1 Introduction

Unconventional natural gas resources (coalbed methane, tight gas, shale gas, etc.) are the most competitive alternative for their large reserves and low-carbon emissions (Hafezi et al. 2021; Liu et al. 2022a). In China, huge amounts of unconventional natural gas resources are stored in coal measure strata, particularly in the Linxing–Shenfu gas field. In detail, Linxing–Shenfu gas field is located at the junction of Yishan Slope and Jinxi Fold Belt in the northeast of Ordos Basin, where the Carboniferous Benxi formation, the Permian Taiyuan formation and Shanxi formation are the predominant pay zones in coal measure strata (Fig. 1). The total gas reserves of major pay zones in the Linxing–Shenfu gas field have proven unconventional natural gas geological reserve exceeding 1 × 1011 m3 (Ju et al. 2017; Mi and Zhu 2021; Wang et al. 2019). The efficient exploitation and utilization of the resources are of great strategic significance to meet the energy needs of economic and social development as well as reduce global warming challenges (Hamza et al. 2021; Yuan et al. 2015).

Fig. 1
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Geo-lithologic profile of coal measure strata in the Linxing–Shenfu gas field, Ordos Basin

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Coal measure strata can be characterized by low permeability and strong heterogeneity. It contains diverse lithologies with thinly interbedded layers, such as coal, sandstone, and mudstone, which are superimposed longitudinally and intercrossed horizontally for each other (Fig. 1). Hence, it is difficult to exploit the single layer effectively and commercially. Multilayer hydraulic fracturing and commingled production are common methods to increase single-well production and decrease exploitation costs in coal measure strata (Fu et al. 2022; Hu et al. 2020). However, the complicated in situ stress states, substantial geomechanical differences and strong heterogeneity among different layers make it difficult to predict and control the fracture propagation path accurately and design the hydraulic fracturing pumping scheme reasonably (Li and Wu 2022; Tang et al. 2019), and thus resulting in lower efficiency and inadequate stimulation of multilayer hydraulic fracturing in coal measure strata. The measurement of the geomechanical properties of such rocks paves the way for the sustainable development of unconventional gas reservoirs.

Geomechanical testing is a widely used and effective method to investigate the mechanical properties of rocks (Shi et al. 2021; Tomac and Sauter 2018). Many researchers have employed laboratory mechanical testing to investigate the strength, deformation and failure behaviors of layered rocks at a macro-scale level. Based on laboratory uniaxial compression tests, Liu et al. (2015) investigated the effect of rock strength on the deformation behavior and fracture mode of rock–coal–rock composite samples, and they found that the peak strain of composite samples decreased with the growth of rock strength and the difference in Young’s modulus between different layers determined the deformation behaviors and failure patterns of the composite samples. Lu et al. (2020) studied the influence of layer thickness on the mechanical properties of layered coal–rock combined samples under laboratory triaxial compression tests. The results showed that the strength of combined samples enhanced with the increase of the thickness of the stiff rock layer. Moreover, Yin et al. (2021) clarified the effect of the lithologies (sandstone–coal, shale–coal) on the mechanical strength and failure modes of the layered rocks under uniaxial loading. They found that the coal was splitting ejection failure, while the shale and sandstone exhibited tensile failure or tensile–shear composite failure. To date, most of the previous laboratory investigations have been performed on inch-sized combined samples. However, in many cases, it is difficult to meet the requirements of rock size for macroscopic geomechanical testing since the unavailability of inch-sized cores or challenges in the coring process (Liu et al. 2018).

The nanoindentation technique provides a choice to measure the mechanical properties (such as Young’s modulus, hardness and fracture toughness) of heterogeneous geomaterials since the advantages of small sample size and optional sample geometry (Graham et al. 2021; Kossovich et al. 2020; Shi et al. 2020; Sobhbidari and Hu 2021; Wang et al. 2021). For instance, Liu et al. (2016) studied the mechanical properties of shale samples by using the nanoindentation technique, and they found that the higher the clay mineral content and the larger the pore structures, the lower the Young’s modulus. According to the deconvolution approach, Sheng et al. (2022) divided Young’s modulus and hardness obtained by nanoindentation tests of shale into three mineral phases. They also found that the overall Young’s modulus and hardness of the sample enhanced with the growth of the burial depth and corresponding in situ stress. Generally, the sedimentary rocks consist of multiple minerals, such as quartz, dolomite and clay minerals. Investigating the mechanical responses of constituent minerals is crucial for understanding multiscale rock behaviors. Some innovative investigations have been conducted to measure the mechanical responses of minerals. For instance, Cheng et al. (2022) investigated the mechanical properties of constituent minerals in shale samples based on the nanoindentation testing and SEM–EDS method. They found that quartz exhibited elastic deformation, whereas the carbonates and clay minerals mainly displayed plastic deformation. The similar findings were also observed in the recent investigation (Liu et al. 2022b).

In short, most of the above-mentioned attempts analyzed the mechanical strength, deformation behaviors and fracture modes of coal–rock combined samples using macroscopic geomechanical testing. However, the downhole thinly interbedded sandstone–mudstone core rocks are rarely investigated, and the deformation behaviors and failure modes are still unclear under in situ stress conditions. Besides, the mineralogical variability and multiscale heterogeneity of rocks indicate that measuring the mechanical responses is intrinsically difficult (Charlton et al. 2021). To the best of our knowledge, the mechanical responses and indentation patterns of individual minerals and the interactions among multiple minerals are not yet clear, which can provide insights into the rock heterogeneity.

In this paper, we focused on the downhole thinly interbedded sandstone–mudstone core rocks (layered core rocks) from typical coal measure strata in the Linxing–Shenfu gas field. Since the thin thickness of each layer in the layered core rocks, the mechanical properties of adjacent layers in layered core rocks were quantified through grid nanoindentation tests. On this basis, the high-resolution scanning electron microscopy and energy-dispersive spectroscopy (SEM–EDS) techniques combined with advanced mineral identification and characterization system (AMICS) were carried out to provide the visual mineralogies of adjacent sandstone and mudstone layers, then the residual indent impressions and the corresponding mechanical responses of individual minerals and multiple minerals were quantified. Finally, the bulk mechanical properties and failure modes of the layered core rocks were investigated under in situ stress conditions based on the laboratory conventional triaxial compression tests. The present work can provide further understanding and reliable input data for multiscale geomechanical modeling and designing hydraulic fracturing pumping schemes in coal measure strata.

2 Materials and Methods

2.1 Sample Preparation

The layered core rocks were collected from the Taiyuan formation (2055.6 m) in the Linxing–Shenfu gas field, Ordos Basin. It can be found that the layered core rock contains the sandstone layers and the mudstone layers (argillaceous interlayers, black parts of the core rock in Fig. 2). For grid nanoindentation tests, the sandstone and mudstone samples were first sliced at the adjacent layers in the same core with a size of 8 × 6 × 4 mm (length × width × height), and then the finely polishing step was required to minimize the impact of surface roughness. First, the sample was polished by sandpapers with meshing from 200# to 4000# to ensure that the sample was coarsely polished and surface roughness was lower than 0.5 μm. Furthermore, the argon ion milling was used to finely polish the sample with a 5° polishing angle and a 2.5 mA current. The above polishing process would make the sample surface achieve great flatness. Besides, the quantitative mineral compositions were interpreted by X-ray diffraction (XRD), and it can be used as a reference to identify the elemental information and mineral interpretation obtained by SEM–EDS. In addition, the standard cylinders with a size of Φ25 × 50 mm were drilled perpendicular to the interlayer direction by wire cutting machine for conventional triaxial compression tests (Fig. 2).

Fig. 2
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Workflow of mechanical properties testing for the thinly interbedded sandstone–mudstone core rock

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2.2 Grid Nanoindentation Tests

The grid nanoindentation tests were used to determine the mechanical properties of sandstone layer and mudstone layer in the layered core rock due to the small intervals between them (Fig. 2). Two regions of each sample were randomly selected for grid nanoindentation tests, and the indentation grid of each region was set to 7 × 9 with a grid spacing of 100 μm to acquire adequate data. The grid nanoindentation tests were carried out with Agilent Nano Indenter G200 at room temperature and ambient pressure. The maximum penetration depth of the device is 500 μm with a resolution of 0.01 nm, and the load resolution is 50 nN. The routine three-sided pyramid Berkovich diamond indenter, with an angle of 65.27° between the centerline and the three faces, was selected to evaluate the modulus and hardness of rocks (Bor et al. 2019). The continuous stiffness measurement (CSM) mode was used to obtain the variation process of Young’s modulus and hardness with penetration depth continuously and efficiently (Hay et al. 2010; Oliver and Pharr 2004). The grid nanoindentation tests were running with a penetration depth of 3000 nm, holding time of 10 s, and strain rate of 0.05 s−1 for a frequency of 45 Hz. In this paper, the Poisson’ ratio of tested samples was assumed to be 0.30.

The nanoindentation process and typical load–displacement curve of homogeneous materials as shown in Fig. 3, including the loading, holding and unloading stages. The loading stage can be regarded as the combination of elastic and plastic deformation. The holding stage is necessary to reduce the error caused by the cohesion between the indenter tip and samples. The unloading stage can be seen as the recovery of the pure elastic deformation, which is usually chosen to calculate the Young’s modulus and hardness of different constituents (Liu et al. 2018). In nanoindentation tests, the total energy (Ut) is composed of elastic energy (Ue) and plastic energy (Up) (Cheng et al. 2002), as the enclosed area shown in Fig. 3b. The elastic energy is induced by the pure elastic deformation, whereas the plastic energy is caused by the pure plastic deformation and energy dissipation that induced micro-cracks. In this paper, the energy dissipation caused by micro-cracks creation was not considered since the unknown complex crack geometries in nanoindentation tests.

Fig. 3
figure 3

Principles of grid nanoindentation tests. a Schematic of the penetration by indenter tip, b schematic of the typical load–displacement curve and related energy. Ut, Ue and Up are the total energy, elastic energy, and plastic energy, respectively. Pmax is the maximum load of the indenter, hmax, hf and hc are the maximum penetration depth, residual depth and contact depth, respectively

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2.3 SEM–EDS Technique

The high-resolution scanning electron microscopy and energy-dispersive spectroscopy (SEM–EDS) techniques can provide a quantitative and direct mapping of the mineral distributions and indent impressions in the indentation region. In this work, the ZEISS Merlin field emission environment scanning electron microscopy (FE-SEM) equipped with Bruker XFlash6|30 energy-dispersive spectroscopy (EDS) was used to identify the indentation morphology and mineral composition of the typical area. The resolutions of SEM and EDS were 0.9 nm and 127 eV, respectively. First, the indent impressions of the indentation region can be captured by a high-resolution area scanning technique. Then, the atomic compositions of the corresponding region were analyzed by EDS at the micro-scale and the final mineral mapping was interpreted by advanced mineral identification and characterization system (AMICS) (Zhong et al. 2019; Schulz et al. 2020).

2.4 Conventional Triaxial Compression Tests

The bulk mechanical properties and failure modes of the layered core rocks can be obtained by conventional triaxial compression tests with different confining pressures of 0 MPa, 10 MPa, 20 MPa and 30 MPa. The conventional triaxial compression tests were performed on the TRA-1500 high-temperature and high-pressure rock rheometer in the Rock Mechanics Laboratory of China University of Petroleum (Beijing). The displacement-control mode was chosen and the loading rate was 0.06 mm/min. The sample was wrapped with the thermoplastic sheath before the testing, and the stress–strain curves and rock failure patterns were recorded during and after the testing, respectively.

3 Results and Analysis

3.1 Mineral Compositions of Different Layers

The primary mineral compositions of the sandstone layer and the mudstone layer interpreted by XRD and EDS are displayed in Fig. 4. It can be observed that the main mineral types interpreted by EDS are consistent with the XRD results, while the proportions are different. It is related to rock heterogeneity and the principles of the test method. In detail, XRD is a bulk-sensitive analytical method that can indirectly infer the volume percentages of each mineral phase through the mass fractions, while the EDS interpretations are based on the atomic structures and compositions of the surface in the detected region. Overall, quartz and clay minerals (kaolinite, illite and chlorite) are the most dominant contents both in the sandstone layer and the mudstone layer. Besides, there exist some minor contents of components in samples, such as pyrite, rutile, and apatite. The mineral compositions are the key factors to impact the mechanical properties of rocks. Generally, quartz, feldspar and pyrite belong to brittle minerals with strong deformation resistance and chemical stability. On the contrary, phyllosilicate minerals, including clay minerals and muscovite, can be regarded as ductile minerals that can be characterized by weak mechanical strength and chemical instability (Zhang et al. 2018). Compared with the sandstone layer, the mudstone layer has a higher content of ductile minerals, while lower content of brittle minerals, which results in substantial differences in overall mechanical strength and deformation behavior between the sandstone layer and mudstone layer.

Fig. 4
figure 4

Mineral compositions: a in the samples by XRD; b in the detected regions by EDS

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The mineral distributions of typical regions obtained by the SEM–EDS technique can be seen in Fig. 5. It is observed that the characteristics of mineral particles vary among different layers, which is related to the sedimentary environment and history (Groves et al. 2005; Wang et al. 2020). The sandstone layer contains a lot of coarse-grained particles and they appear as clusters. In contrast, the mudstone layer consists of fine-grained particles and they are sparsely distributed on the clay matrix. In addition, kaolinite is the most dominant composition in clay minerals of the tested samples. Notably, the samples are heterogeneous geomaterials that consist of diverse minerals and micro-structures based on the SEM–EDS mapping. The above results provide the essential precondition for identifying the minerals of the typical indentation region in SEM–EDS analysis.

Fig. 5
figure 5

The SEM images and mineral distributions of the typical indentation regions. a, b Sandstone sample, c, d Mudstone sample. Note: The white triangles denote the indentations

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3.2 Mechanical Responses and Indent Impressions of Different Layers

3.2.1 Mechanical Properties of Different Layers

The Young’s modulus and hardness induced by nanoindentation tests are sensitive to the indentation depth, as shown in Fig. 6. With the increase of indentation depth, the Young’s modulus and hardness gradually decrease and finally converge to a certain value with small fluctuations after the indentation depth reached 2000 nm. This indicates that the indentation area has reached the mineral-scale (Luo et al. 2020). Note that since the higher stiffness and strength of quartz in the sandstone layer, the load–displacement curves reached the load threshold of the device (800 mN) before the indenter reached the preset penetration depth (see Fig. 8a), thus entering the unloading stage in advance (red ellipses in Fig. 6). In this paper, the mean statistical method was used to calculate the mechanical parameters at the indentation depth of 2000–3000 nm, as listed in Table 1. Overall, the magnitudes of mechanical properties of the sandstone layer are higher than that of the mudstone layer. The mean Young’s modulus and mean hardness of the sandstone layer are 1.28 times and 2.40 times larger than that of the mudstone layer, respectively. The substantial differences are largely related to their mineral compositions. Generally, the higher the brittle mineral content, the greater the strength and stiffness of the rock (Li 2022). The sandstone layer has a higher content of brittle minerals (such as quartz and k-feldspar) and lower content of ductile minerals (such as clay minerals and muscovite) compared with the mudstone layer. Therefore, the sandstone layer has a stronger ability to resist deformation and failure than that of the mudstone layer. Although not all minerals can encounter the indenter since the randomly distributed minerals, the comparison based on the adequate indentation data can provide qualitative knowledge for mechanical properties between sandstone and mudstone layers.

Fig. 6
figure 6

The Young’s modulus/hardness–displacement curves of grid nanoindentation tests

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Table 1 The statistical data of mechanical properties for different layers
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The distributions of mechanical properties in different layers show diverse performances, and it can fit the Weibull model well, as illustrated in Fig. 7. Here, the coefficient of variation (COV, ratio of standard deviation to mean value, dimensionless) was used to evaluate the degree of data dispersion. Compared with the sandstone layer, the data dispersion of the mudstone layer is relatively lower due to its relatively smaller COV, implying the lower probability of indenter pressing into different minerals in the mudstone layer, which is consistent with the mineral distribution characteristics of the mudstone layer. Notably, the substantial mechanical differences among indentations confirm the strong heterogeneity of different layers since the variation in the mineral compositions and distributions. Consequently, those key factors can affect the strength, deformation and failure behaviors of the layered rocks from the macroscopic perspective.

Fig. 7
figure 7

The distributions of mechanical properties of different layers. a Young’s modulus, b hardness

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3.2.2 Mechanical Responses of Typical Minerals

Rock is a kind of heterogeneous geomaterial that consists of diverse minerals and micro-structures. Since the heterogeneous particle sizes and mineral distributions and the limitation of the same grid spacing of nanoindentation tests, the indenter cannot press into all the minerals (Fig. 5). In particular, the indenter can press into a single mineral or multiple minerals simultaneously at a micro-scale in nanoindentation tests, and the latter is often the case, especially in mudstone layer. In this work, the indenter falls into a single mineral is called as the single mode. When the indenter encounters multiple minerals simultaneously, it is classified as the mixed mode.

The load–displacement curves are vital references for analyzing the mechanical responses of materials. The typical load–displacement curves of the single mode and the mixed mode are shown in Fig. 8. When indentation is inside a single mineral, the load–displacement curve of quartz in the sandstone layer is smooth without abnormal phenomena, and the peak load is the highest (Fig. 8a). In contrast, the peak loads of k-feldspar, hematite and kaolinite are lower than that of the quartz in the sandstone layer and decreased successively, whose load–displacement curves are fluctuant since the occurrence of “pop in” and “elbow” events. In general, the “pop-in” event occurs in the loading stage, which is caused by the creation of cracks or embedded in micro-structures. The “elbow” event is generated in the uploading process, and it is induced by the material expansion due to the phase transformation (Domnich et al. 2000; Liu et al. 2016). Compared with the sandstone layer, the peak load of quartz in the mudstone layer is relatively lower. The “pop in” and “elbow” events can also be found in the quartz and kaolinite in the mudstone. When indentation is inside multiple minerals, due to heterogeneous stress distributions and deformation behaviors among multiple minerals, the “pop in” and “elbow” events are inclined to be generated (Fig. 8b).

Fig. 8
figure 8

The load–displacement curves of typical minerals. a Single mode, b mixed mode. Q Quartz, KF K-feldspar, H Hematite, K Kaolinite, Q-K Mixed quartz–kaolinite, KF-K Mixed k-feldspar–kaolinite, H-K Mixed hematite–kaolinite)

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Mechanical responses of minerals display different performances, the hardness, Young’s modulus, residual depth ratio and plastic work ratio of typical minerals in the sandstone layer are illustrated in Fig. 9. In the single mode, quartz has the highest hardness and Young’s modulus with the mean values of 9.57 GPa and 84.06 GPa, respectively. On the contrary, kaolinite has the lowest hardness and Young’s modulus with the mean values of 0.80 GPa and 47.56 GPa, respectively. In contrast, k-feldspar and hematite have the medium hardness and Young’s modulus. Compared with the k-feldspar, the hardness of hematite is relatively lower, whereas the Young’s modulus is relatively higher. On one hand, since the Young’s modulus represents the resistance to elastic deformation, whereas hardness measures the resistance to plastic deformation. The aforementioned inconsistency may be related to the crystal structures of k-feldspar and hematite. On the other hand, due to the hematite being distributed in clusters (Fig. 5b), the surrounding soft minerals can also affect the mechanical properties of hematite.

Fig. 9
figure 9

The hardness, Young’s modulus, residual depth ratio and plastic work ratio of minerals in the sandstone layer. a Hardness. b Young’s modulus. c Residual depth ratio. d Plastic work ratio. Q Quartz, KF K-feldspar, H Hematite, K Kaolinite, Q-K Mixed quartz–kaolinite, KF-K Mixed k-feldspar–kaolinite, H-K Mixed hematite–kaolinite)

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To relate the mineralogy to the mechanical responses, we compared residual depth ratio (ratio of residual depth to maximum indentation depth, hf/hmax) and plastic work ratio (ratio of plastic energy to the total energy, Up/Ut) to identify the elastic-dominated or plastic-dominated deformation behaviors of minerals. In general, the higher the residual depth ratio, the larger the irreversible deformation of the minerals. The results show that the residual depth ratio of quartz is the lowest, followed by k-feldspar and hematite, and kaolinite has the largest residual depth (Fig. 9c). It is opposite to the variation trends of the hardness of minerals. In detail, the residual depth ratios of quartz and k-feldspar are lower than 0.50, which indicates that elastic deformation is predominant. In contrast, the irreversible plastic deformation dominated in hematite and kaolinite since the residual depth ratios are larger than 0.70. The magnitudes and variations of the plastic work ratio also confirm the above-mentioned conclusions, as illustrated in Fig. 9d. The plastic work ratio of quartz is the smallest with a mean value of 0.38, followed by k-feldspar with a mean plastic work ratio of 0.43. It indicates that the elastic energy is predominated in quartz and k-feldspar during nanoindentation that induced elastic deformation. Since the effect of surrounding soft minerals (such as kaolinite), the plastic behavior of hematite is noticeable. Besides, kaolinite is also dominated in plastic behavior with a mean plastic work ratio of 0.81, which is related to the laminar micro-structures.

When indentation covers multiple minerals, the magnitudes of mechanical properties of minerals in a mixed mode are between the soft and hard minerals that correspond to the single mode. For instance, compared with the mixed quartz–kaolinite minerals (Q-K), the hardness and Young’s modulus of quartz are higher 453.18% and 33.68%, respectively, and those values of kaolinite are lower 53.76% and 24.36%, respectively. The same conclusions can be observed in the mixed k-feldspar–kaolinite (KF-K) and mixed hematite–kaolinite (H-K), as illustrated in Fig. 9. This suggests that the mechanical properties of minerals in the mixed mode are mainly determined by soft minerals at the micro-scale. Moreover, with the growth of hardness and Young’s modulus of the hard minerals, the overall mechanical properties of minerals in the mixed mode can be enhanced. This can be explained by the variation trends of hardness and Young’s modulus of minerals in the mixed mode (such as Q-K, KF-K and H-K). In addition, the deformation behaviors of minerals in the mixed mode are also plastic-dominated. The residual depth ratio and plastic work ratio of minerals in the mixed mode are between the hard and soft minerals in the corresponding single mode, which is consistent with the variation of hardness.

Minerals exhibit various mechanical responses in different layers. The comparison of hardness, Young’s modulus, residual depth ratio and plastic work ratio of minerals in different layers are shown in Fig. 10. Compared with sandstone layer, quartz in mudstone layer has the lower hardness and Young’s modulus, with mean values of 2.43 GPa and 55.40 GPa, respectively. Although the residual depth ratio of quartz in different layers is similar, the plastic work ratio is different. Quartz in mudstone layer mainly displays plastic deformation behavior with a mean plastic work ratio of 0.64. The differences in the mechanical properties of kaolinite and mixed quartz–kaolinite (Q-K) between the sandstone layer and the mudstone layer are relatively smaller. The deformation behavior of kaolinite and mixed quartz–kaolinite (Q-K) are also plastic-dominated. Since the lower hardness and Young’s modulus of quartz in the mudstone layer, the residual depth ratio and plastic work ratio of mixed quartz–kaolinite are higher, and the plastic behavior is severer. The substantial differences in the same mineral phases between the sandstone and mudstone layers are related to the different sedimentary and diagenetic environments (Bjørlykke 2014).

Fig. 10
figure 10

The comparison of hardness, Young’s modulus, residual depth ratio and plastic work ratio of minerals in different layers. a Hardness. b Young’s modulus. c Residual depth ratio. d Plastic work ratio. Q Quartz, K Kaolinite, Q-K Mixed quartz–kaolinite)

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3.2.3 Indentation and Cracking Patterns of Typical Minerals

The elastic and plastic deformations were generated during the indenter pressing into the sample surface. The initiation and growth of defects (micro-cracks and dislocations) in the deformation area depend on the plastic energy dissipation. In the nanoindentation tests, the cracking events can also be captured by SEM images, although the occurrence of cracks should be avoided as much as possible. The indent impressions of typical minerals and the related sketches are illustrated in Fig. 11. When the indentation is inside a single mineral, the indent impression is a regular triangle with three equal-length edges (Fig. 11v). Moreover, it is apparent that the indent impressions are seriously different among various minerals. In particular, the indent impression of quartz in the sandstone layer is the smallest at the same magnification (Fig. 11a–c), followed by k-feldspar and hematite (Fig. 11g–i). In contrast, the indent impression of kaolinite is the largest in the sandstone layer (Fig. 11j–l). The same phenomenon can also be found in the mudstone layer (Fig. 11d–f, m–o).

Fig. 11
figure 11

The indent impressions and their sketches of the typical minerals. D Dolomite, H Hematite, K Kaolinite, KF K-feldspar, P Pyrite, Q Quartz. Rectangles stand for the laminar cracks; Ellipses represent the radical cracks)

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The ultimate indent impressions are the direct performances of the micro-structures and mechanical properties of minerals. For indentations of minerals in the sandstone layer, the “sink-in” events can be found around the sides of the indent impressions in quartz and k-feldspar (Fig. 11a–g). This is caused by the elastic recovery in the sides of the indentation, while the corners did not in the process of unloading (Wu et al. 2016). The aforementioned mismatched deformation results in the occurrence of shear cracks around the indentation boundary. Moreover, since stress concentration occurs at the indenter corners during the loading, the radical cracks were prone to initiate with higher stiffness and lower plastic work ratio, especially for brittle minerals such as quartz and k-feldspar (ellipses in Fig. 11), which is consistent with the previous research results (Liu et al. 2022b). This is because brittle minerals generate less plastic work and smaller irreversible deformation during the process of indentation.

In contrast, since the higher plastic work ratio in hematite and kaolinite, the elastic recovery is not apparent and the radical crack cannot be found (Fig. 11h–l). It is worth mentioning explicitly that the chipping damage can be found adjacent to the edges of indentations in the minerals except for quartz in the sandstone layer. On one hand, since the shear stresses and interactions among radial cracks, parts of materials will detach from the bulk (Bor et al. 2019). On the other hand, it is related to the cementation strength among multi-compositions or micro-structures. For instance, kaolinite is a 1:1 layered silicate mineral that consists of the two-dimensional arrangement of alumina octahedral sheet (Si2O52−) and silica tetrahedral sheet ([Al2(OH)4]2+), and the layered structures are bonded together by hydrogen bonds (Cao et al. 2021). The compaction and slipping phenomena can be found in sheet structures of kaolinite, along with the occurrence of laminar cracks adjacent to the indentation during the indenter loading, and the proportions of them were chipped due to the weak cementation (rectangles in Fig. 11). Besides, the orientation of the mineral particles substantially impacts the mechanical properties. For instance, the hardness and Young’s modulus of kaolinite changed with the angles between the sheet structures and the indenter (Fig. 11j–o).

As for indentations of minerals in the mudstone layer, quartz exhibits medium-plastic deformation behavior due to the lower hardness and Young’s modulus, and the size of indent impressions is larger than those in the sandstone layer (Fig. 11d–f). Compared with quartz in the sandstone layer, the number or length of radical cracks and shear cracks of quartz in the mudstone layer decline and the elastic recovery is relatively weaker. The differences in indent impressions of kaolinite between the sandstone layer and the mudstone layer are minor since they have similar mechanical responses (Fig. 11g–o). The chipping damage can also be found both in quartz and kaolinite in the mudstone layer.

When the indentation covers multiple minerals simultaneously (mixed mode), since the variations in mechanical properties and micro-structures among adjacent minerals, the indenter tends to press toward the soft minerals with lower stiffness and strength. This is an important reason why the mechanical properties of minerals in the mixed mode are mainly determined by the soft mineral phases. Consequently, irregular indent impressions were formed. For instance, when the quartz and kaolinite were under the indenter simultaneously (Fig. 11p, s–u), since the higher Young’s modulus and hardness of the quartz than that of the kaolinite, the kaolinite experienced larger deformation under the same loadings. As a result, the edge length of the indentation located on the kaolinite side was longer. Besides, the chipping damages are prone to be generated on the soft minerals side, whereas radical cracks are also inclined to occur in stiff minerals. The indent impressions for the indenter located at the mixed k-feldspar–kaolinite (KF-K) and mixed hematite–kaolinite (H-K) are also consistent with the above phenomena (Fig. 11q–r).

In short, the permanent residual impressions are the reflections of the micro-structures and mechanical properties of minerals. The higher is the stiffness of the mineral, the lower the plastic work ratio and residual depth ratio of indentation, and the smaller the irreversible indent impression. Furthermore, the crystal structures and the orientation of mineral particles greatly affect the mechanical behaviors and utilize indentation characteristics of minerals, which are the key reasons for rock heterogeneity. Based on the above analysis, a schematic of indentation and cracking patterns is summarized in Fig. 12, including elastic-dominated, medium-plastic, and plastic-dominated indentation patterns. The elastic-dominated pattern shows the smallest indent impressions with noticeable elastic recovery and radical cracks, such as quartz and k-feldspar in the sandstone layer. In contrast, the plastic-dominated pattern displays relatively larger indent impressions and apparent chipping damages, such as hematite and kaolinite. Different from the elastic-dominated deformation of quartz in the sandstone layer, quartz in the mudstone layer mainly shows medium-plastic patterns because of the lower mechanical properties and higher plastic energy. When the indentation occupies multiple minerals simultaneously, the indent impressions in the mixed mode are more complicated and the deformation directions are highly dependent on the locations of soft minerals. This can provide evidences in the mineral scale for the statement that the strength, deformation and failure behaviors of layered rocks mainly depend on the weak layers at the macro-scale (Chen et al. 2019; Yin et al. 2021).

Fig. 12
figure 12

Schematic of indentation and cracking patterns observed in the nanoindentation tests

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3.3 Bulk Mechanical Properties and Failure Modes of Layered Rocks

3.3.1 Strength and Deformation Characteristics

The bulk mechanical properties and stress–strain curves of layered rocks in conventional triaxial compression tests are shown in Table 2 and Fig. 13. Similar to the typical stress–strain curves of rock specimens under compressive loading, the stress–strain curves of the layered rock can be divided into five stages, including (1) crack closure or initial compaction, (2) linear elastic deformation, (3) crack initial and stable growth, (4) crack damage and unstable growth, and (5) ultimate failure (Hoek and Martin 2014; Li et al. 2021). Under the unconfined compression condition, the layered core rock entered the linear elastic deformation stage after a long initial compaction stage (V-4 and V-5). With the increase of confining pressure, the initial compaction stage became shorter and inconspicuous, especially when the confining pressure reached 20 MPa and 30 MPa (Fig. 13a). It indicates that the micro-cracks in the layered core rock had been compacted under the confining pressure. When the peak strength is reached, the stress–strain curve decreases rapidly due to the layered core rock failing and losing its bearing capacity.

Table 2 Results of conventional triaxial compression tests of the layered core rocks
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Fig. 13
figure 13

a Stress–strain curves of the layered core rocks, b compressive strength and Young’s modulus

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Overall, the confining pressure has a significant effect on the rock strength and deformation behaviors of the layered core rock. The compressive strength of the layered core rock increases gradually with the increase of the confining pressure (Fig. 13b). Compared with the unconfined compression condition (mean compressive strength of V-4 and V-5), the compressive strength under the confining pressures of 10 MPa, 20 MPa and 30 MPa increased by 39.56%, 43.15% and 78.56%, respectively. However, since the stress–strain curve under the confining pressure of 20 MPa entered the crack initial and stable growth stage in advance and experienced multiple fluctuations, its compressive strength did not increase drastically compared with the confining pressure of 10 MPa, and Young’s modulus even decreased, which was related to its complex failure modes.

3.3.2 Failure Modes

The failure characteristics of the layered core rocks changed with the increase of confining pressure, as shown in Fig. 14. Under the unconfined compression conditions, the failure of the layered core rocks was mainly caused by tensile splitting and thus generated several tensile cracks. Furthermore, since the lower Young’s modulus and higher deformation ability of the mudstone layer, the obvious radical expansion deformation can be seen at the argillaceous interlayer compared with the sandstone layer (Fig. 14a–b). With the increase of confining pressure, the argillaceous interlayers and micro-cracks were gradually compacted, while it still needed to go through a certain initial compaction stage under normal stress. Therefore, the failure of the layered core rocks was dominated by tensile–shear mixed failure mode (Fig. 14c). Under the higher confining pressure (20 MPa and 30 MPa), the argillaceous interlayers and micro-cracks of the layered core rocks were completely compacted, and it transformed into shear failure mode (Fig. 14d–e).

Fig. 14
figure 14

The failure modes of the layered core rocks in conventional triaxial compression tests

Full size image

It should be pointed out that the argillaceous interlayers seriously affect the failure patterns of the layered core rocks. Generally, the thinly argillaceous interlayer can be regarded as a weak structural plane with a certain thickness (Tavallali and Vervoort 2010). The computed tomography (CT) of the V-1 sample can also confirm that there exist a lot of discontinuous micro-cracks in the argillaceous interlayer of the layered core rocks. Since the lower ability to resist deformation and failure of argillaceous interlayers, the failure tends to be generated along them. During the crack extension process, several phenomena such as arrest, crossing, and diversion would occur at the argillaceous interlayers. Eventually, the bulk failure of the layered core rock was formed. In addition, the failure of V-2 sample was mainly concentrated in the vicinity of the argillaceous interlayer, showing progressive local damage until the overall failure. Therefore, the compressive strength of V-2 was slightly increased compared with V-3 sample, but the ability to resist deformation was weakened, and Young’s modulus was decreased.

4 Discussion and Implication

Accurately measuring the geomechanical and mineralogical properties of rocks is one of the most challenging works in designing hydraulic fracturing pumping schemes (Du et al. 2021; Sone and Zoback 2013). In this paper, a combination method of micro- and macro-scale measurements was used to investigate the mechanical properties of adjacent layers and the bulk mechanical properties of layered core rocks. Our laboratory experiments indicate that the mechanical responses and indentation morphologies display various performances among minerals, which reveals that the mineral compositions, spatial distributions, micro-structures and sedimentary and diagenetic environments are the root reasons to result in the mechanical differences and inherent heterogeneity among different layers in layered rocks at mineral scale. These factors ultimately control the bulk mechanical responses and failure patterns of layered rocks. Hence, the mineralogies and geomechanics of different layers at the micro-scale are essential considerations for establishing multiscale numerical simulations in the layered rocks.

In terms of multilayer hydraulic fracturing in coal measure strata, the control of the fracture height growth and holding the fracture conductivity are critical for designing the hydraulic fracturing treatments and achieving economical and commercially viable development (Li and Wu 2022; Liao et al. 2022). The mechanical differences between adjacent layers can significantly affect the fracture propagation and proppant pack. Statistical results from grid nanoindentation tests show that the sandstone layer has higher Young’s modulus than that of the mudstone layer. The hydraulic fractures tend to propagate from a formation with a higher Young’s modulus to a formation with a lower Young’s modulus (Gao and Ghassemi 2020; Gu and Siebrits 2008). Therefore, the perforation location should be optimized for connecting the isolated pay zones or preventing the fracture from crossing nonpay zones. Furthermore, the hardness affects the proppant embedment and fracture conductivity. The conductivity decreases with the decrease of fracture aperture since the proppant crushing and proppant embedment under the in situ stress (Katende et al. 2021; Mueller and Amro 2015). The strong heterogeneity of indent impressions among different minerals can create complex proppant embedment patterns. The visual indent impressions and cracking patterns of typical minerals can provide insights into the proppant embedment mechanism and optimal proppant types during hydraulic fracturing treatments.

Besides, brittle minerals are crucial indicators for evaluating rock brittleness and fracability, such as quartz, dolomite, and carbonate minerals (Jin et al. 2014; Xu et al. 2021). In the layered core sample, although the proportions of quartz in the sandstone layer and mudstone layer are similar, the mechanical responses are substantially different. Therefore, the evaluation of rock brittleness and fracability only from the contents of brittle minerals will lead to inaccurate results. The mechanical responses, sedimentary and diagenetic environments of minerals and rocks should also be carefully considered. Hence, quantifying and comparing the geomechanical properties related to the mineralogies of different layers at the micro-scale can provide reliable input data that is essential for establishing multiscale geomechanical and hydraulic fracturing simulations to understand the macro-evolution of layered formations.

In addition, the bulk mechanical behaviors of the layered core rocks under in situ stress conditions suggest that the failure tends to be created along the argillaceous interlayers. The thin interlayer can be considered as the weak structural plane with a certain thickness. The existence of the weak structural planes complicates the fracture morphology during hydraulic fracturing treatments, such as T-shaped fractures, kinks and offsets (Tang et al. 2019; Zhang et al. 2017). Consequently, the controlling and predicting fracture morphology in the layered formation become more challenging, particularly in thinly interbedded formations with various lithologies. It is essential to establish mechanical properties variations on the millimeter scale in thinly interbedded formations for accurately geomechanical modeling and predicting fractures. Clarifying the mechanical properties and heterogeneity of the layered rocks on multiscale can help to make an in-depth understanding of fracture height growth prediction and proppant embedment mechanisms in coal measure strata, and ultimately guide the optimization of proppants and perforation positions for designing and operating the hydraulic fracturing treatments.

5 Conclusions

We investigated the mechanical differences between sandstone and mudstone layers of the downhole layered core rocks by employing a combination of grid nanoindentation tests and SEM–EDS techniques. Subsequently, the mechanical responses and indent impressions of individual minerals and multiple minerals were quantified and compared. On this basis, the bulk strength, deformation and failure behaviors of the layered core rocks under in situ stress were analyzed via conventional triaxial compression tests. The following conclusions can be observed:

  1. (1)

    Mechanical properties and indent impressions of minerals exhibit distinct characteristics. Quartz exhibits the highest hardness and Young’s modulus with the smallest indent impression in each layer, while the kaolinite is the opposite. Interestingly, mechanical properties of quartz in the mudstone layer are lower than that of the sandstone layer. When an indenter covers multiple minerals simultaneously, the mechanical responses of which are determined by the softer phases.

  2. (2)

    Minerals exhibit different deformations and cracking patterns in different layers. Quartz shows elastic-dominated deformation with noticeable elastic recovery phenomenon in the sandstone layer, whereas medium-plastic deformation in the mudstone layer. Since the unstable sheet structures, kaolinite exhibits plastic-dominated deformation in the layered core rocks. Shear cracks and radical cracks are prone to occur in elastic-dominated minerals, while chipping damage is induced in plastic-dominated minerals.

  3. (3)

    Statistical nanoindentation data suggest that the mean Young’s modulus and mean hardness of the sandstone layer are 1.28 times and 2.40 times larger than that of the mudstone layer, respectively. The failures of the layered core rocks tend to create along the mudstone layer since the lower mechanical properties. The confining pressure greatly influences the bulk mechanical properties and failure modes of layered core rocks. With the increase of confining pressure, the compressive strength of layered core rocks gradually grows, and the failure changes from tensile splitting to tensile–shear mixed failure and shear failure mode.