivations
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Fig. 7
figure 7

a Comparative diagrams of texture coefficient (TC) values and b histogram of TC for the rocks

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Statistical analysis

Statistical analyses consist of determining relationships between variables namely minerals content, texture coefficient, and geotechnical properties of the studied rocks were performed by simple regression analysis (SRA) method in statistics software IBM SPSS (V.24.0.) [26]. The values of R were calculated from the following equation:

$$R = \frac{{n\Sigma X_{i} Y_{i} - (\Sigma X_{i} )(\Sigma Y_{i} )}}{{\sqrt {n(\Sigma X_{i}^{2} ) - (\Sigma X_{i} } )^{2} \sqrt {n(\Sigma Y_{i}^{2} ) - (\Sigma Y_{i} } )^{2} }}$$
(6)

For simple regression evaluation, in the first step, main mineral constituents, namely quartz (Q.) and calcite (C.) percent, were considered as independent variable and TC was considered as the dependent variable. The diagrams of correlation between calcite and quartz content with texture coefficient are presented in Fig. 8a and b, respectively. A direct linear relationship exists between percent of calcite and texture coefficient with good correlation coefficient equal to R = 0.79. Stronger linear relationship was found between percent of quartz and texture coefficient with high correlation coefficient (R = 0.85). It is obviously seen that quartz content has more effect on TC than calcite content. Equation 7 and 8 were presented in order to calculate the texture coefficient by mineralogy study and value of major minerals of rocks:

$$TC = 0.03C - 0.59$$
(7)
$$TC = 0.04Q + 0.06$$
(8)
Fig. 8
figure 8

a Correlation between calcite percent and texture coefficient and b Correlation between quartz percent and texture coefficient

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The relationship between percentages of calcite and quartz versus texture coefficient is presented by a three variable map in Fig. 9. This shows the effect of minerals content on texture coefficient. This figure shows that increasing in calcite and quartz content results an increase in the texture coefficient. Therefore, the texture coefficient of studied rocks is controlled by the presence of major minerals including quartz and calcite.

Fig. 9
figure 9

Three variable map of texture coefficient versus calcite and quartz percent

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In the second stage of statistical analyses, each geotechnical parameters of the rocks had been taken as a dependent variables and TC values were considered as independent variables. The correlations between texture coefficient (TC) and specific gravity (GS), dry unit weight (γdry), saturated unit weight (γsat), water absorption (Wa), porosity (n), P-wave velocity (VP), elasticity modulus (E), Schmidt rebound hardness (HS), second cycle of slake-durability index (Id2), uniaxial compressive strength (UCS), point load strength index (IS(50)), Brazilian tensile strength (BTS) and block punch strength (BPS) are presented in Fig. 10a to k, respectively. Also, obtained empirical equations and the statistical parameters including R2, R and P-values (Sig. 2-tailed) are detailed in Table 6.

Fig. 10
figure 10figure 10

Correlations between texture coefficient (TC) and a dry and saturated unit weights (γdry, γsat), b water absorption (Wa), c porosity (n), d P-wave velocity (VP), e elasticity modulus (E), f Schmidt rebound hardness (HS), g slake-durability index (Id2), h uniaxial compressive strength (UCS), i point load strength index (IS(50)), j Brazilian tensile strength (BTS) and k block punch strength (BPS)

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Table 6 Empirical equations and statistical parameters from regression analyses
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In order to assess the performance degree of regression analyses root mean square error (RMSE), coefficient values account for (VAF), mean absolute percentage error (MAPE) and performance index (PI) were calculated and their values are presented in Table 7. These statistical parameters are calculated from the following equations:

$${\text{RMSE}} = \sqrt {\left( \frac{1}{N} \right)} \times \sum\limits_{i = 1}^{N} {(y - y^{\prime } } )^{2}$$
(9)
$${\text{VAF}} = \left[ {1 - \frac{{{\text{var}} y - y^{\prime } }}{{{\text{var}} y}}} \right] \times 100$$
(10)
$${\text{MAPE}} = \left[ {\frac{1}{N}\sum\nolimits_{i = 1}^{N} {\left| {\frac{{y - y^{\prime } }}{y}} \right|} } \right] \times 100$$
(11)
$${\text{PI}} = \left[ {R^{2} + \left( {\frac{{{\text{VAF}}}}{100}} \right) - {\text{RMSE}}} \right]$$
(12)

where, y and y′ are the experimental and calculated values of the geotechnical parameters, respectively, and N is the total number of data (samples). The model will be excellent if R = 1, RMSE = 0, VAF = 100, MAPE = 0 and PI = 100.

Table 7 Values of RMSE, VAF and MAPE in obtained models
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Calculated values of geotechnical properties that were obtained by models of simple regression analyses are presented in Table 8. Also, the mean values and standard deviation of calculated values for all models are presented in this table. In order to compare the mean values and standard deviation of experimental and calculated values of geotechnical properties, comparative diagrams are presented in Fig. 11a and b. Based on the results, the obtained values of the mean and standard deviation in SRA models are approximately similar to experimental values or vary close to them, and have less variety than calculated values.

Table 8 Calculated values of geotechnical properties obtained from TC
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Fig. 11
figure 11

Comparative diagram of a mean values and b standard deviation for experimental and calculated values of geotechnical properties

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In order to compare the results of SRA models for predicting the geotechnical properties, experimental and calculated values; also a 45° line (y = x) has been plotted in diagrams and presented in Fig. 12a to f. It should be noted that the adaption rate of trend lines with 45° line shows the validity of predictive models.

Fig. 12
figure 12

Plots of experimental and calculated values of a dry and saturated unit weights (γdry and γsat), b water absorption, porosity and P-wave velocity (Wa, n and VP), c elasticity modulus and Schmidt rebound hardness (E and HS), d slake-durability index (Id2), e uniaxial compressive strength (UCS), f point load strength index, Brazilian tensile strength and block punch strength (IS(50), BTS and BPS)

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The correlation between experimental and calculated values of dry and saturated unit weight that were obtained from TC is presented in Fig. 12a. Based on this graph, the trend lines partly fit to 45° line and show the moderate validity of the experimental equations. Whereas, trend lines of Wa, n and VP intercept to 45° line (Fig. 12b). The correlation between experimental and calculated values of E and HS is presented in Fig. 12c. It is clear that the trend lines partly overlap together and fit to 45° line and show the high validity of predictive models. Moderate validity of the experimental equations of SRA for estimating Id2 is showed in Fig. 12d. The correlation between experimental and calculated values of uniaxial compressive strength is presented in Fig. 12e. It shows the trend line of UCS entirely fits to 45° line. The graph of relationships between experimental results and calculated values of IS(50), BTS and BPS is shown in Fig. 12f. It can be obviously seen from this figure that the calculated values of IS(50) and BPS are closer to the corresponding experimental values and completely fits to 45° line. It means that the trend line of BTS model does not completely fit to 45° line and the results of IS(50) and BPS are better than BTS.

Discussions

Thin section studies indicated that the rock samples were commonly composed of quartz and calcite. Based on the physical test results, the samples of TS6 and LS1 have the minimum and maximum values of dry unit weight and the TS1 and LS2 samples have the minimum and maximum values of porosity, respectively. Results show the TS6 and TS1 samples have the minimum and maximum P-wave velocities, respectively. Based on the rock classifications by IAEG [25], most of the samples are moderate in dry unit weight, low to moderate in porosity and have low to very high values of P wave velocity. The LS1, LS3 and TS2, TS6 samples have the minimum and maximum values of Schmidt rebound hardness, respectively. The TS6 and TS1 samples have the maximum and minimum slake-durability index values in the third cycle (Id3) of the test, respectively. According to the results from UCS test, the TS6 and LS3 samples have the minimum and maximum UCS values, equal to 18.52 and 51.51 MPa, respectively. The TS2 and LS3 samples have the minimum and maximum IS(50) values, equal to 6.28 and 11.86 MPa, respectively. On the basis of the results from Brazilian test, the LS2 and LS3 samples have minimum and maximum BTS values, equal to 4.76 and 9.22 MPa, respectively. Based on the results from block punch test, the TS2 and LS3 samples have the minimum and maximum BPS values, equal to 4.25 and 10.27 MPa, respectively.

The regression analyses indicated that the most of the geotechnical properties of the studied rocks are related to petrographic and textural characteristics. So, this method is an efficient technique for assessing the relationships between the parameters. Figure 10a shows direct polynomial relationships between TC and dry and saturated unit weights with acceptable correlation coefficients (R = 0.85 and 0.87). This means that the TC values are increased with increasing the unit weight in the tested rock samples. Figures 10b and 7c indicate poor reverse power and linear relations between TC and water absorption and porosity, respectively. This means that the TC values of the studied rock samples is not related to these parameters. Because, texture of rocks is defining as the shape, arrangement and size of crystals or grains of the rock. Based on this definition, porosity is not a textural factor and it is not considered in JMicroVision software. So, the TC is not related to porosity and the obtained results from the present study confirm this issue. On the other hand, the water absorption and P-wave velocity of the studied rocks are controlled by porosity. So, these two parameters are not related to the TC either. Based on Fig. 10f, a direct logarithmic relationship exists between HS and TC with good correlation coefficient (R = 0.96). Whereas, moderate correlations have been found between TC and VP, Id2 and BTS as power, polynomial and linear with correlation coefficients of 0.53, 0.65 and 0.71, respectively (Fig. 7d, g, j). Very good direct relations were found between TC and elasticity modulus and mechanical properties including UCS, IS(50) and BPS as linear and power with correlation coefficients of 0.93, 0.95, 0.95 and 0.98, respectively (Fig. 10e, h, i, k). Significance level for models of E, HS, UCS, IS(50) and BPS calculated equal to 0.000 that indicated when TC is considered as an input the obtained predictive models can predict values of independent variable with 99% confidence limit. As a general result from the regression analyses, texture coefficient (TC) is very helpful parameter for determining geotechnical properties of the studied rocks especially dry and saturated unit weight, HS, UCS, IS(50) and BPS. Statistical indexes including RMSE, VAF and MAPE show the performance degree, validity and errors values of created model and obtained empirical equations by TC values and simple regression analyses. Based on the results, Model 3, 4 and 5 has not enough validity for predicting related parameters. Whereas, Model 9, 10 and 12, which correlate UCS, IS(50) and BPS with TC (with VAF values of 90.60, 88.98 and 96.83, respectively) are valid and have high prediction capacity. Also, Model 1 and 2, for determining dry and saturated unit weight, have lowest values of RMSE and MAPE implying the low errors and high performance degrees of the models. Performance appraisal by PI shows model 12, that correlated BPS and TC, has a higher performance than the other models.

Conclusions

In the current study, mineralogical, petrographic and textural characteristics of nine carbonate rock samples of limestone and travertine were investigated by thin section studies and XRD analyses. Some geotechnical tests for determining physical properties, Schmidt rebound hardness, slake-durability index, ultrasonic P-wave velocity and mechanical properties namely uniaxial compressive strength, point load strength, Brazilian tensile strength and block punch strengths were performed on standard obtained core specimens. Mineralogical studies by thin section and XRD analysis show the studied samples dominantly composed of quartz and calcite. The texture investigations were performed by calculating related parameters containing length, width, perimeter, area and orientation of mineral grains composing the rocks using JMicroVision 1.27 software and microscopic images obtained from thin sections studies. Results indicated that the limestone samples have higher TC values than the travertine ones. In order to study the effect of mineralogy on TC values, direct linear relationships were found between percentages of calcite, quartz and texture coefficient with high correlation coefficient. Also the three variable map shows that when calcite and quartz increase, texture coefficient increases. The relations between geotechnical properties and TC were investigated by statistical analyses. According to simple regression analysis results, the relationships between obtained parameter were direct linear, polynomial, power and logarithmic functions with correlation coefficients between 0.10 and 0.98. In fact, there was not found good relations between TC and porosity, water absorption and P-wave velocity, because the parameters are not textural factors and they are not considered in JMicroVision software. But, strong, meaningful and acceptable relations were obtained between TC and γdry, γsat, HS, UCS, IS(50) and BPS, as well as moderate correlations were found between TC and VP, Id2 and BTS. Also, it was found that strength of the studied rock samples increased with increasing the values of TC. Significant level values (Sig.) in the range of 0.000 to 0.933 show the engineering parameters are significantly related together. Validity and performance degrees of obtained empirical equations were investigated by statistical parameter including RMSE, VAF and MAPE which showed the errors of models are negligible and high performance capacity were detected in some models. Geotechnical properties were calculated by obtained models of simple regression analyses and mean and standard deviation of them were compared together. Based on the results, the obtained values of the mean and standard deviation of calculated values are approximately similar to experimental values. Experimental and calculated values of geotechnical properties that were obtained from laboratory tests and were predicted by the simple regression analysis models were compared with 45° line (y = x). The results show the trend lines of E, HS, UCS, IS(50), and BPS models are more fit to y = x line. This means that the predicted values are approximately equal to the experimental values. Finally, the results indicated that the geotechnical properties of the studied samples were closely related to petrographic properties and especially texture coefficient. So, the obtained empirical equations provide good predicting model for mechanical and physical properties of the rocks.