Crack Initiation , Propagation , and Coalescence Experiments in Sandstone Brazilian Disks Containing Pre-Existing Flaws

.is study aims to investigate the fracture behaviors of cracks and crack systems in Brazilian disk (BD) sandstone specimens under compressive line loading. We conduct a series of rock fracture experiments to investigate crack initiation, propagation, and coalescence in samples with one or more pre-existing flaws under radial compressive stress..e displacements and failure loads of the tested specimens are measured. Experimental results show that there are two main types of cracks growing from the preexisting flaws: wing cracks and secondary cracks. Both initiate mostly from the tips of the pre-existing flaws and propagate in a stable manner. .e results reveal that wing cracks appear first and propagate toward the loading direction. Secondary cracks can form in some multiple pre-cracked cases after wing cracks are already present. We also provide a characterization of the observed crack propagation paths and patterns and discuss the influence of pre-existing crack or crack systems. .e results help in investigating the failure mechanisms and mechanical properties of rock or rock-like materials.


Introduction
In general, rock mass is a natural formation of mineral aggregates which may contain voids, cracks, and other defects at different scales.
is makes rocks' internal structure discontinuous [1][2][3], as shown in Figure 1. e presence of pre-existing defects may reduce the fracture toughness of rock mass, and such defects are also a source of initiation of new fracture lines or cracks.Crack growth and catastrophic failures initiated from the pre-existing defects subjected to multiaxial loads is one of the main concerns for geotechnical engineers and designers of underground structures.Under external and internal pressures, cracks can initiate and propagate from those pre-existing cracks or pores and then coalesce into macrofailure of the rock structure.
Because of the difficulties of in-situ tests, the laboratory experiment is an important and effective research method to investigate rock failure modes and fracture mechanisms, in the presence of pre-existing defects that can be easily inserted into the samples.Over the last few decades, many experiments have been devoted to using semi-circular core in three-point bending (SCB) specimen [4], Brazilian disk (BD) specimen with chevron flaws or other pre-existing flaws [5], radial cracked ring (RCR) specimen [6], and modified ring (MR) specimen [7] to investigate rock fracture toughness and crack propagation.Brace and Bombolakis [8] conducted an experimental study on fracture mechanisms in rock material, and it is considered one of the earliest studies in this field.en, the extensive studies have been performed on cracking failure processes evolution from pre-existing discontinuities that emerged in brittle materials.And a series of fracture experimental tests were conducted to study crack initiation, propagation, and coalescence under compressive diametric or cyclic uniaxial compression loading using precracked specimens or intermittently joint rock models [9][10][11][12][13][14][15][16].
e crack propagation patterns usually obtained in previous studies of brittle material contain pre-existing flaws under uniaxial compression loading, as shown in Figure 2. Two types of cracks were observed: wing cracks and secondary cracks [17][18][19][20].Based on different experiment conditions (such as the type of specimen, specimen size, pre-existing flaws geometry, and load arrangements), the researchers observed common crack characteristics: wing cracks come into being first, which are tensile cracks and they mostly initiate from the tips of the pre-existing flaws at an angle and then propagate to be parallel to the compressive direction.Secondary cracks are usually shear cracks that appear later than wing cracks.ose researchers believe that cracks coalesce on account of the development of shear cracks.Wong and Einstein [21,22] studied the systematic evaluation of cracking behaviors in specimens with pre-existing flaws and observed the cracking mechanism with enough details under uniaxial compression using the high-speed camera.Figure 3 shows the category of coalescence patterns and seven crack types with different trajectories and initiation mechanism.Other researchers found cracks coalescence in the linkage areas of the pre-existing flaws, which is caused by the secondary cracks or the combined effects of wing cracks and secondary cracks.is can better illustrate the damage processes [23][24][25][26][27][28][29][30][31][32][33].
However, because of the complexity of natural rock mass, researchers usually used artificial materials such as resin, cement mortar, organic glass, or gypsum, which cannot reveal the fracture mechanisms and mechanical properties effectively.Moreover, the experimental studies about pre-existing crack systems in natural brittle sandstone material from deeper underground are still poorly.Crack initiation and propagation, especially coalescence, is dependent on the types of pre-existing flaws.Some pre-existing flaws may play a role in preventing cracks' propagation and coalescence as barriers.So, the crack propagation paths and load-carrying ability in practical applications can be significantly affected by the cracked flaw forms and types of conducted loading [34,35].To investigate crack propagation and crack coalescence in linkage areas, we develop precracked specimens with different inclination angles and new types of specimens with pre-cracked crack systems.In this paper, the term "flaws" is used to describe the artificially created single crack or crack systems.e new types of crack systems consist of the forward echelon cracks system, inverse echelon crack system, two parallel cracks, three parallel cracks, and crack system with barrier cracks.e geometries of those pre-cracked flaws are expected to improve the understanding of fracture mechanisms of underground sandstone.Loads and displacements are recorded for all specimens during the whole breakage process.In addition, the load-displacement curves are shown to discuss the process of the tested specimens.erefore, the motivation for this work will focus on two points: (1) investigating the effects of pre-existing flaws on the cracking behaviors and the crack coalescence patterns in sandstone specimens containing different types of pre- existing flaws and (2) characterizing and analyzing the crack initiation, propagation, and coalescence patterns from preexisting flaws. is paper is organized as follows.In Section 2, the preparation of disk specimens and the experimental procedure are introduced.e experimental results are discussed in Sections 3 and 4. Finally, in Section 5, we draw some conclusions.

Preparation of Disk Specimens and Experimental Procedure
To study the fracture behavior of sandstone BD specimens, we cut specimens with pre-existing different inclination angles of crack and different types of the crack systems and tested them under compressive line loading.e sandstone is from about 900-meter depth underground strata in Juye Coalfield, Shandong Province, China.

Preparation of Specimens.
e sandstone samples were excavated by geologic drilling from Juye Coalfield, whose Cenozoic formation is very thick.e average thickness of strata in the fourth system is 158.43 m, the average thickness of the upper tertiary strata is 497.01 m, and the thickness of the new boundary layer is 530∼720 m, mainly composed of clay, sandy clay, sand, fine sand, and gravel.Main coal seam roof and floor sandstone thickness is 4.80∼75.65m, mainly composed of fine sandstone, local sandstone, and siltstone.e preparation of tested specimens for pre-cracked flaw procedures is explained as follows.
For manufacturing the test specimens, the whole tests used five samples and each one was cored into 30∼50 cm long, with the diameter D � 62 mm cylindrical columns in the construction site.In order to avoid being influenced by surroundings, the surface of the samples was wrapped in a multilayer food preservation film after being removed from the formation.e specimens were cut into Brazilian disk shape, with a size of Φ 62 × 30 mm. e pre-existing flaws were created by high-speed water jet cutting machine.Figure 4 shows the pre-existing flaws preparation setup for tested specimens.e pre-existing flaws thickness is 30 mm. e flaw length, 2b, is equal to 20 mm and the pre-existing flaws width is 1 mm.e radius and thickness of the tested BD specimens are R � 31 mm and H � 30 mm.Crack length ratio is an important parameter for the pattern, trajectory, and the number of fractures; in this work, the ratio b/R is 0.32.
Various Brazilian tests were conducted on BD specimens containing a single crack and different types of crack systems.Figure 5 shows geometries of pre-cracked specimens; the inclination angle (angle with the horizontal, β) varies from 0 °to 90 °at 15 °interval.Furthermore, Figure 6 shows a schematic view of BD specimens containing different types of pre-existing crack systems.Finally, a total number of 31 pre-cracked specimens were tested, with two or three specimens at each inclination angles: β � 0 °, 15 °, 30 °, 45 °, 60 °, 75 °, and 90 °.Two or three specimens at each type of crack  (a)  Several specimens with the same pre-existing flaw geometries were prepared to guarantee the reproducibility of the following experimental results presented.Table 1 shows the specimens containing different types of pre-existing flaws.e types of specimens are present as SC and CS for specimens with single pre-existing crack and the pre-existing crack systems; the flaws inclination angle, which is denoted by β, and followed by the sequential number of specimens.For example, SC15-2 represents the second, single preexisting crack specimen with inclination angle β � 15 °. e specimens in italics mean that those are shown as the experimental results in Section 3.

Experimental
Procedure.Generally, the underground rock mass exists in a state of compression stress, and the cracks propagate toward a direction parallel to the maximum compressive stress [20].In the experimental process, the specimens were located in an appropriate position inside the two flat plates of the test machine and loaded by a diametric compressive force P. As shown in Figure 7, all samples were tested by an electronic universal testing machine with a capacity of 100 kN.e tests were carried out under displacement control conditions with a constant displacement rate of 0.05 mm/min.Monotonic loading was applied until the final crack propagation and coalescence form are reached.

Crack Propagation Process of Pre-Cracked Specimens with a Single Crack.
In the single pre-cracked specimens, most cracks are tensile cracks, but shear cracks may also be accompanied.Figure 8 shows the experimental results of crack propagation paths and the breakage process of specimens with different pre-existing inclination angles.e patterns are quite different for the specimen (β � 0) than those (β � 15 °, 30 °, 45 °, 60 °, 75 °, 90 °): wing cracks propagated in curved paths, starting their extension from the crack tips and continue their growth in a direction approximately parallel to compression direction.Meanwhile, crack propagation growth stopped at the release of the load.Figure 8(a) shows that there is no crack initiated from the tips of the pre-existing crack when β � 0.
e wing cracks initiated from the middle of the pre-existing crack, and along the pre-crack perimeter, the tangential stresses are maximum like the uncracked specimen in a conventional Brazilian test.However, the cracks immediately propagated toward the edges of the specimens once they initiated.

Crack Propagation Process of Pre-Cracked Specimens with
Crack Systems.In the specimens containing pre-existing crack systems, because of the propagation of wing cracks and secondary cracks, crack coalescence phenomenon occurred.Wing cracks propagated toward the direction of the maximum compressive stress.However, secondary cracks propagated and formed a corner with the opposite direction of preexisting flaws.Even the cracks coalescence in the bridge areas may appear during the cracks' initiation and cracks propagation processes.Figure 9 illustrates the experimental results of crack propagation and coalescence in the specimens with different types of pre-existing crack systems.
e crack propagation and coalescence patterns are different depending on the types of crack systems.Figure 9(a) presents a specimen with the forward echelon crack system; cracks at the tips pre-existing crack systems were initiated in both directions and tip C of L 2 propagated to tip A of L 1 and coalesced at tip A. Crack from tip B of L 1 propagated to tip D of L 2 and coalesced at tip D. In the specimen containing inverse echelon crack system as shown in Figure 9(b), the crack at tip A of L 1 was initiated in an upward direction and the crack at tip D of L 2 was initiated in a downward direction steadily, and coalescence paths appeared between tips A and D. Figure 9(c) illustrates that cracks at the upward tips were initiated both toward upward  In the experiments, the wing cracks and secondary cracks interrelated with and propagated toward each other, which caused cracks coalescence in the bridge areas.Coalescence cracks originated from the tips of one pre-cracked flaw to another.Crack propagation patterns and characteristics in both single pre-cracked and pre-cracked crack system specimens are summarized in Table 2.  Wing cracks were initiated from the tips of the pre-existing crack in the direction parallel to the maximum compressive stress 2. No secondary cracks Forward echelon crack system Inverse echelon crack system Two parallel cracks 1. Wing cracks were initiated from the tips of the pre-existing cracks in the direction of the maximum compressive stress 2. Secondary cracks were initiated after wing cracks 3. Cracks coalescence paths appeared between the two pre-existing cracks ree parallel cracks 1. Wing cracks were initiated from the tips of the pre-existing crack in the direction parallel to the maximum compressive stress 2. No secondary cracks Crack system with barrier cracks 1. Wing cracks were initiated from the tips of the pre-existing crack in the direction of the maximum compressive stress 2. Crack propagation of the pre-existing crack was not blocked by the barrier cracks 3. Crack propagation paths have changed after they passed through the barrier cracks Advances in Civil Engineering

Discussion
In this section, we discuss the experimental data.Figure 10 indicates the load-displacement curves of the pre-cracked specimens with different inclination angles.It can be seen that pre-cracked specimens fractured suddenly from the crack tips in a typical brittle manner after the loaddisplacement curves reach its peak.at means the specimens began to fracture when the wing cracks extended to a critical length of the specimens' edges and the specimens were split into two nearly same halves.Typical load-displacement curves for the specimens containing pre-cracked crack systems are shown in en, the secondary cracks began to propagate.After the secondary peak value in the load-displacement curves, those specimens began to fail, and cracks coalescence occurred.In other words, the cracks coalescence appeared mainly caused by the wing cracks or their propagation and the combined effects of wing cracks and secondary cracks.In Figure 11(d), the specimen with three parallel cracks, wing crack extends to the specimen's edges and the specimen splits into two same halves.e fracture and failure patterns are similar to those with single pre-cracked specimens.

Conclusions
Crack initiation, propagation, and coalescence are a rather difficult and complicated process.It is not only determined by the material but also dependent on the geometries of the pre-existing flaws.In this paper, BD specimens with single pre-existing crack and the pre-existing crack system were experimentally investigated, and the effects of fracturing on the failure load of the tested specimens have been discussed.
e following conclusions can be drawn from the results presented above: (1) Two type cracks were observed: wing cracks and secondary cracks.Both mainly initiated from tips of the pre-existing flaws and propagated in a stable manner.Wing cracks appear at the first stage of loads applied and propagate toward the compression direction, and then the secondary cracks initiate afterward.is can lead to crack coalescence with breakage processes.According to the different geometries of pre-existing flaws, the tested specimens experienced wing crack propagation failure or crack coalescence failure.
(2) In this experimental work, crack coalescence appears by the linkage of two pre-existing flaws through combinations of the wing and/or secondary cracks.
According to the different geometries of pre-existing flaws, crack coalescence patterns are different.Cracks propagation and coalescence were not blocked by the barrier cracks, and the crack propagation paths have changed after they passed through the barrier cracks.(3) From the results, the pre-existing flaws or fractures play a significant role in the overall integrity that can help to analyze the stability of rock masses and rock structures.

Figure 1 :Figure 2 :
Figure 1: Schematic view of pre-existing defects in the natural rock mass.

Figure 4 :Figure 5 :
Figure 4: Pre-existing flaws preparation in sandstone BD specimens using a water jet cutting machine.

1 L 2 LFigure 6 :
Figure 6: Geometries of different types of crack systems: (a) forward echelon crack system, (b) inverse echelon crack system, (c) two parallel cracks, (d) three parallel cracks, and (e) crack system with barrier cracks.

Figure 10 :
Figure 10: Load-displacement curves of the tested specimens with different pre-existing crack inclination angles: (a) β � 0, (b) β � 15 °, Figure 11.Based on Figures 11(a), 11(b),11(c), and 11(e), one of the noticeable characteristics is the decrease in loading after the wing cracks appeared.It means that the wing cracks propagated to the edges from tips of the pre-existing cracks after the first peak value in the load-displacement curves.

Figure 11 :
Figure 11: Load-displacement curves of the specimens with different types of crack systems.(a) Forward echelon crack system.(b) Inverse echelon crack system.(c) Two parallel cracks.(d) ree parallel cracks.(e) Crack system with barrier cracks.

Table 1 :
Specimens containing different types of pre-existing flaws.

Table 2 :
Crack propagation patterns and characteristics in pre-cracked specimens.Wing cracks were initiated from the middle portion of the pre-existing crack in the direction of the maximum compressive stress 2. Specimens fractured and split away due to the indirect tensile effect like uncracked specimens in conventional Brazilian tests 3.No secondary cracks β � 15 °, 30 °, 45 °, 60 °, 75 °, and 90 °1.