Introduction

The mechanical behavior of rocks is of great importance to such investigations regarding open-pit and underground mining applications, tunneling, and extraction of natural resources such as coal, petroleum, natural gas, and hydrocarbons. In this respect, the fracture evolution of rocks stemming from drilling–blasting, excavation methods, and in situ stress states takes an important part in assessing the stability, reliability, and sustainability of those applications. Attempts to understand fracture mechanism around a rock mass have mainly involved laboratory investigations of rock materials, physical models as well as numerical analyses. On a theoretical basis, fracture evolution of rock materials under axial loading conditions is typically divided into four stages. These are crack initiation (1), crack propagation (2), unstable crack growth (3), and failure (4), each of which occurs at specific stress states [1, 2]. Crack initiation represents the stress level (σci, MPa), where the first microfracture occurs in the rock itself. After the σci has been reached, secondary cracks are initiated with progressive loading, which is called crack propagation. The crack damage stress (σcd, MPa) describes the point, where unstable crack growth commences followed by crack propagation. At the end of the σcd, fracture evaluation in a rock material ends up with a failure (Fig. 1).

Fig. 1
figure 1

(modified after [1])

Schematic representation of different stages of fracture evolution in a rock material under axial loading

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Recently, the physical meaning and interpretation of stress state corresponding to crack initiation and damage have been investigated profoundly with a view to several rock engineering approaches. The σci was used in excavation damage and stability analyses of several rock masses [3,4,5,6]. Martin and Christiansson [7] suggested that the σci could be drawn on estimations of the in situ spalling strength of crystalline rock masses. Damjanac and Fairhurst [8] pointed out that the σci could also be utilized for the evaluation of long-term behavior of crystalline rocks.

Jiang et al. [9] performed several numerical analyses to investigate the effects of water jet applications on the fracture evolution of rocks. According to the numerical analyses, the researchers pointed out that crack initiation and propagation are key parameters to water jet applications. Lu et al. [10] indicated that controlling hydraulic fracturing and permeability of coal measure rocks could be possible with a branched tree-type borehole array whose performance has a link to crack initiation of rocks.

Liu et al. [11] expressed that higher values of σci could give rise to lower penetration rates of tunneling boring machines (TBMs). Niu et al. [12] performed extensive research on sandstones that was focused on the variations in the σci due to freezing–thawing (FT) cycles. The researchers demonstrated that the σci decreased substantially due to progressive FT cycles. They consequently claimed that the variations in σci values could be a complementary parameter in such rock engineering applications in cold regions.

The quantifications of σci and σcd under axial loading are mainly conducted based on two different methods. The first method deals with stress–strain curves of rock materials, where axial (εz), lateral (εx), and volumetric strain (εv = 2εx + εz) has been regarded [1, 13,14,15,16,17,18,19].

The latter covers cumulative acoustic emission (CAE) counts varying throughout the axial loading [2, 20,21,22,23,24]. In general, the σci and σcd are mainly defined as a function of uniaxial compressive strength (UCS, MPa) of rocks. Typical intervals of σci and σcd are listed in Table 1. It was reported in such previous studies that a number of factors have influences on the σci and σcd. The main factors are mineralogical and textural features, rock weathering, mechanical properties as well as loading conditions (i.e., uniaxial or triaxial loading).

Table 1 Typical values of σci and σcd under uniaxial compression for several rock types
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Erişiş et al. [24] found that increasing the ground mass (Gm) in basaltic rocks results in an increase in the σci. For igneous rocks, the increase in alkali feldspar (K-Feld.) minerals escalates the σci, whereas those in plagioclase (Plg) and biotite (Bt) lower the σci [25]. On the other hand, for sedimentary rocks (i.e., shale, calcareous shale, and argillaceous shale) cracks are initiated at higher stress levels when the carbonate content is greater than that of clay content (Cc) [25]. Basu and Mishra [27] found that increasing effective porosity (ne, %) and rock weathering in granites lower the σci.

Similar to what Nicksiar and Martin [25] stated, Ündül et al. [29] reported that the increase in the Bt quantities of andesitic rocks decreases the σci. In addition, using mineral contents of Plg, amphibole (Amp), and Gm, the researchers determined a positive correlation between the ratio of \( \left( {{\text{Plg}} + {\text{Amp}}} \right) / {\text{Gm}} \) and the σci.

Köken [31] demonstrated that textural features of limestones have effects on their stress–strain behaviors. Nicksiar and Martin [32] performed discrete element analyses to investigate factors affecting crack initiation in low-porosity crystalline rocks and concluded that the sorting degree of grains in the rock samples modeled has enormous impacts on the peak and crack initiation stresses. For dolomitic rocks, the increase in grain size and porosity also cause a decrease in the σci [33]. However, increasing grain size in granitic rocks has enormous impacts on the σcd rather than the σci [34]. Backers and Stephansson [35] and Haeri et al. [36] reported that crack propagation has a link to KII type fracture toughness as a mechanical property. The σci and σcd were also investigated by triaxial compression tests [19, 37,38,39]. Accordingly, the σci increases remarkably in parallel with confining pressure (σ3, MPa).

The above-mentioned studies put into different perspectives on the applicability and importance of crack initiation and propagation for issues relating to rock engineering practices. The present study aims to explore the fracture evolution of the coal measure sandstones located in the Zonguldak Hardcoal Basin (ZHB, Zonguldak/Turkey) under axial loading conditions. Eight types of coal measure sandstones with different textural and mineralogical features were considered. Mineralogical and textural features of the sandstones were explored by different quantitative approaches. Fundamental physical and mechanical properties were determined for each rock type. Based on the stress–strain relations of the rocks, the variations in σci and σcd were investigated.

Materials and Methods

Representative rock blocks of the sandstones were obtained from several underground coal mines in the ZHB, and they were used to prepare rock samples for laboratory studies. The determination of physical [i.e., dry unit weight, γd (kN/m3), and effective porosity, ne (%)], and mechanical properties [UCS (MPa), pulse wave velocity, Vp (km/s), tangential Young modulus, Eti (GPa), and tangential Poisson’s ratio, vti] was conducted in accordance with the suggestions of International Society of Rock Mechanics [40]. For this purpose, representative rock blocks were drilled using a drill core with a diameter of 54.7 mm (Fig. 2a). Following the drilling procedure, cylindrical core samples were prepared for each rock type (Fig. 2b). The physical and mechanical rock properties were determined, using core samples with a length-to-diameter ratio of 2.0–3.0 under oven-dried conditions.

Fig. 2
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Laboratory equipment and materials used in laboratory studies. a Drilling procedure, b some of the cylindrical samples prepared, c pulse wave velocity test, d determination of UCS, Eti, and vti

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The pulse wave velocity (Vp, km/s) of the sandstones was determined using a Pundit Plus ultrasonic testing apparatus (Fig. 2c). For each rock sample, ten measurements of pulse waves were recorded and average values were presented. The UCS and static elastic constants (i.e., Eti and vti) were determined using a stiff loading machine whose stress rate was within the limits of 0.5–1.0 MPa per second. In order to measure lateral and axial displacements, linear variable differential transformers (LVDT) were utilized (Fig. 2d).

Since previous methods (i.e., Lajtai [1], Brace et al. [13], and Stacey [14]) estimating the σci necessitate drawing tangential lines, these methods could be declared somewhat subjective or variable according to users [18, 41]. Therefore, more precise and objective methods to estimate the σci were adopted in the present study. These are lateral strain response (LSR) method [17], objective volumetric strain response (OVS) method [18], and relative compression strain (RCSR) method [19].

The implementation and calculation steps of the above-mentioned methods are illustrated in Fig. 3. The implementation of the above-mentioned methods starts with the determination of σcd. Practically, the σcd represents the stress state corresponding to the point of εv reversal [13]. Establishing a reference line between the zero point (i.e., σz = 0) and the σcd, the strain differences between the reference line and relevant axial stress–strain curve (e.g., lateral strain difference plotted with red line segments, ΔLSR) were calculated for several axial stress states. The variations in strain differences as independent variables form a parabola [e.g., f (σz) = t1x2 + t2x + t3], and the peak of this parabola is defined as the σci (i.e., σci = −t2/2t1). In the light this description, the σci was determined using the methods given in Fig. 3.

Fig. 3
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Quantitative strain-based methods adopted in this study to define the σci. a LSR method [17], b OVS method [18], c RCSR method [19]

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Mineralogical and textural features of rock materials were investigated through thin sections, X-ray diffraction (XRD), and Fourier transform infrared (FTIR) analyses. In those analyses, quantities of rock-forming minerals and textures properties (i.e., grain size, sorting of grains) were determined. Furthermore, the number of Cc in the sandstones was also investigated through scanning electron microscope (SEM) analyses.

The XRD analyses were carried out, using a Bruker D8 diffractometer, whereas FTIR and SEM analyses were performed through a Thermo Scientific Nicolet 6700 spectrometer and Gemini SEM 300 analyzer, respectively. In addition, textural properties of rock materials were investigated through modal analyses of thin sections.

For each rock sample, four thin sections (two pieces at bottom and upper surfaces) perpendicular to loading direction were prepared. In thin section observations, the point-counting method was adopted to quantify rock-forming minerals. The XRD patterns were analyzed, using Panalytical Highscore Plus software with a database of PDF 2, so that the quantities of rock-forming minerals were determined semiquantitatively.

The FTIR patterns were also utilized to reveal common rock-forming mineral types and possible cement type of the sandstones. Wavenumbers (cm−1) obtained from the FTIR analyses were compared with the XRD patterns, thin section analyses, and relevant previous studies as well. Based on the quantities of rock-forming minerals, the sandstones were classified according to Folk [42].

Texture-based variations in the sandstones were revealed, considering the sorting coefficient (Sc) and average grain size (d50, mm). The determination of the Sc deals with calculating surface areas of rock-forming minerals and analyzing them for specific areas occupied in thin sections. The surface area of any rock-forming mineral is digitized using MATLAB R2019a and determined by the following equation:

$$ A = \frac{1}{2}\left| {\sum\limits_{i = 1}^{n} {x_{i} \left( {y_{i + 1} } \right)} - \sum\limits_{i = 1}^{n} {y_{i} \left( {x_{i + 1} } \right)} } \right| $$
(1)

where xi and yi are digitized coordinates of the boundary surfaces.

For specific areas in each thin section (e.g., 30–45 mm2), surface areas of rock-forming minerals were determined and analyzed statistically. Based on the assumption that the anhedral grains could be acknowledged somewhat spherical or elliptical for sandstones, the surface area determined by Eq. 1 was equalized to the area of a circle in two dimensions.

Consequently, the Sc is determined by the following equations:

$$ D_{\text{e}} = \sqrt {\frac{4A}{\pi }} $$
(2)

where De is the equivalent diameter of the grain (mm) and A is the surface area of the grain (mm2) determined by Eq. 1.

$$ \varphi = - \log_{2} \left( {D_{\text{e}} } \right) $$
(3)

where φ is the size value of the grain; De is in mm.

$$ S_{\text{c}} = \frac{{\varphi_{84} - \varphi_{16} }}{4.0} + \frac{{\varphi_{95} - \varphi_{5} }}{6.6} $$
(4)

where φ95, φ84, φ16, and φ5 represent the size values at 95%, 84%, 16%, and 5% at cumulative percentages, respectively [43].

Laboratory Studies

Mineralogical and Textural Properties

Typical thin sections, SEM images showing the presence of clay content, XRD, and FTIR patterns of the sandstones are given in Fig. 4. From mineralogical and textural points of view, it is obvious that the sandstones differ from one another. Based on the mineralogical inspections, mineralogical compositions of the sandstones are given in Table 2.

Fig. 4
figure 4figure 4

Typical thin sections, SEM images, XRD, and FTIR patterns of the sandstones [Qtz quartz, Plg plagioclase, K-Feld. alkali feldspar, Prx pyroxene, Bt biotite, Cal calcite, Chl. chlorite, Op opaque minerals, Cl. clay minerals, F feldspar (including both Plg and K-Feld. minerals), LF: lithic fragment (including Prx., Bt., Cal., Op., etc.)]

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Table 2 Mineralogical composition of the sandstones
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According to the classification of Folk [42], the sandstones were identified, varying from Sublitharenite to Lithic arkose. The cement type of the sandstone mainly comprises the mixture of silica and clay particles lower than 20 µm.

Focusing on the SEM and FTIR analyses, it was determined that the Cc in the sandstones differs at average rates of 2–10%. The types of clay particles are mainly illite, montmorillonite, and sometimes kaolinite.

In the FTIR patterns, clay particles are typically characterized with wavenumbers between 3418 and 3819 cm−1, whereas siliceous minerals (quartz, feldspar, etc.) are characterized by wavenumbers ranged from 582 to 1163 cm−1. Calcium-based mineral associations (i.e., calcite, aragonite, Ca–rich plagioclases) are observed at wavenumbers between 1417 and 2832 cm−1.

The modal analysis results are given in Table 3. The d50 of the sandstones was found to be between 0.061 and 0.741 mm. Based on the Sc classification of Folk and Ward [43], the sandstones were identified as from moderately well to very poorly sorted. Furthermore, during modal analyses, it was determined that the increase in LF contents results in achieving higher Sc values. However, combining the values given in Tables 2 and 3, it could be claimed that there is no remarkable relationship between the Sc and Cc.

Table 3 Modal analysis results of the sandstones
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Physical and Mechanical Properties

The physical and mechanical properties of the sandstones are listed in Table 4. It was determined that the UCS of the sandstones is between 54 and 167 MPa. The ne is approximately between 0.8 and 8.0%. The Vp of the sandstones varies from 2.50 to 4.60 km/s. The static elastic constants of Eti and vti vary also between 10–38 GPa and 0.12–0.28, respectively. Typical stress–strain curves of the sandstones are given in Fig. 5.

Table 4 Physical and mechanical properties of the sandstones
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Fig. 5
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Typical stress–strain curves of the sandstones

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Using these stress–strain curves of the sandstones, the σci and σcd were determined according to the methods mentioned previously in “Materials and Methods” section. As a result, the σci and σcd were found to be in the range of 0.27–0.43 and 0.61–0.83 of the UCS, respectively. In general, it was determined that the σci and σcd correspond to 0.37 and 0.71 of the UCS, respectively.

Results and Discussion

Effects of Mineralogical and Textural Features on the σci and σcd

It was determined that the fracture evolution of the sandstones is associated with the variations in mineralogical and textural features. For instance, the σci and σcd decrease with increasing the d50, Sc, and contents of F and LF, whereas they increase in parallel with Qtz content. The effects of mineralogical and textural features on the strength properties are summarized in Table 5.

Table 5 Pearson’s correlation matrix of the mineralogical and textural features
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It can also be seen in Table 5 that the ratio of σcd/σci(mean) increases with increasing the Sc and d50. Since the higher values of Sc describe heterogeneity in the rock itself, the σci and σcd decrease with increasing the Sc (Fig. 6a). Increasing d50 also acts on the σci and σcd in a similar manner to that of the Sc (Fig. 6b). From mineralogical perspectives, the increase in the content of LF also poses heterogeneity in the rocks and therefore reduces the strength properties (Fig. 6c).

Fig. 6
figure 6

Variations in σci and σcd due to several mineralogical and textural features. a The Sc, b the d50, c the content of LF

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The decrease in σci and σcd arising from textural and physico-mechanical properties might be interpreted, referring to release surfaces enlarged exponentially in the rock itself and therefore dislocation of grains during axial loading. As given in Fig. 6, though the interrelation between the Sc and d50 is not obvious, their variations together could provide satisfactory results in assessing the heterogeneity in the sandstones. The adverse effects of increase in grain size on strength properties of various rock types were also reported by several researchers [3, 25, 33, 34, 44,45,46]. From this aspect, the findings given in Fig. 6 are in good agreement with these studies.

Effects of Physico-Mechanical Features on the σci and σcd

Laboratory studies showed that the σci and σcd increase with decreasing ne, whereas they increase with increasing the properties of γd, UCS, Vp, and Eti (Table 6). In particular, the first cracks in the rock itself were initiated much earlier when the ne of rocks exceeds 3% (Fig. 7a). When it comes to the changes in Vp values, remarkable changes in the σci and σcd were obtained when the Vp exceeds 3.00 km/s (Fig. 7b). In the direction of these findings, apart from the UCS, it could be claimed that fracture evolution of the sandstones could also be assessed, considering the variations in ne and Vp values.

Table 6 Pearson’s correlation matrix of the physico-mechanical properties
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Fig. 7
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Variations in σci and σcd due to several physical and mechanical properties. a The ne, b the Vp

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Moreover, it was also revealed that the crack initiation and propagation in the sandstones are independent from the Modulus ratio (MR: Eti/UCS). However, the fracture evolution of the sandstones seems to be associated with the static elastic constants of Eti and vti (Table 6). The remarkable changes in σci and σcd corresponding to the conditions of ne ≥ 3% and Vp ≥ 3.00 km/s could be declared the threshold values that might pave the way for estimations relating strata control and stability analyses of the longwalls and galleries whose roof strata of longwalls located in the ZHB are composed of the investigated sandstones.

Statistical Analyses

Based on the mineralogical analyses and laboratory test results (Tables 2, 3, 4), statistical analyses were performed. Excluding the UCS as an independent variable, statistically remarkable relationships are listed in Table 7. In general, the statistical analyses indicated that textural features of sandstones could take a part in the assessment of crack initiation for the sandstones.

Table 7 Statistical analysis results
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In view of the fact that the correlation of determinations (R2) for Eqs. 2 and 3 (0.58 and 0.61, respectively) is greater than those of Eqs. 10 and 11 (0.48 and 0.50, respectively), it is clear that the textural features of d50 and Sc are relatively more influential in estimating the σci rather than the σcd. Similar results could also be observed, comparing the R2 of Eq. 14 (0.67) with that of Eq. 15 (0.53). In the light of this finding, it is possible to state that the textural features are reasonable factors that affect crack initiation of the sandstones investigated.

In terms of mineralogical effects on fracture evolution of the sandstones, the increase in the LF content gives rise to pose heterogeneity that has similarities with the effects of Sc. Therefore, its increase lowers the σci and σcd (Eqs. 1 and 9 in Table 7). As for the mineralogical and physico-mechanical features, the σci could be predicted reliably, using Eqs. of 1 and 5–8. However, other relationships such as Eqs. 9 and 13 could be utilized to predict the σcd (Table 7).

According to the strain-based methods to quantify the σci, it was statistically determined that the OVS method provides σci values approximately 4% lower than those of the LSR and RCSR methods (Eqs. 17, 18). On the other hand, the methods of LSR and RCSR methods provide nearly similar results (Eq. 18).

Links to Utilization of Mineralogical and Textural Features for Underground Excavations in the ZHB

In the direction of the previous studies [3,4,5,6,7], it seems logical to suppose that crack initiation could be explored for V-cut gallery blasting operations and overburden analyses in the ZHB. In this respect, the findings obtained from the present study could contribute to those of applications.

According to practices on V-cut gallery blasting operations in the ZHB, it could be acknowledged that mineralogical and textural analyses in the direction of sandstone lithofacies for underground coal mining are not taken into consideration. However, focusing on systematical records of mineralogical and textural features, practical experiences and data could be collected for relevant engineers in the ZHB. With the help of these systematical records through sampling/logging, an example of which is illustrated in Fig. 8, the optimization of explosive consumption in a gallery blasting could be explored.

Fig. 8
figure 8

Simplified illustration of systematical data recording for the assessment of V-cut gallery blasting optimization

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In Fig. 8, a gallery face, which is composed of a single sandstone stratum and observed frequently in the ZHB, is given as Case I. For single but various sandstone lithofacies, crack initiation stress thresholds in conjunction with rock mass classifications [47, 48] could be a key parameter for the optimization of gallery blasting operations and overburden control. Within this scope, present and upcoming gallery faces should be explored profoundly from mineralogical and textural perspectives. It may cover several stages including a dataset, where the amount of explosive consumption and its blasting pattern per V-cut operation, the quantitative data intentionally blanked for other sandstone lithofacies in Fig. 8, amount of face advance after blasting and overburden observations might be present. Thanks to this comprehensive dataset, sensitive analysis could be carried out for the optimization of V-cut gallery blasting operations.

On the other hand, considering the presence of lithological changes followed by face advance (e.g., the transition between Case I and Case II in Fig. 8), stability analyses in conjunction with rock mass fracturing beyond the acceptable excavation line and over breaking minimization in gallery blasting operations could also be performed. In this context, stability considerations given by Gerçek [49] could be highly appreciated. Last but not least, hydraulic fracturing applications could be enhanced or further investigated, considering rock mineralogy and texture for various sandstone facies.

Conclusions

The present study investigates the factors affecting the fracture evolution of the sandstones located in the ZHB. For this purpose, detailed mineralogical and textural analyses were performed on eight coal measure sandstones. Physico-mechanical properties of the rocks were determined. The σci and σcd were determined for each rock type, considering quantitative strain-based methods. The laboratory studies indicate that mineralogical, textural, and physico-mechanical features have substantial effects on the σci and σcd. The other results obtained from the present study could be drawn as follows:

  • The σci and σcd are found to be at average rates of 0.37 and 0.71 of the UCS, respectively (Table 4). The σci and σcd decrease with increasing the Sc, d50, F, LF of the rocks. On the other hand, increasing Qtz content leads to increase those variables (Table 5). Remarkable changes are determined in those variables when the ne and Vp exceed 3% and 3.00 km/s, respectively (Fig. 7).

  • When comparing the strain-based methods to quantify the σci, it was determined that the OVS method provides σci values approximately 4% lower than those of the LSR and RCSR methods do. The methods of LSR and RCSR methods provide more or less similar results (Table 7).

  • With the purpose of utilizing the mineralogical and textural features in underground mining applications in the ZHB, several suggestions related to V-cut gallery blasting operations were given. Considering the achievements obtained from the present study, V-cut gallery blasting operations could be optimized. Thus, the amount of explosive consumption during V-cut operations and overburden problems could be handled elaborately. However, V-cut blasting applications/case studies are required to examine whether rock texture and mineralogy would be effective as much as the laboratory test results obtained.

  • It should be mentioned that the laboratory studies were performed under oven-dried conditions. Considering the saturation degree of the rock materials, fracture evolution of rocks should also be investigated by further studies. By this way, the relationship between mineralogy and dehydration of rocks could be explored in terms of fracture mechanics.

  • Since underground coal mining applications in the ZHB are gradually carried out at greater depths, the fracture evolution of the rocks should be investigated by triaxial compression tests.