Introduction

Drillability is an important factor that affects the drilling rate and tool wear. Therefore, various rock properties should be taken into account when determining the drillability (Thuro 1997). Understanding the individual effects of rock properties on the drillability is essential if we are to improve the planning of underground excavations (Dahl et al. 2012). The drilling rate index (DRI) is by far the most important rock drillability parameter; it is commonly used to predict performance in drill and blast tunneling (Dahl et al. 2010; Zare and Bruland 2013; Yasar et al. 2015). The DRI is also a classification parameter in several models for estimating TBM performance. The Norwegian University of Science and Technology (NTNU) model is among the most commonly used models for estimating TBM performance based on the DRI (Dahl et al. 2007, 2012; Zare and Bruland 2013).

Although many studies (Lien 1961; Howarth and Rowland 1987; Bruland et al. 1995; Ersoy and Waller 1995; Thuro and Spaun 1996; Thuro 1996, 1997; Kahraman et al. 2000; Bilgin and Kahraman 2003; Akun and Karpuz 2005; Singh et al. 2006; Hoseinie et al. 2008; Yaralı 2008; Dahl et al. 2010; Yaralı and Kahraman 2011; Dahl et al. 2012; Yarali and Soyer 2013; Saeidi et al. 2013; Capik et al. 2013; Demirdag et al. 2014) have focused on rock drillability, only a few attempts have been made to determine the relationships between the DRI and rock properties. Recently, Yaralı and Soyer (2013) presented an excellent study of the relationships between the DRI and some mechanical properties. However, in the study described in the present paper, we determined the relationships between the DRI and some physical properties, including the apparent porosity and void ratio. We also obtained new regression models for estimating the DRI from physicomechanical rock properties. These modeling results should prove helpful for the rapid estimation of rock drillability.

Studies

Field studies

This study was carried out in the Cankurtaran and Salmankas tunnels in Turkey. The Cankurtaran Tunnel is a highway tunnel that is being constructed in the Artvin province of Turkey. It will be one of the longest highway tunnels in Turkey (5228.00 m long) when the construction is finished. The tunnel consists of two tubes, with each tube containing two lanes of traffic (one in each direction). The Salmankas Tunnel is another highway tunnel that is currently being constructed; it is located on the border of the Gumushane and Bayburt provinces of Turkey. This tunnel again consists of two tubes, each 4150.00 m in length. The locations of these tunnels are shown in Fig. 1.

Fig. 1
figure 1

Locations of the Cankurtaran and Salmankas tunnels

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Schmidt rebound hardness measurements were taken at the tunnel faces using two test devices (yielding N-type and L-type impact energies of 2.207 and 0.735 Nm, respectively). The tests were performed in accordance with ISRM (1981) and ASTM (2005) suggested methods. The types of Schmidt rebound hammer used in the study and the tunnel area in which the measurements were taken are shown in Fig. 2a and b, respectively.

Fig. 2
figure 2

a L- and N-type Schmidt rebound hammers (digital Proceq, Silver Schmidt) and calibration anvil; b tunnel area in which the measurements were taken

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Rock samples from 43 different areas of the tunnels were obtained for laboratory tests. Detailed information on the rock samples are provided in Table 1.

Table 1 Types and locations of rock samples
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Laboratory studies

Drillability tests

The DRI was assessed on the basis of two laboratory tests, the Sievers J-miniature drill test and the brittleness test (Bruland 1998; Dahl et al. 2007). A diagram of the DRI assessment is shown in Fig. 3. The classification scheme used for the DRI values of rocks is shown in Table 2.

Fig. 3
figure 3

Diagram showing the DRI assessment (Dahl 2003)

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Table 2 Classification scheme used for the DRI (Dahl 2003)
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The Sievers J-miniature drill test was originally developed by Sievers in the 1950s. The Sievers J-value is a measure of rock surface hardness or resistance to indentation. It is defined as the mean value of the drill hole depth (in units of 0.1 mm) after 200 revolutions of a 8.5-mm miniature drill bit under a weight of 20 kg. The SJ test is normally performed as 4–8 drillings. The number and placement of the drill holes is determined by the heterogeneity and the variations in the texture of the rock sample. The standard procedure is to use a pre-cut surface of the sample which is perpendicular to the foliation of the rock. The Sievers J-value is hence measured parallel to the foliation (Dahl 2003; Dahl et al. 2012). An outline of the Sievers J-value test and the test equipment used is shown in Fig. 4.

Fig. 4
figure 4

a Outline of the Sievers J-value (SJ) miniature drill test (Dahl 2003); b Sievers J-value test equipment

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The brittleness (S 20) test method was originally developed in Sweden by Matern and Hjelmer in 1943. The original test was initially intended as a means to determine strength properties of aggregates, but several modified versions of the test have since been developed for various purposes. The version of the S 20 test developed for the determination of rock drillability has been used since the end of the 1950s. The test is normally performed on three equal extracts from the 11.2–16.0 mm fraction. For a measured specimen density of 2.65 g/cm3, each extract should have a mass of 500 g. An outline of the equipment used in the brittleness test is shown in Fig. 5 (Dahl 2003; Dahl et al. 2012).

Fig. 5
figure 5

a Outline of the brittleness (S 20) test (Dahl 2003), b brittleness test equipment

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Physicomechanical properties

Uniaxial compressive strength (UCS)

The UCS tests were performed on prepared core samples with length-to-diameter ratios of 2–2.5. The applied stress rate was 0.5–1.0 MPa/s, and five core samples from each rock were subjected to the UCS test. The tests were carried out using an electro-hydraulic servo-controlled stiff press testing machine. The tests were carried out according to ISRM (1979) and ASTM (2010a) suggested methods.

Brazilian tensile strength

The Brazilian tensile strength test method consists of loading a disc of the rock until failure occurs across the diametric axis. The disc was prepared from 54-mm diameter (NX) core samples with a length-to-diameter ratio of 1:2. A loading rate of 200 N/s was applied. The tests were carried out using an electro-hydraulic servo-controlled stiff press testing machine. The test was conducted on ten samples of each rock type and the results were averaged. The tests were performed in accordance with ISRM (1981) and ASTM (2010a) suggested methods.

Point load strength

The point load strength test is intended as an index test for the strength classification of rock materials. The test was performed on core samples with a length-to-diameter ratio of 1:2. The load was steadily increased such that failure occurred within 10–60 s. The test was invalidated if the fracture surface passed through only one loading point. The point load strength test was repeated at least ten times for each rock type, and the average value was recorded as the point load strength. The tests were carried out according to ISRM (1985) suggested methods.

Physical properties

The physical properties of the rock, such as its apparent porosity and void ratio, were determined in accordance with ASTM (2010b). The apparent porosity and void ratio were evaluated for core samples with a diameter of 54 mm and a length-to-diameter ratio of 1:2 (Franklin et al. 2007).

Results and discussion

Linear relationships between the DRI and physicomechanical rock properties are depicted in Fig. 6. The figure shows that there are high correlations between the DRI and the UCS, point load strength, and Brazilian tensile strength. The DRI decreased with increasing UCS, point load strength, Brazilian tensile strength, and L-type and N-type Schmidt rebound hardness. The DRI also increased with the increasing apparent porosity and void ratio. It should also be noted that the correlation coefficients for the DRI with RL ASTM(2005) and RN ASTM(2005) were greater than those for the DRI with RL ISRM(1981) and RN ISRM(1981).

Fig. 6
figure 6

Relationships between the DRI and physicomechanical properties of rock

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Using the relationships between the DRI and the physicomechanical rock properties, the following models (Eqs. 1–9) were developed for estimating the DRI. The determination coefficients (R 2) of the models ranged from 0.67 to 0.84. The models based on point load strength and UCS showed better forecasting performance than the other models.

$${\text{DRI}} = - 0.3089\sigma_{\rm c} + 72.515\quad (R^{2} = \, 0.83)$$
(1)
$${\text{DRI}} = - 4.1505{\rm Is}_{50} + 71.005\quad \left( {R^{2} = \, 0.84} \right)$$
(2)
$${\text{DRI}} = - 2.5623\sigma_{\rm t} + 75.514\quad \left( {R^{2} = \, 0.76} \right)$$
(3)
$${\text{DRI}} = - 1.4934RL_{{{\text{ISRM}}(1981)}} + \, 136.32 \quad (R^{2} = \, 0.70)$$
(4)
$${\text{DRI}} = - 1.2556RL_{{{\text{ASTM}}(2005)}} + \, 111.62 \quad (R^{2} = \, 0.73)$$
(5)
$${\text{DRI}} = - 1.4148RN_{{{\text{ISRM}}(1981)}} + 30.93 \quad \left( {R^{2} = \, 0.67} \right)$$
(6)
$${\text{DRI}} = - 1.2571RN_{{{\text{ASTM}}(2005)}} + \, 111.25 \quad \left( {R^{2} = \, 0.73} \right)$$
(7)
$${\text{DRI}} = 9.2942n + \, 28.302 \quad \left( {R^{2} = \, 0.72} \right)$$
(8)
$${\text{DRI}} = 8.6937e + \, 29.111 \quad \left( {R^{2} = \, 0.69} \right),$$
(9)

where σ c is the uniaxial compressive strength (MPa), Is 50 is the point load strength (MPa), σ t is the Brazilian tensile strength (MPa), n is the apparent porosity (%), e is the void ratio (%), RL ISRM(1981) and RL ASTM(2005) are the L-type Schmidt rebound hardness according to the ISRM (1981) and ASTM (2005) suggested methods, and RN ISRM(1981) and RN ASTM(2005) are the N-type Schmidt rebound hardness according to the ISRM (1981) and ASTM (2005) suggested methods.

The study results were compared with the results of Yarali and Soyer (2013), who tested 32 sedimentary, igneous, and metamorphic rocks and suggested that there were linear correlations between the DRI and mechanical rock properties. Similar trends were observed between the DRI and rock properties in both studies, as depicted in Fig. 7. However, the higher determination coefficients of the models proposed in the current study indicate that they give better prediction performance for the DRI.

Fig. 7
figure 7

Comparison of the results of this study with the results of Yarali and Soyer (2013)

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The proposed models were validated using the F and t tests in SSPS 20.0. The F and t tests were carried out to check the validity of the whole model and the independent variable involved in the model, respectively (Aydin et al. 2013a). If the t value calculated in SPSS is greater than the tabulated t value (obtained from a t distribution table), the independent variable in the model is considered to be significant. If the F calculated by SPSS is greater than the tabulated F value (obtained from a F distribution table), the model is accepted as valid (Berman and Wang 2011; Aydin et al. 2013b; Aydin 2014). As can be seen from Table 3, at the 95% confidence level, the computed t values are greater than the tabulated t values, suggesting that the developed models are statistically valid. Also, at the 95% confidence level, the computed F values are greater than the tabulated F values, indicating the correctness of the models.

Table 3 Validation of the developed models
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Conclusions

The DRI is a reliable measure of rock surface hardness. The following conclusions can be drawn from the present study:

  • The DRI decreases with increasing UCS, point load strength, Brazilian tensile strength, and Schmidt rebound hardness. It was also found to increase with increasing apparent porosity and void ratio.

  • The modeling results showed that the models that included point load strength and UCS give the best DRI-forecasting performance.

  • The derived models can be successfully used to predict the DRI.

Further studies could focus on the mineralogical properties of rocks such as granite in order to determine their effects on the DRI. The mineralogical properties that most strongly influence the DRI could be determined, and the DRI could be modeled as a function of these properties. The estimation of the DRI could also be investigated with multiple regression analysis, neural networks, or another metaheuristic search. The results of the different methods could be compared with simple regression analysis to gauge the performance of the proposed models.