Full- and Local-Field Strain Evolution and Fracture Behavior of Precracked Granite under Coupled Static and Dynamic Loads

Flaws and discontinuities play a crucial role in the failure process of rocks. To investigate the fracturing mechanism of rock with combined flaws composed of crack and hole, the digital image correlation (DIC) method is used to record and analyze the rock failure behavior. Coupled static and dynamic loads are applied on granite specimens with prefabricated flaws by a modified split Hopkinson pressure bar (SHPB) device. )e dynamic mechanical properties of the granite specimens are affected by the flaw inclinations with the loading directions. With the inclination angle increasing, the combined strength and peak strain both decrease first and then increase. Fulland local-field strain evolution of the granite specimens is analyzed in a quantitative way by using DIC technique.)e specimens with a flaw angle of 45° are broken relatively evenly with homogenous small particle sizes.)e variation trend of fragment sizes is consistent with that of combined strength and absorption energy of the specimens.


Introduction
e geometry, size, and spatial distribution of flaws incubating within the rock are of particular importance to the mechanical properties of rock [1]. Under the long-term effect of geological action and external force, numerous micro-and macroflaws, such as faults, discontinuities, holes, and microfissures, have grown inside the rock. e existence of these natural weak surfaces and flaws is the most fundamental cause of rock failure. In general, exploring the fracturing mechanism of rock with flaws has been one of the focuses of rock mechanics in recent decades [2,3].
In engineering practice, rock media exhibit very complex characteristics due to the heterogeneity, nonlinearity, and uncertainty properties [4], and usually contain both cracklike and hole-like flaws. e mechanical properties and fracturing behavior of specimens with one of them have been systematically investigated by using different experimental and numerical methods. It has been concluded that the fracture initiation, propagation, and coalescence behavior of specimens with hole-like flaws are influenced by a multitude of factors, such as hole size [5], hole shape [6,7], number of holes [8,9], and stress conditions [10,11]. Meanwhile, those of specimens with crack-like flaws are likewise closely related to the geometry of cracks [12], crack numbers [13,14], and crack size [15].
Generally, rock mass contains massive flaws in irregular arrangements and of different shapes in rock engineering. e crack-hole combined with flaws is also a common type of flaws in rock mass. Yang et al. [16] conducted experiments to investigate the effect of fissure angle on the strength and deformation behavior of sandstone specimens with combined flaws. By using photographic monitoring observation, crack coalescence mechanism (tensile crack, hole collapse, far-field crack, and surface spalling) and nine different crack types for the combined flaws are identified. Liu et al. [17] carried out a number of laboratory tests and numerical simulations based on the particle flow code method to analyze the cracking process and stress field evolution in specimens containing combined flaws. e arrangement of the flaws in their studies is interconnected crack-like and hole-like flaws. Yin et al. [18] conducted experiments and numerical simulations to investigate the cracking characteristics of specimens with the flaws in a noncontact geometry of combination of single hole and an inclined fissure underneath. However, most of these tests were usually loaded by static uniaxial compression for those studies aforementioned.
In recent decades, scholars have carried out numerous tests based on the SHPB system, to investigate the mechanism of crack initiation and propagation processes on brittle rock. Under individual dynamic loading, the mechanical properties and crack propagation of rock specimens containing a single flaw with different inclination angles are investigated [19][20][21]. Under coupled static-dynamic loading, the influence of dynamic strain rate and the axial static stress on dynamic behaviors of rock specimens with a hole or fissures are considered by some researches [22][23][24], while the study focusing on hole-crack flaws is rather limited. In view of this, further study of the fracturing properties of brittle rock materials containing prefabricated hole-crack flaws under coupled static-dynamic loading is essential.
Conventional sensors such as strain gauges, extensometers, and accelerometers are widely used to monitor the deformation of rock specimens. However, these sensors can only measure the strain at a few discrete locations [25][26][27], and it is obviously not applicable to obtain the local strain surrounding the flaws and cracks in the specimen. To overcome the limitations of traditional contact measurement technology, the digital image correlation (DIC) method, a typical representative of optical technology, has performed its great advantages [28][29][30]. Fracture is of great importance for the behavior of rock engineering structures [31][32][33]. Hence, the crack initiation and fracturing process of specimens with prefabricated flaws have been investigated with different auxiliary experimental means, such as acoustic emission (AE) technology [34], computerized tomography (CT) scanning [35,36], and 3-D X-ray computed tomography [37]. All those mentioned methods are beneficial to provide inspections for rock failure, especially under static compression tests. However, these methods have limitations in recording the strain-field variation in the dynamic experiment.
Besides, there are also many numerical simulation methods. For example, Li et al. [38] adopt the damage smear method (DSM) to investigate trans-scale progressive rock failure process. Damage evolution and accumulation of representative volume elements (RVEs) are used to reveal the characteristics of macroscopic rock failure. In addition, the finite element method (FEM) [39], discrete element method (DEM) [9,40], rock failure process analysis code (RFPA) [41], and particle flow code (PFC) [8,42] are also widely used to reveal the failure mechanism of rock. However, to conduct numerical modeling, reliable and reasonable constitutive relationship must be built as the basic information. Besides, the parameter selection and validation of these numerical models also require experimental results. It is a challenge in directly obtaining the fulland local-field response, especially measuring true dynamic response of the specimen or structure. Based on the calculation of the gray matrix of the digital speckle images, the surface strain evolution of a specimen can be extracted by using the DIC technique without the need to develop a numerical model.
In the current work, a modified split Hopkinson pressure bar (SHPB) equipment is used to apply the coupled static and dynamic loads to a rock specimen. Each rock specimen is precracked with crack-hole flaws in a noncontact geometry. Digital image correlation (DIC) apparatus is adopted to record the real-time fracturing process of specimens.
e full-field cracking process and strain localization evolution are analyzed. e energy dissipation and rock fragmentation size characteristics are summarized. e main purpose of this paper is to obtain the mechanical properties and the strain evolution of brittle rock containing combined flaws under dynamic loading by using the DIC technique. Evidently, the dynamic rock failure analysis by the DIC method will provide some visual observations and proofs for the studies in rock mechanics, particularly for the rocks with natural or artificial flaws.

Specimen Preparation.
e specimens adopted in the experiment were made of granite with high strength and brittleness, which are extracted from Miluo county of Hunan province in China. To determine the basic mechanical properties of the test granite, cylindrical specimens with dimensions of Φ50 mm × 100 mm (diameter × height) were prepared and tested under uniaxial compression. e basic mechanical parameters are listed in Table 1.
Rectangular cuboid specimens (60 mm in length, 45 mm in width, and 15 mm in thickness) were tested under the coupled static and dynamic loads by a modified split Hopkinson pressure bar (SHPB) apparatus. A circular hole (10 mm in diameter) was cut by using a high-pressure water jet apparatus at each specimen center. A contrast group with only circular hole (Group C) and an experimental group with crack unexposed to the hole (Group U) were prepared and tested afterwards. e specific geometrical layout about the test specimen can be seen in Figure 1. e prefabricated combined flaws contain a hole-like flaw and a crack-like flaw 15 mm in length in different inclination angles β (the angle between the crack-like flaws and the loading direction, including 0°, 30°, 45°, 60°, and 90°). e artificial crack has a minimum distance d of 7 mm from the edge of the internal hole, and the layout is displayed in Figure 2. e prefabricated crack is always tangent to a circle with a radius of 12 mm (R � d + r). Tangent point, which is also the midpoint of the crack, rotates counterclockwise in the second quadrant. e angles aimed to investigate in this paper are limited in only one quadrant, and larger angles are not discussed due to symmetry.
Moreover, the dimensions and mechanical parameters of each type of specimens are listed in Table 2. It is noteworthy that the specimen no. in Table 2 describes the number of crack, crack inclination angle, and the specimen number (three specimens are prepared for each type). For example, U-30-2 refers to the second specimen (no. 2) containing a single crack with β � 30°.
Before the tests, artificial speckle patterns should be prepared on the specimen surface. At first, a layer of white paint was sprayed thinly and evenly on the surface of specimens. If the paint is too thick, the crack initiation and propagation of the specimens are difficult to be reflected on the surface in time, which would result in the inaccurate acquisition of images captured by the high-speed digital camera (Phantom V711, produced by Vision Research Inc.). After the paint was dry, speckles were coated manually and randomly, and each speckle was set to cover approximately 4-6 pixels. It is noteworthy that a speckle particle size is the same as the distance between two adjacent speckles to ensure that it can be caught and optimized by computer simulation.

Testing Equipment
2.2.1. Loading System. Rectangular cuboid granite specimens were tested by using a modified split Hopkinson pressure bar (SHPB) system with coupled static and dynamic loads, as shown in Figure 1. e modified SHPB system consists of a gas gun, a cone-shaped striker, an incident bar, a transmitted bar, a momentum bar, a damper, and a set of axial static pressure device [44]. e basic parameters of elastic bars in SHPB device are shown in Table 3.

Digital Image Correlation (DIC)
System. During the test, DIC apparatus is used to monitor the deformation evolution of the specimens and it mainly consists of the high-speed digital camera and software system. e installation of this apparatus is shown in Figure 3. A gooseneck lamp was installed perpendicularly to the specimen to provide illumination. Once triggered, all images were capture and simultaneously stored in a computer for the subsequent processing. e length-pixel ratio of the imaging system is 0.234 mm/pixel. e frame rate of the high-speed camera is set to 79161 fps (frames per second) with a resolution of 256 × 256 pixels so that it can capture an image each 12.63 μs. After impact tests, the captured speckle images are analyzed by two-dimensional visual image correlation (VIC-2D) software from Correlated Solutions, Inc. (CSI). (Please refer to reference [46] for more details about the software). Generally, VIC-2D is advantageous for monitoring in-plane deformation and strain measurements of any planar surface on account of its simple setup. However, there are some limitations for the DIC system: (a) measurement accuracy mostly depends on the quality of speckle particle. (b) Measurements are limited to in-plane surface deformation and strain. (c) Once the strain is less than 100 µε, DIC is not recommended for any applications [47].

SHPB Test.
e main loading stages of the test are as follows. First, static loads of 20 MPa were applied manually on the specimen in a slow and uniform speed by the axial static pressure loading device, and the static loading rate is 0.17 MPa/s. Second, dynamic impact loads were applied to the granite specimen by launching the cone-shaped striker in the SHPB system. e dynamic strain rate is in the range of 50∼60 s −1 . In the test, once a transistor-logic (TTL) signal was generated by the strain gauge attached on the incident bar, the high-speed camera and the oscilloscope were both triggered simultaneously.

Testing Validity.
During the test, a slowly rising half sine wave is generated by launching the cone-shaped striker to impact the incident bar. When the incident wave propagates to the bar-specimen interface, a part of the wave is reflected (reflected wave), and the remainder passes through the specimen and is transmitted into the transmitted bar (the transmitted wave). Hence, stress equilibrium at the two ends of the specimen should be achieved in the test to ensure that results are convinced and reasonable. It means before the rock specimen reaches failure, the transmitted stress wave is almost equal to the superposition of the incident wave and reflected wave.
Taking specimen U-0-3 as an example, the stress waves of the specimen are shown in Figure 4. e transmitted stress wave (Tra) and the superposition of incident wave and reflected wave (Inc + Re) in the middle part almost coincide with each other, indicating that the stress equilibrium of the specimen is satisfied during the dynamic test.

Dynamic Stress-Strain Curve.
e time when impact stress wave propagates to the specimen end is set as the starting point in the test. Figure 5 shows the dynamic stressstrain curves of the granite specimens with prefabricated flaws. It can be approximately classified into three typical stages: (I) linear elastic deformation stage, (II) nonlinear deformation stage, and (III) macroscopic failure stage.
Evidently, the compaction stage which should be concave upward cannot be observed in this curve. Because the initial compaction of microfissures in the interior of rock specimens has achieved in prestatic loading, the curve goes directly to the stage of linear elasticity. e first stage has a quite short duration. With further loading, the stress-strain curve exhibits nonlinear property. New crack initiation and propagation occur in this stage.
When reaching the peak stress, the stress-strain curve shows a downward trend, which may result from the propagation of macrofractures. Hence, the postpeak stage is defined as macroscopic failure stage. In this stage, macroscopic fractures form and propagate to the specimen ends, finally causing the brittle failure.

Mechanical Properties.
According to the one-wave propagation theory in the SHPB test, the axial stress σ (t) , strain ε (t) , and strain rate ε (t) can be derived by the following equations [48]: Loading direction Strain gauge Axial pressure Momentum bar Transmitted bar Incident bar Cone-shaped striker Gas tank Figure 1: SHPB system modified from reference [43] for coupled axial static and dynamic loading and the geometry of the specimen.  Note: σ as is the axial static pressure, σ d is the dynamic strength, and σ cs is the combined strength. e symbol "-" indicates that the data are eliminated for the specimen owing to large deviation. where A e , E e , and C e are the cross-sectional area, Young's modulus, and P-wave velocity of the elastic bar, respectively. A s and L s are the cross-sectional area and length of the specimen, respectively. ε I , ε R , and ε T are the incident, reflected, and transmitted strain pulses, respectively. us, the dynamic mechanical properties of the granite specimens can be obtained. e results are listed in Table 2.
e strain rate ε (t) of the specimens is maintained at about 50-60 S −1 , which can be regarded as a constant strain rate range. Dynamic strength σ d reflects the impact resistance of the specimen, and the peak strain ε (t) refers to the strain corresponding to the dynamic strength. Moreover, the combined strength σ cs is the sum of the prestatic pressure and the dynamic strength, which reflects the actual bearing capacity of the specimens [44]. e average value and the standard deviation of the testing results are provided in Figure 6. e existence of artificial flaws are responsible for strength weakening [49]. Combined strength and peak strain of the specimens in Group U both decrease first and then increase with the inclination angle increasing gradually. e strength reduction of specimens with an artificial crack-like flaw of 0°is only 0.66% lower than that of specimen C-0, while the strength reduction of specimens with a prefabricated flaw of 30°, 45°, 60°, and 90°is 24.40%, 30.79%, 25.17%, and 16.57%, respectively. e peak strain of specimen C-0 is 0.32%, whereas it ranges between 0.177% and 0.204% for the specimens with combined flaws, which has a significant reduction.

Fracturing Process.
During the past few decades, white patches are regarded as a precursor to observe new cracks in many studies [50]. Moreover, the initiation, extension, and coalescence of fractures are described in a qualitative way. In this study, based on DIC technique, the major principal strain contours of the specimen are obtained during the coupled static-dynamic loading, as shown in Table 4. It can reflect the evolution of the surface strain field in the process of loading intuitively and quantitatively.

Shock and Vibration 5
In the evolution of strain field, different types of specimen behave quite differently. It demonstrates the geometries of combined flaws significantly affect the deformation characteristics [18], which are summarized as follows: (1) In static loading pattern, the whole specimen is in the state of compression. However, some local high strains can be observed prior to observable cracks, which usually occur around the combined flaws. ese local high strains are similar to the white patches mentioned earlier [51], which could establish foundation to reveal the new fracture trajectories and initiation mechanisms in the subsequent dynamic loading.
(2) In dynamic loading patterns, at early stage of dynamic loading, the high strain shows obvious migration characteristics with the propagation direction of the stress wave (specimen C-0 is not involved). e incident wave enters from the barspecimen interface, and soon afterwards high strain concentrations are formed in the right half of specimens. Next, they move forward along the propagation of the stress wave and then gradually distribute near the combined flaws of the specimens. With further loading, the high strain zones are widened and propagated, accompanied with some secondary cracks.  No. Static pattern Dynamic pattern C-0 diagonal directions at an angle with the loading direction, generating an X or a half X-shaped fracture, which dominate the rock failure process during the dynamic loading. (4) Fractures emanating from the top or bottom of the hole coalesce with those initiating from crack tips. e crack tip which is near with the internal hole has the precedence. e coalescence modes of five types of flaw geometry will be discussed in Section 4.1 in detail.

Strain Evolution Analysis of the Measurement Points.
In this paper, in order to obtain the strain localization evolution processes, some key measurement points are selected at discrete locations on the specimen surface, as shown in Figure 7. DIC technology is used to extract the strain data during the failure process, and then strain analysis and comparison about these points are conducted.  Table 5, including the maximum principal strain e1 and the minimum principal strain e2.
For specimen C-0, it can be seen from Table 5(a) that when t � 88 μs, the peak strength is 170.3 MPa, and the local strain of all measurement points is in a low fluctuation. After that, the maximum principal strain at the top and bottom of the hole begins to increase significantly, and tensile cracks appear along the loading direction (Table 4). e strain-time (e2) curve in Table 5(b) shows that there are shear fractures perpendicular to the loading direction appearing firstly at the top and bottom of the hole (A, C), and then they are restrained gradually. At t � 200 μs, the value of e2 drops sharply to a small value but later on increases again. At this moment, the specimen is completely destroyed, and shear fractures dominate the failure process.
For the specimens with prefabricated cracks, the statistic results are summarized in Table 6, and the variation rules are summarized as follows:     rather than at the crack tips. As the circular hole is completely located in front of crack and exposed to the stress wave earlier and larger than the preset crack. erefore, the roof and floor of the internal hole could become the preferable location for microcracks to gather and develop, rather than at the tip of the crack.  Figure 8 shows the crack coalescence modes of precracked specimens with different flaw inclination angles. ere are three types of crack coalescence modes in the present study: regional failure (Figure 8 It can be seen that tensile fractures are usually occurred from the crack tip, while shear fractures are often formed at the boundary of circular hole. However, this phenomenon is not applicable in the situation that the crack tip is relatively close to the hole. In this condition, the microfissures which initiate from the crack tip and crown area of the hole propagate toward each other rapidly, and then a visible fracture is formed afterwards (Figures 8(c) and 8(d)).

Average Strain Evolution of Failure
Zone. Based on the above analysis about the crack coalescence modes between the combined flaws, the main failure zones which involve combined flaws are selected to analyze the average strain in specimens. As shown in Figure 9, taking the specimen with a flaw angle of 45°as an example, a circle with the center of point C and a radius of 12 mm is delineated. e average strain (only e1 is analyzed) of the area is calculated by DIC technique, and the strain-time curves of five typical specimens are plotted in Figure 10.
It can be seen from Figure 10 that the average strain of the failure zone in specimen U-90-3 (symmetrical mixed fractures along the loading direction) is most prominent.
en, specimen U-0-3 (regional failure) follows. In specimens U-30-1, U-45-3, and U-60-1, there is a dominant fracture connecting the prefabricated crack with the hole. e order of the average strain within the three failure zones is 45°> 30°> 60°. e characteristics of this trend are consistent with the crack coalescence modes in Figure 8.

Energy Characteristics.
Rock failure is actually a process of energy dissipation. e specimens applied prestatic loading are in the compressive state with considerable elastic energy accumulated. Once it is subjected to sufficiently large dynamic disturbances, the stored elastic energy is rapidly released and may result in severe damage. erefore, it is of great importance to analyze the law of energy consumption. Based on the one-dimensional stress wave theory and data recorded in the SHPB tests, the average value of incident energy E I , the reflected energy E R , the transmitted energy E T , and the absorption energy E A can be calculated [48] by the following equations. e results are listed in Table 7: where σ I (t), σ R (t), and σ T (t) are the incident, reflected, and transmitted stress at time t, respectively, and ρ e C e is the wave impedance of the bars. At different flaw inclination angles, the incident energy E I , the reflected energy E R , the transmitted energy E T , and the absorption energy E A of the granite specimens have different values. Particularly, E A is the energy absorbed by

Angle
Measurement points Note: "e1, e2" denotes an obvious rise process as shown in its strain-time curves. e symbol "-" denotes a relatively low fluctuation of the straintime curves, generally less than 0.2. the rock specimens, and this part of energy has the main contribution for the failure of rock and also the new fractures in the specimen. Figure 11 plots the relationship between the absorption energy E A and the flaw inclination angle. It is obvious that E A first decreases then rises gradually with the inclination angle increasing, and it reaches the lowest value at 45°. is is because the precracked specimens with a flaw of 45°absorb only a relatively small amount of energy, fractures generate inside the specimens, and failure occurs, while other types of specimens require more energy to break. e variation trend of absorption energy is similar to that of combined strength of the specimens, as shown in Figure 6.

Rock Fragmentation Size Analysis.
Macrofractures are formed in the rock specimens under coupled static-dynamic loading. is behavior inevitably leads to the fragmentation and energy dissipation in the rock failure process. e distribution characteristics of rock fragmentation size can reflect the extent of deformation and failure behavior of rocks. e greater the damage degree of rock specimen will result in better dispersion and more homogenous diameter of rock fragment. Figure 12(a) shows the fragment of the granite specimen after impact load. It is worth noting that in order to make the results of size analysis more reasonable, all fragments of the specimens in the same inclination angle are mixed together. en, the split desktop, a rock fragmentation size measurement software, is used to analyze the size data in each group. e processed picture of Group U-30 is  shown in Figure 12(b), and all rock fragmentation size data are summarized in Table 8. It lists the percentage of rock fragment in each interval, as well as the average size and top size in each group. Almost all the fragment size is less than 5.08 cm, except for some fragment in Group U-90, which accounts for 5.87%. Furthermore, it is clear that with the increase of inclination angle, the average size and top size of the specimens show a trend of decreasing firstly and then increasing, and they both reach the lowest at the angle of 45°, which is consistent with the variation trend of combined strength and absorption energy. Figure 13 shows the fragment size distribution of granite specimens with different angles after crush. It reflects the fragmentation degree of the specimens. It can be seen that when the crack inclination angle is 45°, the specimens are broken into smaller particle sizes with homogenous size distribution. e specimens with an angle of 30°rank second; nevertheless, the amount of rock fragment with the size  less than 0.5 cm is the maximum at this angle. e specimens with flaw angles of 0°and 60°have less small size fragments but more large size fragments. e uniformity of fragment size distribution for the specimen with 90°flaw angle is the worst.

Conclusions
A series of impact tests are conducted on granite specimens with combined hole and crack flaws. e DIC technique is used to monitor the surface strain evolution and failure behavior of the specimens. e conclusions are drawn as follows: (1) Mechanical properties of granite with crack-hole flaws are susceptible to the crack inclination angles. e combined strength and the peak strain of the specimens both decrease first and then increase with the flaw inclination angle increasing, and both of them reach the lowest value at the angle of 45°.
(2) e influence of flaw inclination angle on the deformation of the specimen reflects the fracturing behavior. Two crack tips (A, B), and the top and bottom of the internal hole (D, E) are the main stress concentration zones, and their local maximum strain is basically more than 0.5 at postpeak stage. (3) e crack coalescence modes between combined flaws are summarized, i.e., regional failure, monotype fracture, and mixed mode fractures. Tensile fractures tend to occur at the crack tip, while shear fractures usually emerge at the top and bottom of the hole and dominate the ultimate rock failure process under dynamic impact loading. (4) e absorption energy E A first increases and then decreases with the flaw inclination angle. Furthermore, the size distribution of rock fragments is analyzed. e specimens with crack of 45°are broken relatively evenly with homogenous particle size distribution. e characteristics of absorption energy and size distribution are consistent with the variation trend of combined strength.

Data Availability
e relevant data could be found in the manuscript.

Conflicts of Interest
e authors declare that they have no conflicts of interest.  Shock and Vibration 13