Evaluation of the single compressive strength test in estimating uniaxial compressive and Brazilian tensile strengths and elastic modulus of marlstone

Engineering Geology 248 (2019) 256–266

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Evaluation of the single compressive strength test in estimating uniaxial compressive and Brazilian tensile strengths and elastic modulus of marlstone

T

⁎

Mahdi Ashtaria, Seyedeh Elham Mousavib, Akbar Cheshomib, , Mashallah Khamechiana a b

Department of Structural and Engineering Geology, College of Science, Tarbiat Modarres University, Tehran, Iran Department of Structural and Engineering Geology, School of Geology, College of Science, University of Tehran, Enghelab Ave., Tehran, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Marlstone Particles Uniaxial strength Brazilian strength Elastic modulus

Uniaxial strength (UCS), tensile strength (BTS), and elastic modulus (E) are important rock strength parameters used in many engineering projects such as dam, bridge, and tunnel constructions. Several direct and indirect methods have been proposed to measure these parameters. For direct methods, standard samples should be prepared and loaded. Indirect methods are used to estimate these parameters when there is no access to the standard core for various reasons. In this regard, the single compressive strength test (SCS) is one of the indirect methods for estimating these parameters using small specimens. In the present study, the possibility of using SCS test for predicting strength parameters of marlstones is investigated. For this purpose, a total of 10 marlstone blocks were collected from different geological formations of Iran. After preparation of the standard samples, an attempt was made to determine uniaxial strength (UCS), Brazilian tensile (BTS), and elastic modulus (E) of each sample. Next, the samples were crushed and 50 small spherical particles with diameters of 3, 5, 8, 9, and 10 mm were prepared from each sample. A total of 500 particles were used for SCS testing. Then, the single compressive strength index (SCSI) was determined for each particle by plotting load-displacement diagrams; the SCSI of each sample was the average SCSI of 10 same size particles. Subsequently, UCS-SCSI, E-SCSI, and BTS-UCS correlations for specific particle sizes were proposed using the regression analysis. The mean values for the correlation coefficients were obtained as 0.93, 0.89, and 0.91, respectively. The empirical relationships were verified by conducting 100 tests on the control samples, which revealed the reliable validity of the outcomes. The results of this regression modeling, compared with the data obtained from SCS experiments on limestone and sandstone particles mentioned in the literature, demonstrated that the empirical relationships were affected by rock types. Therefore, rock-specific diagrams have to be drawn for particles with different lithologies.

1. Introduction Determining strength parameters of rocks such as compressive strength, tensile strength, and elastic modulus is a prerequisite of conducting many engineering projects. Direct standard UCS test (ASTM, 2002) and the Brazilian test (ASTM, 2008) are employed for determining compressive strength and tensile strength, respectively. To perform these tests, however, it is necessary to prepare related standard cores, which is an expensive and time-consuming task. Moreover, tests samples are sometimes inaccessible while drilling oil wells, underground constructions, or TBM excavation. Thus, indirect methods of measuring compressive and tensile strength have been proposed by many researchers. Tensile strength is one of the most reliable strength parameters of

intact rock or rock mass against fraction (Perras and Diederichs, 2014). In this regard, the Brazilian test has been introduced as an indirect method for determining tensile strength by Fernando LLB Carneiro in Brazil (Carneiro, 1943) and by Tsunei Akazawa in Japan (Akazawa 1953). The test was performed on rocks for the first time by Berenbaum and Brodie (1959). Subsequently, various experimental tests and numerical modeling have been developed to predict the tensile strength of rocks (Meulenkamp, 1997; Meulenkamp and Alveraz Grima, 1999; Nie and Zhang, 1994; Singh et al., 2001). The previously proposed indirect methods for determining uniaxial strength such as point load test (D'Andrea et al., 1965), nail penetration test (Kayabali and Selcuk, 2010), block punch index (Sulukcu and Ulusay, 2001), and Schmidt hammer test (Kahraman, 2001) require relatively large samples. Moreover, these tests cannot be used for deep

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Corresponding author. E-mail addresses: [email protected] (M. Ashtari), [email protected] (S.E. Mousavi), [email protected] (A. Cheshomi), [email protected] (M. Khamechian). https://doi.org/10.1016/j.enggeo.2018.12.005 Received 25 May 2018; Received in revised form 9 November 2018; Accepted 7 December 2018 Available online 10 December 2018 0013-7952/ © 2018 Elsevier B.V. All rights reserved.

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strength (UCS) of marlstone using spherical particles was investigated in this study. For this purpose, 14 blocks were collected from marlstone formations (10 blocks for the proposed relation and 4 blocks for its validation). After preparation of the standard cores, uniaxial and Brazilian tests were carried out to determine their UCS, BTS, and elastic modulus (E). Next, the core samples were crushed and after producing small particles in 3, 5, 8, 9, and 10 mm SCS tests were performed. Ultimately, correlations between SCSI results and strength parameters of the samples were evaluated using statistical methods, univariate and multiple regression modeling. Also, in order to verify the proposed relations, they were compared with those of other researchers.

drilling or highly fractured rocks, in which preparation of suitable large core is impossible. Accordingly, researchers have tried to develop some methods for predicting the strength using the drill cuttings. According to Santarelli et al. (1989), since drill cuttings are representative of a formation and possess an adequate and reliable source of information about formation mechanical behavior, the strength of the tested particle could be a function of the uniaxial strength of the related standard core. Therefore, the uniaxial strength could be determined indirectly using drilling particles as small-scale samples and appropriate laboratory equipment. Methods such as indentation test (Mateus et al., 2007; Haftani et al., 2013; Cheshomi et al., 2017), loading reconstructed cores test (Mehrabi et al., 2012), modified point load test (Sheshde and Cheshomi, 2015), and single particle loading test (Cheshomi et al., 2012) have been suggested for indirect determination of UCS by drilling cuttings. Moreover, the single particle loading test (SCS) has been introduced for predicting UCS of limestone spherical particles with 3, 4, and 5 mm diameters (Cheshomi and Ahmadi Sheshde, 2013) and for estimation of UCS in sandstone with diameters of 3, 5, and 8 mm (Cheshomi et al., 2015). They confirmed the repeatability of SCS tests and proposed Eqs. (1) and (2) for prediction of UCS.

2. Material and methodology 2.1. Material As it was shown in the geological maps (Geological survey and mineral exploration of Iran, 2010) given in Fig. 2, materials used in this research are marlstone blocks prepared from geological formations in Iran, including 3 blocks were collected from Abderaz Formation, 4 blocks from Mishan Formation, 3 blocks from Chaman Bid Formation for testing, and 4 blocks from Mishan, Gachsaran, and Aghajari Formations for the verification of the results. All blocks were fresh and unweathered.

UCSlimestone = (6.4949 × D − 1.801) × SCSI + (1.2957 × D + 1.486) (1)

UCSSandstone = (−0.3 D + 1.92) SCSI + (1.24 D + 6.72)

(2)

2.2. Methodology

UCS: uniaxial compressive strength (MPa)D: particle diameter (mm) SCSI: single compressive strength index (N) Furthermore, severe damages have been reported regarding constructions on marly lands (Jones and Holtz, 1973; Akili and Torrance, 1981; Ruwaih, 1987; Chen, 1988; Al-Sanad and Al-Bader, 1990; Alber and Heiland, 2001) due to the insufficient recognition of the engineering properties of marlstone (Paaza et al. 1998). Marlstone is one of the most problematic rocks due to its low strength, quick weathering, and the swelling when exposed to water. Therefore, determination of strength, deformability, and mineralogy parameters of this rock is of great necessity (Azadan and Ahangari, 2013; Azimian and Ajalloeian, 2015; Wang and Strong, 1996). These problems are associated with insufficient recognition of the engineering properties of marlstone (Paaza et al., 1998). Additionally, while preparing standard cores from marlstone samples to determine their strength properties and structural deformability, rapid weathering, and swelling in the presence of water lead to some critical issues (shown in Fig. 1). Consequently, the possibility of utilizing the SCS test to estimate the Brazilian tensile strength (BTS), elastic modulus (E), and uniaxial

2.2.1. Marlstone petrography and physical characteristics Generally, Marlstone is composed of clay, calcium carbonate (35% to 65%), and some other minor minerals (Pettijohn, 1975). Marlstones have a grain structure that is bonded with calcium carbonate cement during the sedimentation and lithification process (Mitchell, 1975). From the mineralogical point of view, physical properties, ductility properties, swelling, strength, and durability of these rocks are influenced by the differences in carbonate content, clay minerals content, the ratio of carbonate to clay minerals, and the type of clay mineral. In this respect, XRD and XRF tests were performed on blocks for determining mineralogy and Bernard calcimeter tests for measuring the calcite content of the specimens (Hulseman, 1966; Muller and Gatsner, 1971). The XRD tests results showed that the dominant components of the studied samples are calcite, quartz, dolomite, albite, muscovite, and clinochlore minerals. Using the XRF test, the oxide-components of blocks was investigated, as presented in Table 1; the CaO content varies between 17% and 39%. The amounts of carbonate obtained from the calcimeter test are

Fig. 1. Core breakage while coring and weathered marlstone at the field. 257

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Fig. 2. Geological and geographical locations of collected samples (Geological survey and mineral exploration of Iran, 2010), utilized blocks were collected from the marked locations; Point A: blocks M8, M9 and M10, Point B: blocks M1,M2 and M3, Point C: blocks M4, M5, M6 and M7, point D: Validation samples.

2.2.3. Brazilian tensile strength test (BTS) In this test, which is carried out according to the ASTM (2008) standard, a cylindrical sample of 54 mm diameter, height to diameter ratio of 1 to 2, and side surfaces polished to a depth of 0.25 mm are provided. Then, the loading is done (Fig. 3b) and the values of the BTS are calculated using Eq. (3) and given in Table 2. Three cores were tested from each block and the obtained mean values were considered as the Brazilian tensile strength.

given in Table 1. Sample M9 with 34% and sample M4 with 75% contained the lowest and highest carbonate, respectively. Furthermore, physical characteristics of the blocks such as porosity and dry density were measured and presented in Table 2. Sample M10 and M4 showed the highest and lowest porosity, respectively. 2.2.2. Uniaxial compressive strength (UCS) test Standard cores were prepared and tested using strain-controlled UCS equipment according to ASTM2002. The average UCS of 3 cores was considered as a representative UCS of a block. Fig. 3a presents a cores after the UCS tests. After the tests, the stress-strain graphs were plotted and the elastic modulus (E) values were calculated at 50% of their maximum strength. The UCS values are given in Table 2.

σt =

0.636 × P (MPa) D×T

(3)

P: Peak load in NewtonD: Sample diameter in mmT: The thickness of the laboratory sample in its center in millimeters

Table 1 Percent components of the blocks were obtained from XRF and Bernard Calcimeter tests.

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10

L.O·I

Na2O

MgO

Al2O3

Sio2

P2O5

SO3

K2O

CaO

TiO2

Fe2O3

Sr

Zr

Carbonate

18.80 17.63 29.56 28.65 22.57 29.88 31.02 25.48 22.98 21.35

0.68 0.74 0.30 0.43 0.56 0.48 0.49 0.25 0.36 0.46

6.54 5.67 3.66 5.74 4.37 3.70 4.15 4.52 6.27 4.53

10.12 11.32 5.85 4.87 9.55 5.56 4.67 6.35 9.35 10.25

35.65 39.63 20.86 17.04 31.65 19.09 18.63 23.68 33.14 34.65

0.14 0.17 0.16 0.08 0.17 0.12 0.09 0.11 0.14 0.15

0.29 0.16 0.44 0.39 0.46 0.65 0.53 0.66 0.26 0.33

1.65 1.95 0.96 0.86 1.68 0.91 1.06 1.16 1.73 1.45

21.56 17.50 34.93 39.49 24.56 36.74 36.56 34.52 21.35 22.45

0.56 0.73 0.29 0.30 0.65 0.41 0.26 0.56 0.51 0.53

3.96 4.41 2.85 1.99 3.71 2.37 2.41 2.58 3.79 3.83

0.05 0.03 0.14 0.16 0.07 0.10 0.13 0.13 0.04 0.03

0.00 0.02 0.00 0.00 0.01 0.00 0.01 0.00 0.02 0.00

40.42 41.21 50.00 75.03 39.33 55.39 64.11 50.00 34.02 37.17

258

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Table 2 Geological and geographical information, physical properties, UCS, BTS and elastic modules (E). No.

M1 M2 M3 M4 M5 M6 M7 M8 M9 M 10

Formation

Abderaz Abderaz Abderaz Mishan Mishan Mishan Mishan Chamanbid Chamanbid Chamanbid

Geological age

Cretaceous Cretaceous Cretaceous Neogene Neogene Neogene Neogene Jurassic Jurassic Jurassic

Dry Density(gr/cm3)

Porosity (%)

6.43 5.89 6.24 4.52 5.49 4.86 6.84 5.84 7.89 8.24

2.46 2.45 2.53 2.56 2.44 2.57 2.54 2.51 2.45 2.42

UCS

BTS

(MPa)

(MPa)

38.12 29.86 46.65 71.05 39.77 62.49 68.39 53.52 23.35 30.5

3.11 2.99 4.73 7.24 3.58 5.38 6.84 6.04 3.18 3.68

E(GPa)

20.76 16.66 28.45 78.28 36.29 64.98 62.55 47.88 13.56 24.25

Kolmogorov-Smirnov test (Razali and Wah, 2011) was used and the significance levels (p-value) in all SCS data were obtained at > 0.05, which results in a normal distribution. Secondly, repeatability and reliability of SCS data were evaluated according to the index of precision (IP) defined by Gill et al. (2005) as follows:

2.2.4. Single compression strength test (SCS) To prepare the samples for conducting SCS tests, blocks were first crushed (Fig. 4a). Since the results are affected by the geometric properties of the samples (Schonert, 1972), to eliminate the shape factor and to investigate the effect of the particles size, spherical samples with 3, 5, 8, 9, and 10 mm in diameter were prepared in accordance to the method proposed by Cheshomi et al. (2013). A total of 50 samples were prepared in 5 different sizes from each block. The SCS tests were carried out by equipment designed by Ahmadi Shshdeh et al. (2011). Next, load-displacement diagrams were plotted (Fig. 4c) and SCSI values were determined. From each block, 10 particles were tested at a given size and the mean values were considered as representative SCSI. As shown in Fig. 4b, most marlstone particles had a triple failure after the SCS test.

M + tβ PI =

M − tβ

S (n − 1) S √ (n − 1)

(4)

where M is the average value of the data, S is standard deviation, n is the number of samples, tβ is the confidence coefficient obtained from the student t-test distribution and is determined by the confidence level (95%). Gill et al. (2005) determined that the value of PI for precise research projects and underground excavation must be < 1.2 and for long-life mining structures and civil engineering works < 1.35. Therefore, precision indexes (PI) were calculated for all samples in 5 different sizes and given in Table 5. As can be seen, the data obtained from SCS tests of marlstone particles in 8 mm, 9 mm, and 10 mm sizes have a PI < 1.2, suggesting that they can be utilized for accurate research projects as well as underground constructions. The SCSI of particles in 3 mm and 5 mm sizes had 1.2 ≤ PI ≤1.35, which firmly proved that the results are repeatable and reliable to be used in civil engineering works.

3. Data analysis The physical properties of the blocks, including dry density and porosity, are measured along with the results of uniaxial tests and given in Table 2. The UCS values are ranging from 23 to 71 MPa. According to Table 3, which illustrates the rock classification based on Deer and Miller's (1966) method, the blocks are very low to moderate considering the uniaxial strength. Moreover, they are also low, in terms of the elastic modulus (E). In Table 4, the results of the SCS tests on the samples prepared from the blocks are presented. The average SCSI values in 10 particles size from each block are considered as representative SCSI of the block.

4.1. UCS-SCSI The UCS-SCSI single-variable regression models for different sizes were plotted, as shown in Fig. 5, and relations 5 to 9 were obtained (Table 6). As can be noted, the significance level (p-value ˂ 0.05) of ANOVA and t-test for all regressions were < 0.05, suggesting that the regression models could effectively predict UCS changes. The highest and lowest coefficients of determination (R2) for UCS_SCSI relationships were for samples with 5 mm and 9 mm diameters, respectively; i.e., R2 = 0.90 and R2 = 0.96. The obtained standard error of UCS estimation was < 5 MPa in all size-dependent regression models. Ultimately,

4. Analyses The purpose of the analysis of the SCS results is to provide the best applicable empirical relationship using the SCSI index for estimating UCS, BTS, and E of marlstone after investigating reliability and repeatability of the obtained data. Firstly, to verify the normal distribution of the data, the

Fig. 3. (a) Marlstone cores after UCS tests, (b) marlstone core while Brazilian test. 259

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Fig. 4. (a) Crushed particles of marlstone, (b) Particles after SCS test, (c) Force-Displacement curve of SCS test.

SCS test, some correlations were established between the SCSI and the Brazilian tensile strength. As shown in Fig. 7, BTS-SCSI correlations were used to predict the BTS using particles of different sizes with an average R2 of 0.89 and standard error < 1 MPa. Eqs. (18)–(22) given in Table 8 present the regression models between these two variables for different sizes. In order to eliminate the size effect and provide a relationship independent of particles size, multivariate regression (similar to the previous section) was used and Eq. (23) was extracted (R2 = 0.63). All p-value values were found to be < 0.05, confirming the 95% validity of the regression models. Since the size of the sample had a significant effect on the Brazilian strength estimation, it is suggested to use size-dependent relationships (Eqs. (18) to (22)) to predict the tensile strength of marlstone. It should be pointed out that all relationships proposed for estimating UCS, BTS, and E can be used only in predicting strength parameters of marlstone and are not usable in other rock types. Moreover, the size of particles can affect the relationships noticeably. Therefore, it is highly recommended using size-related equations for predicting the strength of the particles. Finally, particle shape can play a substantial role in the SCS result. Thus, all particles with an irregular shape should be converted into spherical shapes using RASP manual.

all relationships presented for estimating uniaxial strength using SCSI were acceptable. To propose a relationship incorporating particle size and SCSI parameters simultaneously, a multivariate regression model was developed. Using multivariate regression provides more accurate information on the mechanical properties of rocks (Dehghan et al., 2010; Karakus et al., 2005). In this method, the relationship between independent and dependent parameters is in the form of relation 11: (11)

Y = b0 + b1X + ….+b k Xk

where Y is the dependent variable, X1 … Xk are independent variables, b0 is the constant value, and b1-bk are coefficients of the independent variables. A multivariable regression was established among the sample diameter (D), SCSI and UCS (Eq. 10) for estimation of the uniaxial strength of spherical marlstone particles with a diameter range of 3–10 mm. This relation, which is independent of the particle size, had a lower R2 compared to that of size-dependent relations (Eqs. (5)–(9)). Therefore, although it was possible to provide a size-independent relationship, the accuracy of prediction would decline compared with the relations proposed for a particular size. 4.2. E-SCSI correlations

5. Validation To estimate the elastic modulus of marlstone samples using drill cuttings, some correlation graphs were established between the measured elastic modulus of the samples and the SCSI values in particles with the specified size (Fig. 6) and relations 12 to 16 in Table 7 were obtained. All E-SCSI relationships had R2 values > 0.9 and the significance level of ANOVA and T-student were < 0.05. Additionally, all regression models showed a standard error of estimation < 8 (Gpa), confirming that the E-SCSI regression model can effectively predict the elastic modulus. Likewise, to remove the size effect, the multiple regressions of E, SCSI and sample diameter was used. Accordingly, as shown in Eq. (17), it is possible to propose a relationship with an acceptable significant level (p-value ˂ 0.05) and coefficient of determination (R2 = 0.65). However, the R2 of Eq. (17) compared to Eqs. (12)–(16) declined significantly, it is possible to use Eqs. (17) for different sizes.

In order to validate the proposed empirical relations in this study, 4 marlstone blocks were collected from Mishan, Gachsaran and Aghajari Formations (two blocks from Mishan, one block from Gachsaran, and one block from Aghajari). Then, after preparing the standard cores, they were subjected to uniaxial strength, Brazilian strength, and elastic modulus measurements. Afterward, the blocks were crushed and spherical particles were prepared with diameters of 3, 5, 8, 9, and 10 mm. Next, the SCS tests were carried out on them and the SCSI values were determined. Finally, using the empirical Eqs. (5)–(23), the UCS, BTS, and E values for each sample were predicted. These values are given in Table 9. Fig. 8 compares the measured values (from the standard tests) and predicted values (from the proposed experimental relations in present research). The closer the values are to the 1:1 line, the more accurate the experimental relationships are in the prediction of the strength parameters. According to Fig. 8a, the estimated uniaxial strength values from Eq. (7), which is related to 8 mm size particles, are closer to line 1:1 than

4.3. BTS-SCSI correlations Since most of the marlstone particles had triple failure under the Table 3 Deere and Miller (1966) classification according to UCS and Elastic modulus. Sample No.

UCS (MPa)

Description

M 4, M 6, M 7, M 8, M1, M 2, M 3, M 5, M M9

> 200 100–200 50–100 25–50 1–25

Very hard rock Hard rock Moderately hard rock Weak rock Very weak rock

10

Sample No.

All samples

260

Class

Description

E(GPa)

H

High

> 500

M L

Moderate Low

200–500 < 200

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Table 4 SCS tests result in Newton. No

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10

SCSI (3 mm)

SCSI (5 mm)

SCSI (8 mm)

SCSI (9 mm)

SCSI (10 mm)

Ave

Max

Min

Ave

Max

Min

Ave

Max

Min

Ave

Max

Min

Ave

Max

Min

41.3 36.4 72.5 118.6 53.7 93.7 115.4 76.9 37.8 51.5

56.6 47.3 91.8 141.9 67.9 118.8 147.9 96.5 43.3 65.3

30.7 24.6 54.8 96.4 40.3 68.9 81.4 60.4 26.7 40.3

87.6 94.5 138.3 249.2 98.3 213.9 230.5 153.2 77.3 107.6

105.0 115.2 165.2 315.2 124.7 261.5 278.3 189.9 95.6 135.6

75.8 76.5 119.4 214.1 68.7 178.8 192.0 131.2 66.9 82.7

207.3 190.7 287.4 454.6 235.0 364.7 402.7 285.9 180.0 220.7

241.7 233.1 331.5 524.1 278.9 425.8 459.2 334.2 209.8 271.1

177.5 165.7 240.0 393.5 195.0 311.6 375.7 247.0 155.7 175.3

307.6 276.5 431.5 623.8 338.6 533.5 568.2 431.9 262.2 311.6

368.6 307.4 527.1 715.2 404.2 613.3 664.0 517.4 303.3 360.4

266.3 251.5 373.0 520.9 276.5 466.4 490.1 369.8 226.9 272.6

378.1 368.5 529.5 782.0 448.2 684.5 727.4 518.4 353.3 425.1

429.9 452.1 611.7 921.4 536.2 838.2 899.5 608.5 417.4 523.7

325.7 303.9 453.3 668.2 372.6 594.6 591.8 442.5 280.4 346.2

other equations. The estimated UCS values from Eq. (10), which was obtained from the multivariate regression and was size-independent, had the highest dispersion from line 1:1, thus has a lower accuracy than the relations proposed for particles of a given size. Moreover, as can be seen in Fig. 9, the error of UCS estimation using size-independent equations varies from −0.81 MPa (particle from Block D in 8 mm diameter) to +8.55 MPa (particle from block C in 3 mm diameter), suggesting that size-dependent UCS-SCS relations could predict the uniaxial strength almost accurately. In Fig. 8b, the predicted BTS by 5-mm samples was closer to the line 1:1, with the highest accuracy, while the BTS estimations using Eq. (23), which was size-independent, had the highest dispersion and the least accuracy. The validation error bars in Fig. 10 illustrate that maximum and minimum estimation error of Brazilian tensile strength using SCS test were −1.69 MPa and +0.01 MPa respectively. In Fig. 8c, the E values estimated using Eq. (13), which corresponds to the 5 mm diameter particles, were closer to the line 1:1 with the highest accuracy, while the E values were estimated using the size-independent Eq. (17) had the lowest correlation with the measured values. The error bars in Fig. 11 showed that the relations between E and SCS data have an estimation error varying from 0.66 Gp to 20.91 Gp.

80 70

UCS(MPa)

60 50

3 mm 5 mm

40

8 mm 9 mm

30

10 mm 20 0

200

400

600

800

SCSI(N) Fig. 5. UCS_SCSI correlations. Table 6 UCS-SCSI equations in marlstones, D is diameter of particle, UCS in Mpa and SCS in Newton. Eq. NO

D (mm)

Equation

R2

Std. Error

ANOVA (p-value)

(5) (6) (7) (8) (9) (10)

3 5 8 9 10 3–10

UCS = 0.53 × SCSI +9.28 UCS = 0.25 × SCSI +10.08 UCS = 0.17 × SCSI - 2.44 UCS = 0.13 × SCSI - 5.82 UCS = 0.10 × SCSI - 7.60 UCS = 0 0.121 × SCSI 7.462 × D + 63.98

0.94 0.90 0.94 0.96 0.93 0.66

4.42 4.90 4.36 3.40 4.65 9.55

0.001 0.001 0.001 0.001 0.001 0.001

6. Discussion In order to compare the results obtained in the present study with those of previous works, data from Cheshomi and Ahmadi Sheshdeh (2013) and Cheshomi et al. (2015), which were from single particle loading tests on limestone and sandstone, were used. The method and procedure for performing the loading test in the present study were quite similar to the above-mentioned works. In Table 10, UCS and SCSI values are presented in three types of rock particles with 3 to 5 mm diameters (marlstone, sandstone, and limestone). Diagrams in Fig. 12 were plotted for limestone, sandstone, and marl samples with two

Table 5 CV: observed coefficient of variation, N: number of required samples, PI: precision index of SCS data. Size

(3 mm)

SCSI (5 mm)

SCSI (8 mm)

No.

CV

SD

PI

CV

SD

PI

CV

SD

PI

CV

SD

PI

CV

SD

PI

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 Ave

19.35 20.23 16.44 13.83 16.83 15.31 15.99 14.22 12.90 13.79 15.89

8.5 7.3 12.2 16.9 9.1 15.3 19.4 11.0 5.2 7.8 11.37

1.34 1.36 1.28 1.23 1.29 1.26 1.27 1.24 1.22 1.23 1.27

12.08 15.50 10.44 11.08 17.80 14.65 16.35 13.45 10.51 19.47 14.13

10.73 14.58 17.29 28.58 19.40 32.76 25.66 20.25 8.91 20.27 19.84

1.20 1.26 1.17 1.18 1.31 1.25 1.28 1.23 1.17 1.34 1.24

10.95 12.34 11.47 9.70 10.75 10.06 7.57 11.67 10.55 12.96 10.80

21.2 21.4 33.7 41.9 23.3 34.7 27.9 32.0 17.0 29.0 28.21

1.18 1.21 1.19 1.16 1.18 1.16 1.12 1.19 1.17 1.22 1.18

10.02 6.65 11.34 11.65 10.48 8.25 11.70 11.65 7.06 8.80 9.76

31.7 18.6 49.0 55.3 36.0 50.6 68.4 50.3 23.2 27.9 41.1

1.16 1.11 1.19 1.19 1.17 1.13 1.19 1.19 1.11 1.14 1.16

10.51 12.49 10.35 8.56 12.40 10.19 11.64 10.31 12.04 12.89 11.14

39.7 46.0 54.8 66.9 55.6 69.8 84.6 53.4 42.5 54.8 56.8

1.17 1.21 1.17 1.14 1.21 1.17 1.19 1.17 1.20 1.22 1.18

261

SCSI (9 mm)

SCSI (10 mm)

0.001 0.001 0.001 0.001 0.001 0.001

7

6

5 mm

8 mm

3 9 mm

10 mm

2 400 600 800

SCSI(N)

Fig. 7. Correlations between SCSI and Brazilian test (BTS).

Table 8 BTS-SCSI equations, SCSI (N), BTS (MPa).

Eq. NO D (mm) Equation R2 Std. Error

ANOVA (p-value)

(18) (19) (20) (21) (22) (23)

3 5 8 9 10 3–10

BTS = 0.051× SCSI +1.14 BTS = 0.023× SCSI +1.287 BTS = 0.016× SCSI +0.14 BTS = 0.012× SCSI - 0.1436 BTS = 0.01× SCSI - 0.298 BTS = 0.011× SCSI 0.692D + 6.309

0.93 0.88 0.89 0.90 0.87 0.63

0.42 0.56 0.55 0.52 0.60 0.95

0.001 0.001 0.001 0.001 0.001 0.001

regression models (linear and logarithmic) based on the data in Table 10. As can be seen, the R2 for both models were acceptable. Comparison of rock type in the proposed relationships in this figure shows that the correlation models between UCS and SCSI for rocks with different lithologies were similar; however, by changing the rock type,

262

10

7.43 7.09 6.50 6.27 6.45 13.12

9

0.90 0.91 0.92 0.92 0.92 0.65

8

E = 0.70× SCSI - 9.67 E = 0.33× SCSI - 9.21 E = 0.23× SCSI - 25.91 E = 0.168× SCSI - 29.40 E = 0.139× SCSI - 33.17 E = 0.162 × SCSI – 9.45 × D + 62.84

5

3 5 8 9 10 3–10

31.56 27.60 61.19 58.60 31.56 27.60 61.19 58.60 31.56 27.60 61.19 58.60 31.56 27.60 61.19 58.60 31.56 27.60 61.19 58.60

(12) (13) (14) (15) (16) (17)

4.25 13.85 −5.42 −7.86 −2.94 3.22 −8.33 −9.36 −10.1 −1.65 −9.44 −7.79 −7.28 5.04 2.05 −3.88 0.69 11.3 4.48 7.53

ANOVA (pvalue)

48.16 48.28 50.23 51.71 40.97 37.65 47.32 50.21 33.74 32.78 46.21 51.78 36.63 39.47 57.70 55.69 44.60 45.75 60.13 67.10

Std. Error

−5.88 −4.11 8.55 5.96 4.28 1.67 2.91 0.86 4.97 −3.17 −0.81 −4.72 6.96 −5.57 −3.93 2.15 5.86 −4.58 4.76 2.92

R2

38.03 38.54 47.10 53.61 39.63 32.76 52.74 58.71 38.94 37.60 56.46 64.29 36.95 40.00 59.58 57.42 38.05 39.01 50.89 56.65

Equation

28.30 28.98 40.28 48.88 29.80 20.73 47.11 54.99 30.07 28.26 53.78 64.37 25.88 29.81 55.12 52.33 30.28 31.61 48.13 56.14

UCS

−3.26 1.38 −20.91 −9.72 −1.76 −6.87 −14.08 −3.61 −1.49 0.66 −7.41 5.77 −5.68 2.21 −6.07 −6.27 −1.28 4.01 −13.06 −2.46

Error

43.28 43.43 46.05 48.04 34.74 30.29 43.24 47.10 26.67 25.40 43.37 50.83 31.09 34.88 59.29 56.60 42.29 43.84 63.09 72.43

UCS

14.98 14.45 5.77 −0.84 4.94 9.56 −3.87 −7.89 −3.4 −2.86 −10.41 −13.54 5.21 5.07 4.17 4.27 12.01 12.23 14.96 16.29

Error

Table 7 Correlations between elastic modulus (E) and SCSI.

43.91 34.43 55.65 59.57 43.91 34.43 55.65 59.57 43.91 34.43 55.65 59.57 43.91 34.43 55.65 59.57 43.91 34.43 55.65 59.57

4 4.17 3.83 6.47 5.75 4.17 3.83 6.47 5.75 4.17 3.83 6.47 5.75 4.17 3.83 6.47 5.75 4.17 3.83 6.47 5.75

3.91 3.96 4.78 5.41 4.01 3.37 5.21 5.76 4.03 3.91 5.68 6.42 3.80 4.09 5.89 5.69 4.27 4.36 5.55 6.13

UCS

−0.26 0.13 −1.69 −0.34 −0.16 −0.46 −1.26 0.01 −0.14 0.08 −0.79 0.67 −0.37 0.26 −0.58 −0.06 0.1 0.53 −0.92 0.38

Error

Eqs. (20)–(24)

Predicted BTS using:

4.83 4.84 5.02 5.15 4.15 3.85 4.73 4.99 3.45 3.36 4.58 5.09 3.70 3.96 5.62 5.43 4.41 4.52 5.82 6.46

UCS

0.92 0.88 0.24 −0.26 0.14 0.48 −0.48 −0.77 −0.58 −0.55 −1.1 −1.33 −0.1 −0.13 −0.27 −0.26 0.14 0.16 0.27 0.33

Error

Eq. (25)

90

54.24 55.22 71.35 83.64 118.20 90.74 170.66 194.54 243.40 235.53 346.48 392.53 329.03 352.43 503.11 486.48 456.50 466.07 584.87 642.51

3 mm Error

D (mm)

UCS

Eq. no

Error

Fig. 6. Correlations between SCSI and elastic module (E).

UCS

5 800

A B C D A B C D A B C D A B C D A B C D

200 600

3

0 400

Eq. (19)

SCSI(N)

Eqs. (14)–(18)

10 Measured BTS (MPa)

70

Eq. (12)

200

Predicted E using:

80

Eqs. (7)–(11)

8

Measured E (GPa)

0

Predicted UCS using:

20

Measured UCS (MPa)

30

3 mm 5 mm 8 mm 9 mm 10 mm

SCS(N)

50

Sample ID

60

Particle Diameter (mm)

E(GPa) 40

Table 9 Measured and predicted values using SCS test.

BTS(GPa)

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7 3mm 5mm 8mm 10mm 3-10mm

60 50

6

40 30 20

20

30

40

50

60

70

80

3mm 5mm 8mm 9mm 10mm 3-10mm

5

4

3 3

Estimated UCS (MPa)

a)

3mm 5mm 8mm 9mm 10mm 3-10mm

60

Measured BTS

Measured UCS(MPa)

70

70

Measured E (GPa)

80

4

5 6 Estimated BTS

b)

50 40 30 20 10

7

0 0

10

20

30

40

50

60

70

Estimated E (GPa)

c)

Fig. 8. Comparing measured and estimated values utilizing suggested equations in this study, (a) UCS (MPa), (b) E (GPa) (c) BTS (GPa).

Fig. 9. Error bars of UCS prediction using size-independent equations.

Fig. 10. Error bars of BTS prediction using size-independent equations.

7. Conclusion

the curve position for marlstone was the lowest while it was the highest for limestone. For all the three rock types studied in this work, the curves were close to each other in a low range of strength and with increasing rock strength; the curves get distance from each other. As given in Table 11, The R2 values obtained using linear relations in all 3-mm and 5-mm particles were greater than those of logarithmic relations. In addition, the trend of UCS_SCSI diagrams was similar in marlstone, sandstone, and limestone rocks; except that their location is changed according to the rocks type and this displacement increase with an increase in rock strength.

Due to the difficulties in standard core preparation from marlstone for performing uniaxial strength (UCS) and Brazilian test (BTS) due to cracking and breakage in the open air, the possibility of utilizing single compression strength test (SCS) as a low cost and time-saving test for predicting UCS, BTS, and E were investigated. For this purpose, 14 marlstone blocks were collected from Mishan, Abdderaz, Aghajari, and Gachsaran Formations. After standard core preparation, UCS, BTS, and E of all samples were measured according to ASTM standard. Then, the samples were crushed and spherical particles were prepared with diameters of 5, 3, 5, 8, 9, and 10 mm. A total of 600 spherical samples were 263

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10 5.77 4.01

Error of 'E' peridiction(GPa)

5

2.21

1.38

0.66

0 -5

-1.76-1.49 -3.26

-1.28

-2.46

-3.61

-5.68

-6.07 -7.41

-6.87

-10

-6.27 -9.72

-15

-13.06

-14.08

3mm 5mm 8mm 9mm 10mm

-20 -20.91

-25

Fig. 11. Error bars of elastic modulus prediction using size-independent equations.

Table 10 Values were used for comparing present study with previous achievements, UCS in MPa and SCSI in N. Marlstone

Sandstone

Limestone

UCS

SCSI (3 mm)

SCSI (5 mm)

UCS

SCSI (3 mm)

SCSI (5 mm)

UCS

SCSI (3 mm)

SCSI (5 mm)

41.34 37.35 72.55 118.58 53.67 93.66 115.41 76.88 37.80 51.48

38.13 29.87 46.65 71.06 39.77 62.50 68.40 53.53 23.35 30.50

87.58 94.54 138.25 249.21 98.29 213.87 238.13 153.19 77.33 107.60

73.29 234.30 59.32 12.26 50.57 76.80 52.95 171.22 143.44 79.97

61.23 220.67 81.35 29.56 51.06 66.65 34.38 170.00 108.44 75.00

169.97 573.47 176.33 21.19 95.57 176.09 125.30 429.12 264.82 182.32

196.91 245.98 191.58 93.29 177.18 50.56 44.72 105.73 97.22 248.46

272.8 262.9 225.13 187.35 228.1 90.6 35.4 166.35 118.09 260.45

465.73 583.72 390.55 234.43 434.55 119.61 81.64 270.59 198.9 553.37

400

350

350 300

Sandestone

250

Limestone

200 150

250

Limestone

200 150

50 0

0 0

100

200 300 SCS (N)

a)

400

500

0

600

50

100

b)

350

150

200

250

300

SCS (N) 350

300

5 mm

300

250

UCS (MPa)

UCS (MPa)

3 mm

Sandestone

100

100 50

200 150

Marlstone

100

3 mm

250 200 150

Marlstone Sandestone Limestone

100

Sandestone

50

50

Limestone

0

0 0

c)

Marlstone

300 UCS (MPa)

UCS (MPa)

5 mm

Marlstone

200

400

600

0

800

d)

SCS (N)

50

100

150

SCS (N)

Fig. 12. UCS_SCSI correlations of different lithologies, (a) and (b) logarithmic, (c) and (d) linier. 264

200

250

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Table 11 UCS_SCSI correlations of different rock types. D (mm) 3

5

Linier equations Marlstone Sandstone Limestone Marlstone Sandstone Limestone

y = 0.64 × SCSI y = 0.92 × SCSI y = 1.21 × SCSI y = 0.53 × SCSI y = 0.39 × SCSI y = 0.30 × SCSI

prepared (500) particles for testing and 100 particles for validation) and SCS tests were conducted. The main results of the present study can be outlined as follows:

Logarithmic equations 2

R = 0.88 R2 = 0.93 R2 = 0.78 R2 = 0.83 R2 = 0.96 R2 = 0.86

y = 19.47e0.0115 SCSI R2 = 0.87 y = 31.774e0.0089 SCSI R2 = 0.88 y = 58.178e0.007 SCSI R2 = 0.68 y = 56.807e0.0031 SCSI R2 = 0.73 y = 33.103e0.0037 SCSI R2 = 0.88 y = 19.941e0.0054 SCSI R2 = 0.84

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- SCSI values increased by an increase in the carbonate content of marlstone samples. - Empirical relationships for UCS-SCSI, BTS-SCSI, E-SCSI with R2 of 0.90, 0.87, and 0.9, respectively, were obtained. - Although it is possible to suggest a size-independent relation using multi-variation regression, the obtained R2 was lower than that of size-dependent relationships. - The accuracy of all suggested relations in the present study was evaluated using T-Student and ANOVA statistical tests, which validated the significance level of SCSI variables in the estimation of UCS, BTS, and E. - The data obtained from SCS tests of marlstone particles in 8 mm, 9 mm, and 10 mm sizes show a precision index (PI) < 1.2, which firmly proves that the results were repeatable and reliable to be used in research projects and underground excavation. While SCS of particles in 3 mm and 5 mm sizes show a precision index of 1.2 ≤ PI≤1.35, which is appropriate for civil constructions. - Verification of results proved that the predicted values of UCS, BTS, and E in the present study correlated closely with the measured values using standard tests. - By comparing the obtained data from the present study with the similar data were proposed for limestone and sandstone rocks, a graph was produced to demonstrate the effects of grain size on the empirical UCS-SCSI relationships. It is evident from the graph that rock type and its strength range could affect the suggested relations between SCSI obtained from single particle loading test and UCS. References Akazawa, T., 1953. Tension test methods for concretes, international union of testing and research laboratories for-materials and structures (RILEM). Paris, Bulletin 16, 11–23. Akili, W., Torrance, J.K., 1981. The development and geotechnical problems of sabkha, with preliminary experiments on the static penetration resistance of cemented sands. Q. J. Eng. Geol. Hydrogeol. 14 (1), 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-Sanad, H., Al-Bader, B., 1990. Laboratory study on leaching of calcareous soil from Kuwait. J. Geotech. Eng. 116 (12), 1797–1809. Azadan, P., Ahangari, K., 2013. Evaluation of the new dynamic needle penetrometer in estimating uniaxial compressive strength of weak rocks. Arab. J. Geosci. https://doi. org/10.1007/s12517-013-0921-6. Azimian, A., Ajalloeian, R., 2015. Empirical correlation of physical and mechanical properties of marly rocks with P wave velocity. Arab. J. Geosci. 8, 2069–2079. Berenbaum, R., Brodie, I., 1959. Measurement of the tensile strength of brittle materials. Br. J. Appl. Phys. 10 (6), 281. Carneiro, F.L.B., 1943. Concrete tensile strength, international union of testing and research laboratories for materials and structures (RILEM). Paris, Bulletin 13, 97–123. Chen, F.H., 1988. The Basic Physical Properties of Expansive Soils. In: Proc. 3`d Int. Conf. on Expansive Soils, Haifa, Israel. Cheshomi, A., Ahmadi-Seshde, E., Galandarzade, A., 2012. Introducing single particle loading apparatus and repeatability of the results. Iranian J.Eng.Geol5 17–32 (Persian Language). Cheshomi, A., Hajipour, G., Hassanpour, J., Dashtaki, B.B., Firouzei, Y., Sheshde, E.A., 2017. Estimation of uniaxial compressive strength of shale using indentation testing. J. Pet. Sci. Eng. 151, 24–30. Cheshomi, A., Mousavi, E., Ahmadi-Sheshde, E., 2015. Evaluation of single particle loading test to estimate the uniaxial compressive strength of sandstone. J. Pet. Sci.

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