Dynamic Fracture Evolution and Mechanical Behavior of Sandstone Containing Noncoplanar Elliptical Flaws under Impact Loading

To investigate the effects of preexisting flaws with different geometries, including flaw inclination angle and ligament angle on dynamic strength, deformation properties, and fracture evolution of rock materials, a series of dynamic impact tests were conducted on green sandstone specimens containing double elliptical flaws using a 75mm diameter split Hopkinson pressure bar (SHPB) testing device with a high-speed camera recording in real time. *e experimental results show that dynamic strength of specimens with different flaw angles is reduced between 5.91% and 39.92% but from 18.50% to 28.44% for specimens with different ligament angles, indicating that the effect of the flaw angle on the dynamic strength is more significant than that of the ligament angle. However, the dynamic deformation properties are influenced greatly by the ligament angle. Macroscale cracks mostly initiate at or near the flaw tips and then propagate in different paths with varying flaw geometries, leading to the ultimate failure in five typical modes based on the crack coalescence. Shear crack coalescence and tensile crack coalescence are identified through both macroscopic fracturing photos taken by the high-speed camera and microscopic surface morphology obtained by the scanning electron microscope (SEM).


Introduction
Rock mass is a complex natural medium containing various defects, such as flaws, fissures, pores, and holes, where new cracks always initiate, then propagate, and coalesce with each other into macroscale fractures, leading to the rapid damage and failure to lower the stability of rock structures such as underground mining craven and tunneling [1][2][3][4].
erefore, the investigation of mechanical properties and fracturing process of brittle rock materials with preexisting defects is helpful to guide the underground excavation scientifically.
ere have been a large number of experimental and simulative works carried out to study the crack initiation, propagation, and coalescence of rock and rock-like materials with preexisting flaws under static loading.For a single crack-like flaw, wing cracks first generate at the flaw tips and then grow along the axial stress direction, and subsequently, secondary cracks emerge around the flaw tip and propagate in the coplanar or oblique direction with the preexisting flaw [5][6][7][8][9][10].For a single hole-like flaw, crack propagation is a progressive development of high major principal strain zones based on DIC (digital image correlation) [11][12][13], dominantly resulting in an axial splitting failure mode [14].Great efforts also have been devoted to study the effect of multiple crack-like flaws on the mechanical and fracture behaviors.Bobet and Einstein [15], Wong and Chau [16], Sagong and Bobet [17], Yang et al. [18,19], Park and Bobet [20], and Gratchev et al. [21] investigated the influence of flaw geometries, including flaw number, length, width, frictional coefficient, inclination angle, and ligament angle, on mechanical properties, crack initiation, fracturing process, coalescence, and ultimate failure.Some scholars conducted experiments in more complicated conditions, for instance, an environment-coupled stress, fluid flow, and changing chemical [22], conventional triaxial compressive tests [23], combined static and dynamic loading [24], hightemperature treatment [25], cyclic uniaxial compressions [26], and 3D printing materials [27].Extensive researches also have been done on fracturing processes on rock with multiple hole-like aws.Lajtai and Lajtai [28] introduced failure modes based on interactions involved in the collapse of cavities.Lin et al. [29] performed uniaxial compressive tests to nd whether the coalescence mechanisms for samples with multiple holes depend on the bridge angle and the normalized bridge length and proposed a modi ed Sammis and Ashby [30] crack model to predict the peak stress.Uniaxial compressive tests, AE measuring method, photographic monitoring technique, and PFC numerical simulation were conducted by Huang et al. [31] to study cracking process and failure modes by using granite specimens containing three preexisting holes, showing that they were all in very good agreement with each other.Yang et al. [32] summarized four distinct modes based on uniaxial compressive tests of sandstone specimens with two oval aws: no crack coalescence failure, indirect crack coalescence outside the bridge area failure, single crack coalescence inside the bridge area failure, and tensile crack coalescence outside the bridge area failure.
Under dynamic loading conditions, there has been less number of studies on the dynamic mechanical properties and fracturing evolution of defected rocks.Shear cracks initiate earlier and dominate the propagation process of single crack-like awed specimens under a high loading rate by numerical simulation [33] and experimental tests [10].Li et al. [34] and Li et al. [35] systematically investigated the e ects of a single crack-like or hole-like aw on the dynamic mechanical properties and fracturing behavior.ey found that peak stress and corresponding strain were obviously in uenced by aw shapes.Six typical crack types are identi ed, and the nal failure modes are all in X shape.Jiang et al. [36] used gypsum-like 3D printing materials to analyze the dynamic crack coalescence, and the results of which were consistent with that of the traditional materials like cement concrete and natural rock.Marble specimens with double aws at the end surfaces were also studied by Li et al. [37], showing that there would be a critical inclination angle to maximize the dynamic strength, Young's modulus, and energy absorption.Crack propagation characteristics and failure patterns on both sides of the critical angle are rather symmetric.
In the present study, dynamic impact tests are performed using prismatic green sandstone specimens to investigate the e ect of aw inclination angle and ligament angle on dynamic mechanic properties and fracture mechanisms with a high-speed camera recording in real time.

Experimental Preparation and
Loading Procedure 2.1.Sandstone Material.Sandstone is widely used to investigate the cracking behavior of defected rock because of its crystalline and blocky structure [24,38,39].A type of green sandstone, taken from Neijiang city, Sichuan province, China, was used for the present dynamic compressive tests.As shown in Figure 1, the minerals in the sandstone specimens are mainly quartz (28%), plagioclase (24%), orthoclase (19%), chlorite (18%), and siliceous rock debris (7%), with grain sizes varying from 0.04 to 0.35, 0.07 to 0.35, 0.1 to 0.4, 0.1 to 0.3, and 0.005 to 0.01 mm, respectively.A detailed physical and mechanical description of the sandstone is given in Table 1.

Specimen Preparation.
In this experiment, all specimens were cut along the same direction from the same sandstone block to ensure the isotropy and uniformity of the test results.According to the method suggested by the ISRM [40]    and the validity of using prismatic rock specimens in the split Hopkinson pressure bar (SHPB) tests [41], the tested specimens were made with the length to width ratio of 1.0 to minimize the influence of end friction effects on the test results.erefore, the sandstones were processed into rectangular samples, 60 mm in length (L), 60 mm in width (W), and 25 mm in thickness (T).All surfaces of the sample were grinded and polished to make unevenness and nonperpendicularity less than 0.02 mm. e geometry of double elliptical flaws is defined by five geometrical parameters: flaw inclination angle α (the angle between major axis of elliptical flaw and loading direction), ligament angle β (the angle between the bridge and loading direction), the length of major axis 2a � 15 mm, the length of the minor axis 2b � 5 mm, and the length of the rock bridge 2c � 10 mm, as shown in Figure 2.
e specimens were prepared in three groups, where group I (intact specimens) is referred for comparison, and groups II and III contain specimens with a constant ligament angle β but different inclination angles α and specimens with a constant inclination angle α but different ligament angles β, respectively.e length of the major axis, minor axis, and rock bridge are constant for all specimens.e preexisting flaws were produced by the high-pressure water jet cutting method, which has been proven to cause no disturbance and damage to the other parts of the specimen [34].Detailed description of sandstone specimens with different flaw geometries is listed in Table 2. e specimen number describes the type of rock, flaw inclination angle, and ligament angle.For example, S-45-60 denotes a double-flawed sandstone specimen with α � 45 °and β � 60 °.

Testing Apparatus.
e modified large diameter split Hopkinson pressure bar (SHPB) test system [42,43] in the Central South University is adopted.It comprises a gas gun, a cone-shaped striker, an incident bar (2000 mm), a transmitted bar (2000 mm), an absorbed bar (800 mm), and a data acquisition system (a CS-1D superdynamic strainometer coupled with a DL750 digital oscilloscope).e striker and bars are made from high-strength 40Cr alloy steel, the diameter, P-wave velocity, elastic modulus, and density of which are 75 mm, 5400 m/s, 240 GPa, and 7800 kg/m 3 , respectively.
During tests, the specimen is clamped between the incident and transmitted bars.A slowly rising half sine wave is generated when the cone-shaped striker impacts on the front surface of the incident bar, which can effectively avoid the stress uneven before the failure of the specimens.Strain pulses (Figure 3) are collected in real time by the CS-1D superdynamic strainometer coupled with strain gauges mounted in the bars, displayed and stored by a digital oscilloscope combined with a computer.e assumption of one-dimensional stress wave theory can be achieved by using large slenderness ratio bars.
e assumption of stress equilibrium before failure can be achieved well by using a cone-shaped striker (Figure 4).Based on the "3-wave analysis" [44,45], the axial stress σ(t), strain ε(t), and strain rate _ ε(t) can be derived by the following equations: where A e , C e , and E e are the cross-sectional area, P-wave velocity, and Young's modulus of the elastic bar, respectively.A s and L s are the cross-sectional area and length of the specimen, respectively.ε I (t), ε R (t), and ε T (t) are incident, reflected, and transmitted strain pulses, respectively.
In order to observe the fracture behaviors of defected specimens, a high-speed camera is always used for synchronously recording the failure process [7].During the testing process, a FASTCAM SA1.1 high-speed camera under the illumination of a high-intensity flash light was placed perpendicularly to the specimens so as to capture the images, simultaneously storing in a computer for subsequent processing.e frame rate of the camera is 75000 fps (frames per second) with a resolution of 256 × 208 pixels so that it can capture a picture each 13.3 µs.

Mechanical Properties of Flawed Sandstone with Different
Flaw Inclination Angles.In the present dynamic tests, the peak strain ε d is defined as the strain corresponding to the peak stress σ d and dynamic Young's modulus E 50 is defined as the ratio of the half of the peak stress to the corresponding strain.Table 2 lists the values of dynamic compressive strength σ d , Young's modulus E 50 , peak strain ε d , and strain rate _ ε of intact and defected sandstone specimens.It is obvious that the dynamic strength and corresponding strain of the defected specimens are all lower than those of the intact specimen.
Figures 5-8 reveal the influence of the flaw angle on the strength and deformation parameters of sandstone specimens.e dynamic stress-strain curves of sandstone specimens containing two elliptical flaws with different flaw angles are shown in Figure 5.It is very clear that the flaw angle has a distinct effect on the curve shape especially for α > 0 °.It can be seen from Figure 6 that dynamic strength of the defected sandstone specimens with a constant ligament angle decreases with the flaw angle increasing, reaching the minimum value of 76.30 MPa when α � 90 °.When the flaw angle increases from 0 °to 15 °and from 75 °to 90 °, the dynamic strength marginally decreases with a reduction from 5.91% to 6.29% and from 39.76% to 39.92% (compared to the intact specimen).When the flaw angle increases from 15 °to 75 °, the dynamic strength dramatically decreases with a reduction from 6.29% to 39.76%.Notably, the magnitude of the strength reduction in the range of 15 °∼75 °is much higher than that in the range of 0 °∼15 °and 75 °∼90 °.Advances in Civil Engineering Figure 7 depicts the in uence of the aw angle on the dynamic Young's modulus of defected sandstone specimens.It rst decreases to its lowest value of 8.95 GPa at α 75 °then increases as α increases to 90 °. e in uence of the aw angle on the dynamic Young's modulus is similar to that on the dynamic strength.

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e relationship between the peak strain and aw angle is plotted in Figure 8. e dynamic peak strain increases when α ranges from 0 °to 60 °, reaching the maximum value of 0.864% when α 60 °but then decreases between 60 °and 90 °.

Mechanical Properties of Flawed Sandstone with
Di erent Ligament Angles.
e dynamic mechanical and deformation properties of the defected sandstone specimens are plotted against the ligament angles in Figures 9-12.e dynamic stress-strain curves of sandstone specimens containing two elliptical aws with various ligament angles are shown in Figure 9. e curve shapes are similar when the ligament angle reaches 30 °, and the in uence of the ligament angle on the curve shapes is less insigni cant compared to that of the aw angle.e relationship between the dynamic strength and the ligament angle is presented in Figure 10.e dynamic strength decreases rst, then increases, and nally decreases nonlinearly with the ligament angle increasing, and the maximum value of 103.5 MPa is obtained at a critical angle of β 90 °.When the ligament angle increases from 90 °to 150 °, the dynamic strength decreases with a reduction from 18.50% to 21.26%, which indicates that dynamic strength changes marginally as β reaches 90 °.
Figure 11 shows the e ects of the ligament angle on the dynamic Young's modulus.e trend of Young's modulus is similar to that of the strength decreasing rst, then Advances in Civil Engineering increasing, and nally decreasing with a maximum of 12.66 GPa at β 90 °.It can be seen from Figure 11, the dynamic Young's modulus changes marginally overall, indicating that the in uence of the ligament angle on the dynamic Young's modulus is insigni cant.
e relationship between the peak strain and the ligament angle is shown in Figure 12. e dynamic peak strain rst decreases when α ranges from 0 °to 90 °(except α 60 °), reaching the minimum value of 0.467% when α 90 °but then increases for α between 90 °and 150 °.
From the above analysis, it can be concluded that the dynamic mechanical and deformation parameters are closely related to the aw geometries.e results indicate that the e ect of the aw inclination angle on the dynamic strength and Young's modulus is more signi cant than that of the ligament angle but is less on the deformation.e failure patterns of defected specimens are vital to interpret the entire cracking sequence and the failure mechanisms of rock under dynamic loading.Figures 13 and 14 present the nal failure modes of sandstone specimens with double elliptical aws under dynamic loading.Figure 13(a) shows the nal failure mode of a typical intact specimen.It can be seen that shear and axial splitting cracks are both observed during the crack propagation process, leading to a typical mixed shear and splitting mode.Both aw inclination angle and ligament angle a ect the ultimate failure modes of the awed specimens and make them more complicated.

Crack Propagation and Failure Patterns
Figure 13 depicts the in uence of the aw angle on the nal failure modes of defected sandstone specimens with a consistent ligament angle of 0 °.It can be seen from Figures 13(b)-13(h) that three types of failure modes are identi ed  It is found that there is no crack coalescence inside the bridge area and the dominated cracks are almost all around the preexisting flaws for β within a certain range (60 °-120 °).Totally, five typical types of failure modes are identified based on the crack coalescence.

Microscopic Analysis of Crack Coalescence.
e surface morphology for fracturing usually reveals the failure process and energy evolution [46].Scanning electron microscopy (SEM) has been used for many tests to analyze microscopic cracking characteristics, including triaxial compression tests [47,48], rock after high-temperature treatment [25], and failure mechanism by supercritical CO 2 jet impingement [49].In this investigation, crack coalescence in the bridge area was examined by SEM. Figure 15 represents the petrographic image analysis for shear and tensile crack coalescence, respectively.
As shown in Figures 15(a ) are all obtained.e smooth bands are mainly associated with quartz [50], the cleavage steps are affected by grain size and the orientation of the cleavage plane, and the scratches and the pulverized rock powder are usually dominated by fast crack propagation [51].Shear friction leaves typical features containing river lines, step cracks, and intercalated dislocation on the collapsed surface.From Figures 15(c) and 15(d), the tensile failure section has a relatively flat feature with a small amount of tiny crystal debris, showing obvious traces of tensile cracks.e weaker crystal particles will be broken to produce a transgranular failure with a lumpy surface.However, there will be an intergranular damage along the interface among the grains if the strength of crystal grains is stronger.

Crack Propagation Behavior. Figures 16-20 present the typical visible crack initiation, propagation, and coalescence
processes under dynamic loading.e numbers shown in these figures represent the occurrence sequences of cracks recorded by the high-speed camera, and the superscript letters indicate that the cracks initiate almost simultaneously from different positions of the specimen.

Type I:
Specimen S-0-0. Figure 16 shows a typical fracturing process for type I mode of the defected specimen with α � β � 0 °.Shear crack 1 initiates from the interface between the specimen and transmitted bar with the dynamic stress of 98.5 MPa at the time of 80 μs.
en it widens, intensifies, and lengthens along the loading direction.When the dynamic stress reaches 119.0 MPa at t � 133.3 μs, the dextral crack 2 from the edge of the specimen and incident    Shear crack 1 a coalescence between the ligament area occurs before the peak stress, and shear crack 1 b initiates from the aw tips at the same time.As the dynamic stress increases to 96.2 MPa, another shear crack 2 generates at the outer tips of the other aw and extends to the edge of the specimen.After the initiation of crack 2, the dynamic stress reaches the peak.However, no new obvious crack is observed at the peak strength except the longer and wider original ones than before.When the stress marginally drops to 93.5 MPa at t 200.0 μs, far-eld crack 3 generates at the interface between the specimen and the incident bar and propagates to the upper edge of the specimen.When the stress drops to 67.6 MPa, lateral tensile cracks 4 a-b initiate at the edges.At this moment, original cracks 1 b and 3 have a connection, resulting surface spalling with much pulverized rock powder.

Type III:
Taking Specimen S-90-0 as an Example.
Figure 18 summarizes a typical crack evolution for type III mode of the defected specimen with α 90 °and β 0 °.When the specimen is loaded to 51.4 MPa, tensile crack 1 generates at the inner tips of double aws, and then crack coalescence occurs instantaneously with slight surface spalling in the e typical crack evolution for type IV mode of the defected specimen with α 45 °and β 120 °is plotted in Figure 17.As can be seen from Figure 19, the cracking production is concentrated around the peak value and in the postpeak stage.e initial crack 1 a emerges at the outer tip of the downward aw when the dynamic stress reaches 101.6 MPa; meanwhile, spalling 1 b is observed in the outer tip of the other aw.Subsequently, the dynamic stress increases to the peak.
en, the stress slightly drops to 96.9 MPa, and a tensile crack 2 generates from the edge of the specimen and propagates stably.As the stress continues to unload to 85.4 MPa at t 240.0 μs, a wing tensile crack 3 initiates at the outer tip of the upper aw where original spalling grows.
en, the supporting structure of the specimen is damaged into a tensile-dominated failure, but the bridge area is still in good condition.en, it propagates in a curvilinear path to coalesce with the inner tip of the other aw.Subsequently, the dynamic stress reaches the peak value.
en, the stress drops with an increase in deformation.As the dynamic stress unloads to 93.2 MPa at the postpeak stage, a shear crack 2 initiates at the tip in a diagonal direction of crack 1 tip but gradually propagates into a wing type with the stress continuing dropping.When the stress drops to 81.3 MPa, a pure shear crack 3 is observed at the outer tips of the upper aw and extends to the edge of the specimen along the diagonal direction.Finally, the dynamic stress drops rapidly to point 4, resulting in the generation of shear crack 4 at the interface between the transmitted bar and specimen with a little deformation.It is clear that both shear and tensile cracks are dominated during the failure process.12 Advances in Civil Engineering

Conclusions
(1) It is found that the dynamic strength and Young's modulus of green sandstone specimens with double elliptical aws decrease with the aw angle increasing, but these parameters are not obviously a ected by the ligament angle.However, the inuence of the ligament angle is more remarkable on the dynamic peak strain of sandstone specimens than that of the aw angle.It indicates that the e ect of the aw angle on the dynamic strength and Young's modulus is more signi cant than that of the ligament angle but is less on the deformation.
(2) e geometric parameters including aw inclination angle and ligament angle of noncoplanar aws have a signi cant in uence on the nal failure modes of the sandstone specimen.Five types of failure modes are identi ed based on the fracturing photos taken by a high-speed camera.Macroscale cracks mostly initiate at or near the aw tips and propagate in di erent paths with varying aw geometries,   Advances in Civil Engineering

Figure 1 :
Figure 1: Microscopic structure by mineral composition and optical microscopy analysis: (a) plane-polarized light; (b) perpendicular polarized light.

Figure 4 :
Figure 4: Stress equilibrium of the sandstone specimen S-60-0 between incident and transmitted bars.

Figure 5 :Figure 6 :Figure 7 : 2 )Figure 8 :
Figure 5: In uence of the aw angle on the dynamic stress-strain curves of specimens with a constant ligament angle of 0 °.

Figure 9 :Figure 10 :Figure 11 : 2 )Figure 12 :
Figure 9: In uence of the ligament angle on the dynamic stressstrain curves of specimens with a constant aw angle of 0 °.

Figure 14 °Figure 13 :
Figure14shows the influence of the ligament angle on the final failure modes of defected sandstone specimens with a consistent flaw inclination angle of 45 °.It can be seen from Figure14that the final failure modes are divided into three types by analyzing the crack coalescence under dynamic loading:Type II: shear crack coalescence inside the bridge area, β � 0 °and 30 °Type ) and 15(b), the overall shape of the shear fractography section performs a wavy terrain extending to farther positions.Smooth shear bands (Figure 15(b)), cleavage steps (Figure 15(b)), coarse scratches (Figure 15(a)), and pulverized rock powder (Figures 15(a) and 15(b)

Figure 15 :
Figure 15: SEM images of typical crack coalescence between two aws: (a, b) specimen S-45-0; (c, d) specimen S-90-0.e opposite arrows and the reverse arrows represent slipping and tensile area, respectively, and S and T represent shear and tensile cracks, respectively.

Figure 17
depicts a typical fracturing process for type II mode of the defected specimen with α 45 °and β 0 °.

Figure 20
displays a typical crack evolution for type V mode of the defected specimen with α 45 °and β 150 °.It is obvious that the cracking production is concentrated around the peak value and in the postpeak stage.Shear crack 1 initiates at the inner tip of the downward aw with the dynamic stress of 98.6 MPa at the time of 146.7 μs.

Table 1 :
Basic physical and mechanical properties of the sandstone.

Table 2 :
Geometrical sizes and mechanical parameters of sandstone specimens.