Introduction

Rock shear fracturing is greatly influenced by rock mechanical properties and its stress boundary (Janach and Lan 1980; Brantut et al. 2013; Rathnaweera et al. 2017). The process of brittle rock failure is an important aspect for the safety of underground engineering (Zhou 2005; Clayton 2010). The study of activation mechanism of small- and medium-scale brittle fault is significant not only for the prediction of disasters caused by mining but also for the process of earthquake preparation (Cheng et al. 2019).

Many scholars focused on the characteristics of rock fracturing and the investigation of crack distributions. Peak shear strength and residual shear strength of rock joints within low number of cycles varied from those within high number of cycles (Hawkes and Mellor 1970; Zhou et al. 2015; Fathi et al. 2016; Liu et al. 2018). Different aperture shapes, sizes, normal stress, and shearing rates were considered to research the behaviors of unreinforced and geogrid-reinforced ballast at different rates of shearing. Interface shear strength improved significantly when the ballast was reinforced with geogrids (Sun et al. 2014; Sweta and Hussaini 2018). Present-day deformations occurring reflected complex landslides of kilometric dimensions. Interaction between predisposition factors (inherited structures, topography, slope, gravity) and triggering factors (artificial vibrations and seismotectonic activity) provided favorable conditions to slide (Dhahri et al. 2015). BPI (Block Punch Index) test was used in previous works on size effect. Failure surface initiated at the top of the specimen and propagated along it, which demonstrated that the failure did not produce by true shearing (Sulukcu and Ulusay 2001). Shear behavior of natural coal–rock interface was studied by performing direct shear tests under constant normal loading condition, which showed that the shearing behavior was influenced more by the strength differences between two halves rather than the surface roughness of the interface (Oyanguren et al. 2008; Li et al. 2015; Meng et al. 2016). Different varieties of Hooke’s law were applied to manifest rock regional fractured under different mechanical conditions. Theoretical predictions of this method were generally consistent with empirical expressions (Liu et al. 2009). The correlation of microcracks and macroscopic shear strength was attempted to establish according to Ashby, Mohr–Coulomb failure criterion, and crack–strain relation (Moore and Lockner 1995; Li et al. 2016; Morley et al. 2018). The physics-based theory was used to explain the behavior of “Friction is high according to the rate and state Constitutive law during slow sliding, yet markedly weakens at the sliding velocity approach seismic slip speeds” (Liu et al. 2017; Aharonov and Scholz 2018). A suitable model of stress generated by freezing in open crack discussed the evolution of rock mass stability. This maximum stress generated by freezing along crack was completely defined by the pore network of the limestone matrix and crack geometry (Bost and Pouya 2017). Labaune et al. (2017) used the onset of dilatancy as the design threshold, which was a new approach to salt cavern design.

Previous studies demonstrated the characteristics of rock fracturing in many aspects. They were closely correlated with morphology characteristics, and the stress state of rock considerably affected crack propagation. However, few detailed studies analyzed the effect of cracks in spatial-temporal aspect and discussed the influencing factors of crack status. Many different scales of crack exist along rock/rock mass, and crack existence and development are important to the determined factors of crack status. In this paper, a study was focused on the crack status from the aspects of crack existence and development in terms of spatial-temporal aspects.

Rock fracturing experiment

Specimen preparation and boundary conditions

Granite specimens (150 mm × 150 mm × 150 mm, Fig. 1a) were collected from Laizhou in Shandong Province, China. Laizhou is an important gold production base in China and is rich in gold worldwide. Specimens were prepared in accordance with the Standard for Test Method of Engineering Rock Mass GB/T50266-99. Specimens were labeled from “GS-R1” to “GS-R4,” where “GS” represented Granite Specimen.

Fig. 1
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a Rock specimen; b its boundary conditions

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Boundary conditions of rock specimens in this experiment are shown in Fig. 1b. Shear fracturing occurs in the shear plane. The rock ends do not deform in the fixed boundary. The shear loading boundary is the end of the shearing force. The normal force boundary is the end of positive stress. Furthermore, azimuth on the rock surface (Fig. 1b) is used to describe crack distributions. The upper of the rock surface is expressed as N, the bottom is S, the left is W, and the right is E.

Experimental instrument and its settings

The experimental system (Fig. 2a) is comprised of a loading system (RLW-3000, Fig. 2b), CCD camera (Pike F-421, Fig. 2c), and AE system (PCI-2, Fig. 2d). Equipment setup is guaranteed the coherence of experimental data (Ishida et al. 2017). The system is set as follows: (1) Loading system: the loading settings are from normal direction and shear direction. The normal force boundary is set to 300 kN (GS-R1 specimen), 250 kN (GS-R2 specimen), 200 kN (GS-R3 specimen), and 150 kN (GS-R4 specimen) at the same loading rate of 200 N/s. At the end of shear fracturing, the loading rate in the shear force boundary remains 0.2 mm/min. (2) AE system: sampling time is set to 0.2 μs, storage length is 2k (2048 words), recording time period is 0.4 ms, pre-trigger is 1k, and sampling rate is 1 MHz. (3) CCD camera: sampling speed is 16 fps, and resolution is 2048 pixels × 2048 pixels.

Fig. 2
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Schematic diagram of the experimental setup. a Experiment system, b loading system, c CCD, d AE monitoring system

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Experimental results

Stage characteristics in the shearing failure process

Shearing force, AE energy, and AE accumulative energy versus loading time are shown in Fig. 3; the final fracturing is in Fig. 4. The entire loading process is divided into three stages.

  • Phase I, initial stage: AE activity is due to the opening or closing of micro-cracks. AE energy is low; AE accumulative energy curve increases gradually with shearing force. All specimen curves are downward.

  • Phase II, stage of crack stable expansion: AE activity in this stage is more active than that in phase I. Shearing force curves also increase linearly.

  • Phase III, stage of crack unstable expansion: AE activity is more active than that in phases I and II. AE activity is extremely active, and the curves of AE energy and AE accumulative energy rise up vertically. Weakened rock specimens do not bear such great amount of shearing strain energy, then final failure occurs.

Fig. 3
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Curves of shearing force and AE parameters versus time. a GS-R1, b GS-R2, c GS-R3, d GS-R4

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Fig. 4
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Final fracturing form on four normal force levels. a GS-R1, b GS-R2, c GS-R3, d GS-R4

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The final fracturing form

According to the different normal force, the characteristics of en echelon are not the same, which are similar to dip (α) of en echelon (Fig. 4). ∠αGS − R1 of en echelon of GS-R1 specimen (FN = 300 kN) is 31.57° (Fig. 4a), ∠αGS − R2 of en echelon of GS-R2 specimen (FN = 250 kN) is 27.48° (Fig. 4b), ∠αGS − R3 of en echelon of GS-R3 specimen (FN = 200 kN) is 19.63° (Fig. 4c), and ∠αGS − R4 of en echelon of GS-R1 specimen (FN = 150 kN) is 8.78° (Fig. 4d). A crack splits into a series of en echelon crack, such as shear fracture belt in Fig. 4a~d. The crack surface does not twist and remains a single continuous surface, which may appear a series of small cracks in en echelon arrangement.

A positive correlation exists between normal force and angle (α) of en echelon. The entire angle is less than 45°, and en echelon produces under shearing condition (Pluijm and Marshak 2004). With increasing shearing force, the angle of shearing force and normal force changes, but α does not change. It turns out to be that the only constant factor is the normal force. Then, the shear force guarantees rock unstable failure, and normal force keeps crack directivity.

Crack spacing characteristics

According to the curve of shear force versus time (Fig. 3) and the final fracturing form (Fig. 4), crack existence and development have the following characteristics (Fig. 5).

Fig. 5
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Rock fracturing evolution in different normal force levels

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Phase I (a and b in Fig. 5), the initial stage is divided into two parts. One part is the unruptured time (a in Fig. 5). Internal crystal crack occurs in shear plane and vicinity of granite specimen, it forms “X”-style shape (C11 and C12 in Fig. 5.1a, C21 and C22 in Fig. 5.2a, C31 and C32 in Fig. 5.3a, C41 and C42 in Fig. 5.4a). The other part is the initial fracturing time (b in Fig. 5). In the center of shear plane, cracks begin to develop from two sides of granite specimen to the center, which are similar to crack groups of C13 – C15 in Fig. 5.1b, C23 – C24 in Fig. 5.2b, C33 – C34 in Fig. 5.3b, and C43 – C44 in Fig. 5.4b.

Phase II (c in Fig. 5), crack continues to grow in horizontal and vertical directions. The main crack type is pinnate crack in mesoscale, such as C18, C19, and C110 in Fig. 5.1c, C25 and C26 in Fig. 5.2c, C35 and C37 in Fig. 5.3c, C43 in Fig. 5.4b and C46 and C48 in Fig. 5.4c. Crack on center initially forms a dense cleavage belt, and interspace of cleavage planes are approximately 2 mm. Small-angle intersections stagger between some secondary fracture planes and general direction of shearing zone.

Almost all cleavages propagate by en echelon model. en echelon shows different scales, which vary from 1 to 35 mm, indicating a feature of self-similarity structure. GS-R1 specimen is the most active in developed fracturing, and C16 – C110 crack group exists. GS-R2 specimen has two peeled surfaces, named C27 and C28. The characteristic of crack directions in GS-R3 specimen is located on both sides of the shear plane. Crack distribution area in GS-R4 specimen is larger than that in GS-R3 specimen.

Phase III (d in Fig. 5), en echelon crack represents a basic characteristic of fault combination (Fig. 5.1d, Fig. 5.2d, Fig. 5.3d, and Fig. 5.4d). In response to the rock spalling, GS-R1 specimen appears in C111, GS-R2 specimen in C210 and C214, and GS-R3 specimen as a big rock spalling along the shear plane and forms a spalling zone of C39. GS-R4 specimen does not show obvious rock spalling but forms a crack concentration zone of C412. Lateral growth of cracks, which can be accomplished by the migration of incoherent boundary, occurs simultaneously in response to cracking. All the dense cracks, including en echelon cleavages and gently inclined cleavages, interpenetrate, leading to the surface peeling off in this stage. In horizontal direction, the strength of rock failure follows the trend of “strong → weak → strong.”

Crack mode characteristics

In this part, the degree of fracturing and the fracturing capacity of different specimens were discussed in terms of cumulative energy, ringing count, duration time, and energy index (Xu et al. 2017). It formed the distribution of disturbance stress, which was in an unstable state. RA-AF’s relationship reflected crack model; equations for both types were presented in Eqs. (1) and (2) (Ohtsu et al. 2007a; Shiotani 2008).

$$ \mathrm{RA}=\frac{\mathrm{Rise}\ \mathrm{Time}}{\mathrm{Amplitude}} $$
(1)
$$ \mathrm{AF}=\frac{\mathrm{Counts}}{\mathrm{Duration}\ \mathrm{Time}} $$
(2)

Crack type is classified according to the following factors (Fig. 6), (1) mode I, tensile crack has high AF values and low RA values; and (2) mode II, shear movement had low AF values and high RA values (Farhidzadeh et al. 2014).

Fig. 6
figure 6

Conventional crack classification (Farhidzadeh et al. 2014)

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According to Eqs. (1) and (2), the predefined diagonal lines in figures were based on flexural, tensile, and direct shear tests in laboratory systems (Ohtsu et al. 2007a). As normal force decreases, the crack type in the early state is inversely proportional to shearing crack (Fig. 7).

  • In GS-R1 specimen (Fig. 7(1)), tensile and shearing cracks develop. In the loading process, shearing crack develops faster. The developed tensile crack becomes less during unstable expansion (phase III).

  • In GS-R2 specimen (Fig. 7(2)), the phenomenon of pure tensile crack exists in phase I. After tensile crack generation, cracks open immediately, and the surface of open crack never touches mutually, and slip does not occur. Initially, AE signals that produced by tensile crack dominate the detected emissions, whereas the representing shear fracturing increases.

  • In GS-R3 specimen (Fig. 7(3)), unlike other conditions, shearing crack is the main crack type in phase I. The number of tensile cracks is positively correlated to shear force.

  • In GS-R4 specimen (Fig. 7(4)), AE mainly generates from new tensile microcracks when the stress level is low, which is similar to that in GS-R2 of phase I. In the entire process, little shearing cracks form, but the proportions of shear fracture increases.

Fig. 7
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Density cloud map of RA via AF for each normal force during fracturing evolution

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Results

Cracking development in the entire shearing process

Failure modes under shearing test are influenced by the normal force. As for crack distribution and fracturing degree under the effect of normal force, crack existence is discussed in terms of inheritance and variability based on the scale of space-time (Fig. 8). In this experiment, stress boundary of rock specimen forms in two aspects, namely, normal force and shear force. Cracks display parallel en echelon and end-to-end alignment, that is a vein zone (Crack patterns in Fig. 8). Crack group in macrocosm scale forms a type of en echelon, which is similar to those in A11 and A12 and A14 (GS-R1 in Fig. 8.(1)), A21, A22, and A23 (GS-R2 in Fig. 8.(2)), A31, A32, and A33 (GS-R3 in Fig. 8.(3)), A41, A42, A43, and A44 (GS-R4 in Fig. 8.(4)). In addition, crack tip of shear pivoted to a new orientation from free surface (no cohesion) (Misra et al. 2009). Crack splits into a series of small pinnate cracks model because crack surface still single and continuous, and it may appear as a series of small cracks in a pinnate arrangement. Crack extending in localization scale forms a pinnate crack, which is similar to those in A11 and A13 (GS-R1 in Fig. 8.(1)), A21 and A22 (GS-R2 in Fig. 8.(2)), A31 and A32 (GS-R3 in Fig. 8.(3)), A41, A42, A43, and A45 (GS-R4 in Fig. 8.(4)).

Fig. 8
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Development of crack distribution for the different normal stress on different specimens

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Crack geometry is quantified by crack patterns, Fisher concentrations, and crack percentage (Fig. 8). Fisher method is used as a projection method. Compared with crack distributions in phase I, crack distribute randomly, the angle is from 0° to 90° uniformly (a in Fig. 8). In phase II, crack distribution manifests a relevance to normal force, maximum percentage of crack angle on GS-R1 specimen (FN = 300 kN) is in the range of 60°~70°, GS-R2 specimen (FN = 250 kN) is 30°~40°, GS-R3 specimen (FN = 200 kN) is 20°~30°, and GS-R4 specimen (FN = 150 kN) is 10°~20° (crack percentage of b in Fig. 8). In phase III, cracking develops rapidly (c in Fig. 8). Compared with the crack distribution in phase II, phase III keeps the same status, and crack development remains in the same orientations (Fisher concentrations of c in Fig. 8). The maximum percentage of crack angle of different rock specimens is also the same (crack percentage of c in Fig. 8).

Scale effect of crack

Rock fracturing process is multi-scale. In the end, a macroscopic-scale catastrophism phenomenon occurs. In the “The final fracturing form” section, the microscale of fracturing begins in the form of transgranular cracks, mesoscale develops from the localized grains clusters in the form of pinnate crack, and macroscale derives from the whole size of rock specimen in the form of en echelon crack.

Whereas crack development is cross-scale, and cross-scale distributes along micro-, meso-, and macroscales (Li and Tang 2015). (1) In microscale, cracks are mainly “X”-shaped conjugates, such as C11 and C12 in Fig. 4.1a, C21 and C22 in Fig. 4.2a, C31 and C32 in Fig. 4.3a, C41 and C42 in Fig. 4.4a. Cracks in microscale are in good agreement with all the rock specimens. “X”-shaped crack is mainly shearing crack. From RA via AF (Fig. 7.a), the most common crack belongs to tensile type. (2) In mesoscale, cracks are mainly pinnate model. Pinnate is the secondary crack, such as C17, C18, C19, and C110 (Fig. 4.1c), C25 and C26 (Fig. 4.2c), C211, C213 and C214 (Fig. 4.2d), C37 (Fig. 4.3c), C43 (Fig. 4.4b), C46 and C48 (Fig. 4.4c), C411 and C412 (Fig. 4.4d). The acute angle between pinnate cracks and fracturing indicated the sense of shear in shearing plane (Engelder 1989; Alsop and Holdsworth 2004; Wei et al. 2011; Winter et al. 2017). From Fig. 7.b, the proportion of shearing crack mode increases. Hence, the main crack type in mesoscale is shearing crack. (3) In macroscale, main crack presents in en echelon type. Based on comparison and observation of crack type in macroscale, failure mode bends failure along the surface that occurred by bond-type damage and then takes the place of shear failure, which is similar to C112 and C114 in Fig. 4(1)d, C29 and C210 in Fig. 4(2)d, C39 in Fig. 4(3)d, and C412 in Fig. 4(4)d. Hence, in macroscale, the crack modes of tensile and shearing exist (Fig. 7.c).

Discussion

Influencing factors of crack status

The influencing factor of rock physical property was divided into class I and class II, which was self-sustaining fracturing in brittle compression (Akinbinu and Abioye 2016, 2017). Granite belongs to an igneous rock, the minerals that make up rock usually display a wide range of polytropism. Many mineral particles in granite are integrated with crystallization modes, which probably belong to class II.

On the basis of research contents on crack geometry between different normal force, the increase normal force leads to bigger rock constraint and bigger friction force (Fig. 8). There is some relation between crack angle α and normal force σ1 (Fig. 9). Dip (α) of en echelon crack is influenced by normal force σ1; it exists a positive correlation between σ1 and α (Fig. 9). The larger the normal force is, the bigger angle of α will be.

Fig. 9
figure 9

Statistical relationship diagram of normal force and dip (α) of echelon

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Therefore, crack status is influenced by rock physical properties and normal force. Rock physical property is the internal causes of crack status, and normal force is the external causes of crack status.

Characteristics of crack status on crack existence and development aspects

The characteristic of crack status is explored by the aspects of crack existence and development, and described as follows:

  1. 1

    Crack existence

The most important feature of rock material is the complicated variability of mineral composition in spatial scale. Rock under compression-shearing conditions develops a series of en echelon crack in the whole size (macroscale) and many pinnate cracks in the local region (localization scale) (crack patterns in Fig. 8). That means the crack existence form “the whole size of en echelon crack and the local region of pinnate crack.”

  1. 2

    Crack development

Fisher concentrations and crack percentage are used to manifest in the quantification of fracturing evolution (Fig. 8). Continuous activity of fracturing occurs in the same area, which results in the complexity of crack development. Another crack will produce in the same place next time; that is, crack growth inherits in the scale of time. Principal crack forms in early time, and its development follows the law of Inheritance (Fisher concentrations in Fig. 8) and Variability (crack percentage in Fig. 8). Crack development follows the characteristics of “Inheritance and Variability.”

Conclusions

  1. (1)

    Crack status is determined by the internal and external factors, and rock physical property is an internal factor; normal force is an external factor.

  2. (2)

    Crack existence follows the characteristics of “the whole size of en echelon crack and the local region of pinnate crack” in terms of spatial-temporal distribution.

  3. (3)

    Crack development manifests in different spatial-temporal distribution; it manifests a characteristic of “Inheritance and Variability.”

However, the influencing factors, such as specimen size, water percentage in rock, rock lithology, and confining stress, are not determined in this research and will be our next research focus.