An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression

    An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression Sheng-Qi Yang, Yan-Hua Huang, Wen-Ling Tian, Jian-Bo Zhu PII: DOI: Reference:

S0013-7952(16)30277-0 doi:10.1016/j.enggeo.2016.12.004 ENGEO 4434

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

5 September 2016 8 December 2016 11 December 2016

Please cite this article as: Yang, Sheng-Qi, Huang, Yan-Hua, Tian, Wen-Ling, Zhu, JianBo, An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression, Engineering Geology (2016), doi:10.1016/j.enggeo.2016.12.004

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ACCEPTED MANUSCRIPT Engineering Geology (2nd Minor Revision)

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An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression

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Sheng-Qi Yang a, *, Yan-Hua Huang a, Wen-Ling Tian a, Jian-Bo Zhu b

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a. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, PR China; b. Department of Civil and Environment Engineering, The Hong Kong Polytechnique University, Hong Kong, PR China

Corresponding author: Professor. Sheng-Qi Yang Tel: +86-516-83995856 Fax: +86-516-83995678 E-mail address: [email protected]

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Abstract: To increase the understanding of strength and failure mechanism of fractured rock, a series of uniaxial compression tests on red sandstone specimens containing two pre-existing oval flaws was carried out using a rock mechanics servo-controlled testing system. On the basis of the experimental results, the influences of the coplanar flaw angle and ligament angle on the mechanical parameters and fracture process of sandstone specimens containing two oval flaws were analyzed in detail. The mechanical parameters including peak strength, peak strain and elastic modulus of pre-flawed specimens are all much lower than those of the intact specimens. For the specimens containing two coplanar oval flaws, the peak strength is distinctly related to the coplanar flaw angle, while the peak strain and elastic modulus are not obviously dependent on the coplanar flaw angle. For the specimens containing two non-coplanar oval flaws, the peak strength, peak strain and elastic modulus all have a nonlinear relationship with the ligament angle. By adopting photographic and AE monitoring techniques, the crack initiation, propagation and coalescence process and the AE evolution behavior of sandstone specimens were all observed and characterized. The stress drops in the stress-time curve correspond to a sudden increase in accumulated AE counts in the accumulated AE-time curve, resulting from the initiation and coalescence of cracks. The ultimate failure modes of sandstone specimens containing two pre-existing oval flaws are a mixture of several cracks (wing crack, anti-wing crack, secondary crack, shear crack and far-field crack and surface spalling), which depend on the flaw geometry. The failure patterns of pre-flawed specimens can be identified as the following four distinct modes: 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. The last failure mode was only observed in the specimens containing two non-coplanar oval flaws for β=120°and 150° due to the two pre-existing overlapping flaws.

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Key words: Sandstone; two oval flaws; crack evolution; strength; AE count

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1 Introduction Engineering rock mass consists of intact rock material and structural planes. The strength and deformability of rock masses having pre-existing structural planes are very difficult to evaluate. The failure behavior of the rock mass is heavily controlled by the existence of structural planes. Many real construction projects have shown that unstable failure always starts from these pre-structural planes. Hence, the investigation of the strength, deformability and fracture behavior is very significant for the understanding of the fracture mechanism of the rock mass and predicting the unstable failure of jointed rock engineering. To study the crack initiation, propagation and coalescence behavior of rock containing intermittent structures, many laboratory tests have been performed on rock materials or rock-like materials containing a pair of pre-existing structures. Rock-like materials, in which pre-existing flaws are easily fabricated, have been widely used in laboratory experiments. To investigate the effect of flaw geometry and lateral stress conditions on the fracture phenomena (Bobet and Einstein, 1998), uniaxial and biaxial compression tests were conducted for gypsum specimens with two open or closed flaws, showing that the types of crack and coalescence were dependent on the flaw geometry and stress conditions. Wong and Chau (1998) carried out uniaxial compression tests for sandstone-like material containing two parallel flaws with changing values of dip angle, bridge angle and frictional coefficient. The typical modes of crack coalescence, i.e., shear mode, mixed shear and tensile mode and wing tensile mode were summarized from their experimental results. Wong and Einstein (2009) tested on gypsum specimens containing two open flaws under uniaxial compression. In their study, the flaw angle, ligament length and ligament angle showed different effects on the coalescence patterns. Tang et al. (2015) conducted uniaxial compression tests on a new transparent rock-like material to study crack coalescence modes with changing bridge angle values. Their experimental results showed that the coalescence modes could be classified as shear mode, mixed mode and wing tensile mode, which depend on the bridge angles. Gratchev et al. (2016) studied the effects of the length and width of a flaw on the strength of rock-like specimens. They found that the specimens with longer and wider flaws had lower strength and that failure was mainly caused by a shear crack. Zhao et al. (2016) carried out a series of uniaxial compression tests on rock-like specimens having two pre-existing flaws. They focused on the local strain concentration near the flaw tips to study the relationship between tensile or compression strain concentration and initiation of cracks. Cao et al. (2016) tested rock-like specimens with two and three parallel pre-existing fissures under uniaxial loading. In their study, seven types of crack coalescence were identified from the experimental results of specimens containing various fissure angles. However, although rock-like materials can simulate some behaviors of real rock well, it is very difficult to simulate all properties of real rock materials, such as the heterogeneity, mineral grains, boundary effect and cementation. Some experiments on real rock materials (such as marble, sandstone, limestone and granite) have also been carried out to investigate the crack initiation, propagation and coalescence behaviors of rock. Li et al. (2005) investigated the flaw geometry on the crack evolution and AE characteristics of marble specimens containing a single or two parallel flaws. In their study, two types of crack, i.e. wing crack and shear crack were observed at the tips of pre-existing flaws. The real-time crack evolution process of limestone specimen containing pre-existing flaws after chemical corrosion was experimental studied by Feng and Ding (2007). The cracking velocity, length, width, and orientation of the cracks were analyzed to verify the applicability of their developed MHC test system. Yang (2011) investigated the real-time cracking behavior of sandstone specimen containing two coplanar flaws with different flaw angles under uniaxial compression. In accordance with photographic monitoring results, the relationship between coplanar flaw angle and crack coalescence stress was constructed. Furthermore, Yang et al. (2013) tested the strength and failure behavior of sandstone specimen with a pair of unparallel flaws under uniaxial compression. By adopting photographic monitoring and AE technique, they analyzed the crack coalescence and AE evolution behavior depending on various flaw angles. The crack initiation, propagation and coalescence process of granite specimens with two unparallel flaws (inclined and horizontal) were tested by Lee and Jeon (2011). A white patch was observed before the crack initiated at that place, but the cracks did not always

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emanate at the white patch in the granite specimens. In addition to laboratory tests on specimens containing crack-like flaws, tests have also been carried out on some rock or rock-like specimens containing hole-like flaws to investigate the cracking behavior, such as in the works of Haeri et al. (2015), Li et al. (2016), Lin et al. (2015), Liu et al. (2015) and Wong et al. (2006). However, the pre-existing flaws in natural rock are complicated, and cannot be simplified as crack-like or hole-like flaws. In practical engineering, oval-like flaws are also a common type of pre-flaws. Fig.1 shows a natural rock mass containing pre-existing oval-like flaws. Unstable failure may occur due to crack coalescence between the preexistent flaws. It is clear that pre-existing oval flaws affect the strength, deformation and failure behavior of rock mass (Li et al., 2015; Du et al., 2016). However, no laboratory experiments have been carried out on red sandstone specimens containing a pair of oval flaws with different dip angles (flaw angle and ligament angle) to date. Therefore, uniaxial compression tests were conducted in this study using a rock mechanics servo-controlled testing system to investigate the fracture mechanism of sandstone specimens containing two pre-existing oval flaws. Photographic and AE monitoring techniques were used to study the real-time crack coalescence process and AE characteristics of pre-flawed red sandstone specimens.

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Oval-like flaws

Fig.1. Rock mass containing pre-existing oval-like flaws

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Experimental material and loading procedure

2.1 Sandstone material To investigate the cracking behavior of rock containing two oval flaws under uniaxial compression, sandstone from Rizhao City in the Shandong province of China was chosen as the experimental object for this research (Yang, 2016). The sandstone is a fine-grained heterogeneous material, which has a crystalline and blocky structure (see Fig. 2(a)), and an average unit weight about 24.1 kN/m3 (assuming the acceleration of gravity is equal to 10 N/kg). The tested sandstone has a porosity of 6.88%. Based on X-ray diffraction (XRD), the minerals in the sandstone are quartz, K-feldspar, plagioclase, calcite, dolomite, hematite and clay minerals. The composition of this rock can be described as follows: the content (weight %) of quartz is 10.1%, that of K-feldspar is 11.7%, that of plagioclase is 41.6%, that of calcite is 10.7%, that of dolomite is 13.1%, that of hematite is 2.4% and that of clay mineral is 10.4%. The main minerals were also confirmed by thin section observations (Fig. 2(b)).

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2.2 Preparation of specimens containing two coplanar oval flaws In the present research, sandstone specimens containing two oval flaws were prepared for uniaxial compression tests. The specimens were cut from the same rectangular block. When cutting, the sandstone specimens were machined along the same direction to avoid the anisotropy affecting the experimental results. To obtain the exact results and the best comparison, all the tests were performed under natural and dry conditions. Following previous studies (Zhang et al. 2015; Zou et al. 2016), the height-to-width ratio of the tested specimen is 2.0 to minimize the effect of end friction on the testing results. Therefore, the all tested sandstone specimens were rectangular, 160 mm in height, 80 mm in width and 30 mm in thickness. As a result, all tested specimens with the height-to-width ratio of 2.0 ensure a uniform stress state within the central part of the specimen.

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Micro-pores

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(a) Scanning electron microscopy (SEM) image (b) Thin section observation Fig.2. Microscopic structure of tested sandstone in the present study. (a) Scanning electron microscopy (SEM) image. (b) Thin section observation.

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(c) Detail geometry of two oval flaws

Fig.3. Geometry of two oval flaws in a sandstone specimen. (a) Two coplanar oval flaws. (b) Two non-coplanar oval flaws. (c) Detail geometry of two oval flaws.

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Table 1

b /mm

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c /mm

α/°

β/°

Note

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—

—

—

—

—

—

—

Intact specimen

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Tested sandstone specimens containing two oval flaws in this research

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The geometry of the flawed sandstone is described in Fig. 3. Notice, the term “flaw” is used to describe an artificially created flaw; however the term “crack” is adopted to describe the new fracture or failure during loading. The geometry of the two coplanar oval flaws is defined by five geometrical parameters: the length of the long axis of the oval (a), the length of the short axis of the oval (b), the ligament length (c), the flaw angle α (the angle of the long axis of the oval with horizontal direction), and the ligament angle (β), as shown in Fig. 3. A high pressure water-jet cutting machine was used to cut two coplanar oval flaws into the intact sandstone specimens. To investigate the effect of the pre-existing coplanar oval flaw geometry on the strength, deformation and failure behavior of sandstone under uniaxial compression, different geometries of two coplanar oval flaws were chosen in this study by varying the coplanar oval flaw angle (α =β), while keeping the other three parameters constant (a = 18 mm, b = 6 mm and c = 20 mm). A detailed description of the sandstone specimens with different flaw geometries is listed in Table 1.

18

6

20

30

30

30.0

18

6

20

30

30

28.0

18

6

20

45

45

27.7

18

6

20

45

45

27.9

18

6

20

60

60

28.0

18

6

20

60

60

157.0

27.8

18

6

20

75

75

80.2

158.0

27.8

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6

20

75

75

SE49

80.3

158.0

27.6

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6

20

90

90

SE50

80.1

158.4

28.1

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6

20

90

90

SE51

80.0

159.9

29.8

18

6

20

30

0

SE52

80.3

158.4

27.7

18

6

20

30

0

SE53

80.1

157.9

27.7

18

6

20

30

30

SE54

80.2

157.6

27.6

18

6

20

30

30

SE55

80.0

158.8

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30

45

SE56

80.3

158.5

27.7

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45

SE57

80.1

157.6

29.9

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60

SE58

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158.4

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158.6

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90

SE61

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157.7

27.5

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30

120

SE62

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158.4

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SE63

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157.3

28.1

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30

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150

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SI02

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SI03

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158.3

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157.5

28.9

SE40

80.2

158.5

27.6

SE41

80.1

158.7

27.8

SE42

80.3

158.4

SE43

80.2

158.4

SE44

80.1

158.5

SE45

80.1

158.4

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158.6

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Specimen

Specimens containing two coplanar oval flaws

Specimens containing two non-coplanar oval flaws

Note: W－Width; H－Height; T－Thickness.

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2.3 Loading procedure and AE monitoring All uniaxial compression tests of the sandstone specimens containing two ovals were carried out using a rock mechanics servo-controlled testing system. Axial stress was imposed on the surface of the rock specimen until failure took place. The tests were conducted under displacement-controlled conditions, with a strain rate of 4.977×10-6/s. During the uniaxial compression experiment, the loads and deformations of the specimens were recorded simultaneously and continuously. Two rigid steel blocks, with dimensions of 33×83×15 mm, were placed between the loading frame and the rock specimen. To investigate the fracture coalescence characteristics of the deforming specimens containing two oval flaws during testing, the AE technique was adopted. The AE counts were recorded by a DS2 full-information AE measuring system. The frequency of the AE system was set to 3 MHz. We attached two AE sensors on the back face of the red sandstone specimens using a hot bar as a coupling agent to measure the AE signals and fixed it slightly by using cellulose tape. At the same time, the crack evolution process of sandstone specimens containing two pre-existing oval flaws was captured with a digital video camera. This is a continuous triggering progress, which yields 25 frames per second to ensure clear cracks. Strength and deformation behavior In accordance with the axial stress-time curve and the ultimate failure mode of the two intact sandstone specimens shown in Fig. 4, we determined that the tested sandstone is brittle, i.e., the axial stress drops abruptly to zero after the peak strength. We did not observe any crack coalescence for intact specimens prior to the peak stress. A loud failure sonic was recognized due to rapid failure several seconds after the peak stress, which was also testified by the general absence of AE counts. As seen in Fig. 4, the strength and deformation properties of the two intact sandstone specimens have a good consistency. However, the failure modes of specimens SI02# and SI03# are different. They show typical shear type and splitting type after the UCS tests, respectively. The differences to the two intact sandstone specimens may be caused by from the mineralogy, shape, size and size distribution. Therefore, to obtain the best possible results, we repeated the tests of the two specimens for each flaw angle.

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Fig.4. Experimental results of intact sandstone specimens under uniaxial compression. (a) Specimen SI02#. (b) Specimen SI03#.

Fig. 5 shows the axial stress-strain curves of the sandstone specimens containing two oval flaws under uniaxial compression. In general, the effect of the specimen variability on the mechanical parameters (e.g., the uniaxial compressive strength) is smaller. However, it should be noted that the axial stress–strain curves of the specimens for the same flaw angle (Fig. 5), due to the different crack coalescence processes in the rock, especially

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(a) Specimen containing two coplanar oval flaws (α = β = 0°)

(b) Specimen containing two coplanar oval flaws (α = β = 60°)

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Fig.5. Effect of heterogeneity on the stress-strain curves of sandstone specimens containing two pre-existing oval flaws. (a) Specimen containing two coplanar oval flaws (α = β = 0°). (b) Specimen containing two coplanar oval flaws (α = β = 60°). (c) Specimen containing two non-coplanar oval flaws (β = 30°). (d) Specimen containing two non-coplanar oval flaws (β = 90°).

3.1 Strength and deformation behavior of sandstone containing two coplanar oval flaws Fig. 6 shows the axial stress-strain curves of sandstone containing two coplanar oval flaws under uniaxial compression. From Fig. 6, we can also see that red sandstone specimens containing two coplanar oval flaws show an initial nonlinear deformation, which is caused mainly by the closure of the original fissures or pores in the rock material. Subsequently, elastic deformation begins to dominate the axial stress-strain curve, and the axial stress has an approximately linear relation with the axial strain. However, distinct stress drops are observed in the axial stress-strain curves of the specimens when tensile cracks are initiated at the tips of the two pre-existing oval flaws. Note that, each stress drop corresponds to one crack coalescence in the specimen. We will make a detailed analysis of their relationship in the fifth section of this paper. After several stress drops, the specimen will rapidly reach the peak strength and brittle unstable failure occurs with the increase of axial deformation. Fig.7 depicts the influence of the flaw angle on the strength and deformation parameters of red sandstone containing two coplanar oval flaws. In Fig.7, σc and ε1c are the uniaxial compressive strength and peak axial strain of red sandstone, respectively, and ES is the secant Young's modulus from zero stress to its uniaxial compressive strength.

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α=β=45° α=β=60° α=β=75° α=β=90°

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α=β=0° α=β=15° α=β=30° α=β=15°

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The relationship between peak strength and flaw angle is plotted in Fig. 7a. The peak strengths of red sandstone specimens containing two coplanar oval flaws first decrease and then increase with the flaw angle, reaching the minimum value when α =15°. When the flaw angle increases from 0° to 15°, the peak strength decreases from 52.17 MPa to 51.17 MPa. However, when the flaw angle increases from 15° to 90°, the peak strength increases from 51.17 MPa to 88.39 MPa. Furthermore, the magnitude of the peak strength increase in the range of 60°-90° is slightly higher than that in the range of 15°-60°.

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The relationship between the peak strain and flaw angle is plotted in Fig.7b. As the flaw angle increases, the peak strain changes nonlinearly. When the flaw angle increases from 0° to 45°, the peak strain increases from 2.627×10-3 to 3.218×10-3. The peak strain drops from 3.218×10-3 to 2.971×10-3, when the flaw angle increases from 45° to 60°. However, the peak strain increases from 2.971×10-3 to 3.930×10-3, when the flaw angle increases from 60° to 90°. The relationship between the elastic modulus and the flaw angle is shown in Fig.7c. It is clear that the elastic modulus is not closely related to the pre-existing flaws when the flaw angle in the range of 0° to 45°. However, when the flaw angle is higher than 45°, the elastic modulus increases slightly with the increase of the flaw angle, i.e., the elastic modulus increases from 12.10 GPa (α = 45°) to 14.13 GPa (α = 90°).

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3.2 Strength and deformation behavior of sandstone containing two non-coplanar oval flaws Fig. 8 shows the axial stress-strain curves of the sandstone specimens containing two non-coplanar oval flaws under uniaxial compression. The shape of the curve of the sandstone specimens containing two non-coplanar oval flaws is similar to that of the sandstone specimens containing two coplanar oval flaws. Moreover, the ligament angle has an obvious influence on the stress-strain curve of the sandstone specimen containing two non-coplanar oval flaws.

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β=60° β=90° β=120° β=150°

60 40 20

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4

0 0

1

2

3

4

ε1 / 10-3

Fig.8. Stress-strain curves of sandstone specimens containing two non-coplanar oval flaws under uniaxial compression.

Fig. 9 shows the influence of the ligament angle on the uniaxial mechanical parameters of the sandstone specimens containing two non-coplanar oval flaws. Obviously, the peak strength, elastic modulus and peak strain of the pre-flawed specimens are lower than those of the intact specimens. The relationship between the peak strength and ligament angle is presented in Fig. 9a. As can be seen from Fig.9a, the peak strength changes nonlinearly with the increase of ligament angle. As the ligament angle increases, the peak strength first increases, then decreases and finally increases. When the ligament angle increases from 0° to 30°, the peak value increases from 57.00 MPa to 58.00 MPa. When the ligament angle increases from 30° to 60°, the peak value decreases from 58.00 MPa to 51.75 MPa. However, when the ligament angle increases from 60° to 150°, the peak value increases from 51.75 MPa to 75.62 MPa. The relationship between the peak strain and ligament angle is plotted in Fig. 9b. Overall, the trend of the peak strain is similar to that of the peak strength, except for β = 150°. As can be seen from Fig. 9b, when the

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(a) Peak strength

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□ Experimental value ■ Average value

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ligament angle increases from 120° to 150°, the peak strain decreases from 3.624×10-3 to 3.391×10-3. The relationship between the elastic modulus and ligament angle is shown in Fig.9c. It is clear that the elastic modulus first decreases and then increases with increasing ligament angle. When the ligament angle increases from 0° to 60°, the elastic modulus decreases from 12.24 GPa to 11.42 GPa. However, the elastic modulus increases from 11.42 GPa to 13.01 GPa, when the ligament angle increases from 60° to 150°.

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Fig.9. Influence of ligament angle on strength and deformation parameters of sandstone containing two non-coplanar oval flaws. (a) Peak strength. (b) Peak strain. (c) Elastic modulus

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Crack evolution behavior in specimens containing two coplanar oval flaws Fig. 10 shows the ultimate failure modes of sandstone specimens containing two coplanar oval flaws under uniaxial compression. As seen in Fig.10, the failure of the pre-flawed specimen was induced by the coalescence of cracks from the pre-existing flaws. Furthermore, the two images with α= 60° shown in Fig. 10(f) and (g), indicated that, the failure modes with the same flaw geometry are approximately the same, except for some minor differences, which indicates that the heterogeneity has almost no effect on the failure characteristics. Based on the analysis of the failure modes, the main types of cracks can be classified as wing crack, anti-wing crack, secondary crack, shear crack, far-field crack and surface spalling which are marked in Fig. 10. The crack types of the sandstone in this study are similar to those in Yang and Jing (2011). Therefore, the detailed crack characteristics will not be analyzed here. As can be seen from Fig.10, the cracks in the failed specimens are combinations of several types of crack. The failure modes and crack coalescence types depend on the flaw angle. Three distinct failure modes can be

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summarized as follows. Mode I: No crack coalescence failure, α=β=0° and 15°. Mode II: Indirect crack coalescence outside the bridge area failure, α=β=30°. Mode III: Single crack coalescence inside the bridge area failure, α=β=45° to 90°.

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(f) α=β=60°

(g) α=β=75°

(h) α=β=90°

Fig.10. Ultimate failure modes of red sandstone specimens containing two coplanar oval flaws. (a) α=β=0°. (b) α=β=15°. (c) α=β=30°. (d) α=β=45°.(e) α=β=60°. (f) α=β=60°. (g) α=β=75°. (h) α=β=90°.

To investigate the crack propagation process of sandstone specimens, photography and acoustic emission (AE) monitoring were used during the test. Figs.11-13 show the typical AE counts and the corresponding crack evolution process of sandstone specimens containing two coplanar oval flaws. The numbers in these figures denote the order of cracking in the specimen observed by photographic monitoring, and the superscript letters on the same numbers mean that these cracks were simultaneously initiated from different positions. Fig. 11 shows the failure mode and AE count curve of red sandstone specimen containing two coplanar oval flaws for α=β=0°. There is no obvious macro crack in the specimen at the initial deformation stage. The axial stress increases nonlinearly with axial deformation. When the axial stress increases to some extent, cracks 1a-b initiate at flaw ②. A small stress drop occurs and a sudden increase in the accumulated AE count curve is observed. The axial stress drops to point 2, which results from the initiation of cracks 2a-b from flaw ②. Cracks 3a-b initiate at the right tip and the surface of flaw ①. The axial stress drops again, and the AE count increases suddenly. The axial stress continues to increase until the peak value of 52.46 MPa is reached. At the peak strength, two cracks, i.e., cracks 4a and 4b, initiate at the left tip of flaw ② and flaw ①, respectively. The initiation of

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(b) Ultimate failure mode

Fig.11. AE curve and crack coalescence process of red sandstone specimen containing two coplanar oval flaws (α=β=0°). (a) Stress-time-AE counts curve. (b) Ultimate failure mode. (c) Sketch of failure mode.

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Fig. 12 shows the failure mode and AE count curve of red sandstone specimen containing two coplanar oval flaws for α=β=30°. As seen from Fig. 12, no obvious macro cracks are observed at the initial deformation under low stress level. The AE count increases slightly with increasing axial deformation. When the axial stress reaches the peak value, cracks 1a-d initiate at the tips and surfaces of the pre-existing flaws. The axial stress drops slightly and the AE count increases rapidly. The axial stress drops again after point 1, because of the initiation of cracks 2a-b. The maximum AE count is observed at that time. The axial stress increases gradually with the increase of axial deformation. The AE count is relatively low during this period. When the axial stress reaches 57.89 MPa, the initiation of crack 3 results in a drop of the axial stress to point 3. Crack 3 emerges from the right tip of flaw ②, which propagates in the opposite direction to crack 2a. Subsequently, the axial stress increases with axial deformation. However, the axial stress-time curve shows small stress fluctuations. At point 4, the ultimate failure mode forms due to the propagation of shear cracks 4a-b, tensile crack 4c and far-field cracks 4d-h. An indirect crack coalescence occurs between the two pre-existing flaws because of the propagation of cracks 1b, 4b and 3. 3

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Fig.13 shows the failure mode and AE count curve of red sandstone specimen containing two coplanar oval flaws for α=β=75°. When the specimen is loaded to point 1 (64.45 MPa), crack 1 is generated at the lower tip of flaw ①, but it does not coalesce into the bridge area. At this moment, an obvious AE event can be observed. After emerging of crack 1, the axial stress increases with increasing axial deformation. When the specimen is loaded to point 2 (74.91 MPa), crack 2 initiates at the upper tip of flaw ① and grows upward. Meanwhile, crack 1 propagates downward and finally coalesces into the upper tip of flaw ②. The crack initiation and coalescence cause a relatively high AE count. At the peak strength (point 3), the maximum AE count is observed due to the surface spalling 3 from the lower tip of flaw ①. After the peak value is reached, the axial stress drops rapidly to point 4. The crack 4a initiates at the lower tip of flaw ②, crack 4b emerges at the upper tip of flaw ① and several far-field cracks 4c-e are initiated far away from the flaws. It is clear that only one crack coalescence occurs due to the propagation of crack 1.

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Fig.13. AE curve and crack coalescence process of red sandstone specimen containing two coplanar oval flaws (α=β=75°). (a) Stress-time-AE counts curve. (b) Ultimate failure mode. (c) Sketch of failure mode.

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Crack evolution behavior in specimens containing two non-coplanar oval flaws Fig.14 presents the ultimate failure modes of sandstone specimens containing two non-coplanar oval flaws under uniaxial compression. As can be seen from Fig.14, the failure was caused by the coalescence of cracks from pre-existing flaws. Moreover, the similarity of the two specimens with the same flaw geometry (see Figs. 14g and h) further implies that they have a very good consistency. The failure modes were closely related to the ligament angle, which were divided into the following four typical modes based on the crack coalescence between the pre-existing flaws: Mode I: No crack coalescence failure, β=0°. Mode II: Indirect crack coalescence outside the bridge area failure, β=30° and 45°. Mode III: Single crack coalescence inside the bridge area failure, β=60°and 90°. Mode IV: Tensile crack coalescence outside the bridge area failure, β=120°and 150°. Mode I, II and III have also been observed in the specimens containing two coplanar oval flaws. However, the typical failure mode IV was only present in the specimens containing two non-coplanar oval flaws for β=120° and 150°, which may be caused by the two overlapping flaws in these sandstone specimens.

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Figs. 15-18 show the typical crack initiation, propagation and coalescence process, and the corresponding AE count curves of red sandstone specimens containing two non-coplanar oval flaws under uniaxial compression. The numbers in these figures denote the order of cracking in the specimen observed by photographic monitoring, and the superscript letters mean that these cracks were simultaneously initiated from different positions. Based on Figs. 15-18, the crack process and AE evolution behavior of sandstone specimens containing two non-coplanar oval flaws were analyzed as follows.

(b) β =30°

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Fig. 14. Ultimate failure modes of red sandstone specimens containing two non-coplanar oval flaws under uniaxial compression. (a) β =0°. (b) β =30°. (c) β =45°. (d) β =60°. (e). β =90° (f) β =120°. (g) β =150°. (h) β =150°.

Fig. 15 shows the typical no crack coalescence failure mode and the corresponding AE count curve of sandstone specimen containing two non-coplanar oval flaws under uniaxial compression, respectively. Tensile cracks 1a-c initiate from the tips and surface of flaw ① for β = 0° when the axial stress level is 53.87 MPa, i.e., at point 1 (Fig. 15a) at the non-linear deformation stage. At that moment, a high AE count and a slight stress drop can be observed in Fig.15a. When the axial stress drops to point 2, upward crack 2 is found at the left tip of flaw ①, which also induces the maximum AE count. The axial stress increases with the axial deformation afterwards. When the specimen is loaded to point 3, two macro cracks emerge from the flaw ②. They are wing crack 3a at the surface of flaw ② and wing crack 3b at the left tip of flaw ②. After the initiation of crack 3, the axial stress increases to the peak. However, no obvious crack is observed at the peak strength. Far-field crack 4 is generated in the specimen at point 4, which also induces a high AE count. The axial stress drops abruptly to zero (point 5).

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1: ε1 =2.709×10-3 σ1=53.87 MPa

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4: ε1 =2.969×10-3 σ1=52.18 MPa

Fig.15. Crack evolution process and AE curve of red sandstone specimen containing two non-coplanar oval flaws (β=0°).

Fig.16 shows the typical indirect crack coalescence outside the bridge area failure mode and the corresponding AE count curve of sandstone specimen containing two non-coplanar oval flaws under uniaxial compression, respectively. There are not obvious macro cracks before the peak strength for β =45°, No high AE count is observed at the pre-peak stage. When the stress reaches the peak value of 61.60 MPa, tensile cracks 1a-c initiate at the pre-existing flaws. A slight stress drop occurs due to the initiation of crack 1. When the stress increases to point 2 (σ1=61.19 MPa), cracks 2a-c initiate at different positions of pre-existing flaws. Meanwhile, the original crack 1b lengthens. The axial stress continues to drop afterwards. When the specimen is loaded to point 3 (σ1=53.46 MPa), tensile crack 3 initiates at the left tip of flaw ②, which induces an obvious AE count. When the axial stress reaches 57.09 MPa (point 4), shear crack 4 emerges in the ligament area. Crack 4 connects to crack 2c during the propagation, resulting in crack coalescence between the two pre-existing flaws. At this moment, two surface spallings are clearly seen in the specimen. There is a sudden increase in the accumulated AE count curve. The supporting structure of the specimen damages is seriously damaged after the crack coalescence between the pre-flaws. During the final failure, lateral tensile cracks 5a-b occur.

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4: ε1 =3.260×10-3 σ1=57.09 MPa

Fig.16. Crack evolution process and AE curve of red sandstone specimen containing two non-coplanar oval flaws (β=45°).

Fig.17 shows the typical single crack coalescence inside the bridge area failure mode and the corresponding AE count curve of sandstone specimen containing two non-coplanar oval flaws under uniaxial compression. For β =90°, the crack propagation characteristics were distinctly different from the above models with relatively lower ligament angles. At point 1, i.e., at a stress level of 21.12 MPa, wing cracks 1a-d initiate at the pre-existing flaws. However, no obvious AE count is observed during the initiation of cracks 1a-d. The stress continues to increase linearly with the increase of axial deformation afterwards. When the stress increases to point 2 (σ1=61.19 MPa), the initiation and propagation of crack 2 leads to coalescence between the two pre-existing flaws. At the following point 3, crack 3 emerges from the lower tip of flaw ②. The initiations of crack 2 and crack 3 induce high AE counts and a sudden increase in accumulated AE counts. However, the specimen still has a good supporting structure, thus the axial stress continues to increase with the axial deformation. When the specimen is loaded to the peak value of 50.33 MPa (point 4), minor secondary crack 4 is initiated at the upper tip of flaw ①. No obvious AE count but a relatively obvious increase is observed in the accumulated AE count curve. After the peak strength, the axial stress drops rapidly and the ultimate failure mode is finally formed. During the final failure, two secondary cracks 5a-b initiate at the outer tips of the flaws. The abrupt failure also induces the maximum AE count.

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4: ε1 =2.929×10-3 σ1=50.33MPa

Fig.17. Crack evolution process and AE curve of red sandstone specimen containing two non-coplanar oval flaws (β=90°).

Fig.18 shows the typical tensile crack coalescence outside the bridge area failure mode and the corresponding AE count curve of sandstone specimen containing two non-coplanar oval flaws under uniaxial compression, respectively. For β =150°, the cracking behavior is concentrated in the post-peak stage. As can be seen from Fig. 18, the initial wing cracks 1a-b and 2a-b emerge at point 1 and point 2, respectively. Two obvious AE counts are observed during the initiation of these wing cracks. When the axial stress increases to the peak strength of 72.16 MPa (point 3), far-field crack 3a and secondary crack 3b are initiated in the specimen. At the following point 4, the original crack 2a grows to the left tip of flaw ②, resulting in the first crack coalescence between the two pre-existing flaws. Although no new macro cracks are generated during this process, the crack coalescence induces a high AE count. Subsequently, the axial stress slightly drops with an increase in deformation. When the axial stress reaches point 5 (σ1=70.13 MPa), secondary crack 4 emerges from the right tip of flaw ②. The supporting structure of the specimen is seriously damaged. The axial stress drops rapidly to near zero (point 6), and the ultimate failure mode forms. During the final failure, two far-field cracks 5a-b initiate and an obvious AE count is observed.

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Fig.18. Crack evolution process and AE curve of red sandstone specimen containing two non-coplanar oval flaws (β=150°).

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Conclusions (1) The pre-existing oval flaws greatly reduce the mechanical parameters of sandstone specimens under uniaxial compression. For the specimens containing two coplanar oval flaws, the peak strength is distinctly related to the coplanar flaw angle, while the peak strain and elastic modulus are not obviously dependent on the coplanar flaw angle. For the specimens containing two non-coplanar oval flaws, the peak strength, peak strain and elastic modulus have a nonlinear relationship with the ligament angle. (2) The crack initiation, propagation and coalescence of the tested sandstone specimens were observed using photographic monitoring. The ultimate failure modes of sandstone specimens containing pre-existing oval flaws are mixtures of several cracks (wing crack, anti-wing crack, secondary crack, shear crack and far-field crack and surface spalling). The AE characteristics, which are more decentralized than those of the intact specimens, were analyzed using AE monitoring. The stress drops correspond to a sudden increase of accumulated AE counts, resulting from the initiation or coalescence of cracks. (3) The ultimate failure of pre-flawed sandstone specimen depends on the flaw geometry and can be divided into four distinct modes: no crack coalescence failure, indirect crack coalescence outside the bridge area failure,

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Acknowledgements

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The research was supported by the Fundamental Research Funds for the Central Universities (2015XKZD05). We would also like to acknowledge the editor and the anonymous reviewers for their valuable comments, which have greatly improved this paper.

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Lee, H., Jeon, S., 2011. An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int. J. Solids Struct. 48, 979–999. Li, Y., Peng, J., Zhang, F., Qiu, Z., 2016. Cracking behavior and mechanism of sandstone containing a pre-cut hole under combined static and dynamic loading. Eng. Geol. 213, 64–73. Li, Y. P., Chen, L. Z., Wang, Y. H., 2005. Experimental research on pre-cracked marble under compression. Int. J. Solids Struct. 42, 2505–2516.

Lin, P., Wong, R. H. C., Tang, C. A., 2015. Experimental study of coalescence mechanisms and failure under uniaxial compression of granite containing multiple holes. Int. J. Rock Mech. Min. Sci. 77, 313–327. Liu, J. P., Li, Y. H., Xu, S. D., Xu, S., Jin, C. Y., Liu, Z. S., 2015. Moment tensor analysis of acoustic emission for cracking mechanisms in rock with a pre-cut circular hole under uniaxial compression. Eng. Fract. Mech. 135(6), 206–218. Tang, H. D., Zhu, Z. D., Zhu, M. L., Lin, H. X., 2015. Mechanical behavior of 3D crack growth in transparent rock-like material containing preexisting flaws under compression. Adv. Mater. Sci. Eng. http://dx.doi.org/10.1155/2015/193721. Wong, L. N. Y., Einstein, H. H., 2009. Crack coalescence in molded gypsum and Carrara marble: part 2-microscopic observations and interpretation. Rock Mech. Rock Eng. 42(3), 475–511. Wong, R. H. C., Chau, K. T., 1998. Crack coalescence in a rock-like material containing two cracks. Int. J. Rock Mech. Min. Sci. 35(2), 147–164. Wong, R. H. C., Lin, P., Tang, C. A., 2006. Experimental and numerical study on splitting failure of brittle solids containing single pore under uniaxial compression. Mech. Mater. 38(1), 142–159. Yang, S. Q., Jing, H. W., 2011. Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int. J. Fract. 168(2), 227–250. Yang, S. Q., Liu, X. R., Jing, H. W., 2013. Experimental investigation on fracture coalescence behavior of red sandstone containing

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ACCEPTED MANUSCRIPT two unparallel fissures under uniaxial compression. Int. J. Rock Mech. Min. Sci. 63, 82–92 Yang, S, Q., 2011. Crack coalescence behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure. Eng. Fract. Mech. 78, 3059–3081. Yang, S. Q., 2016. Experimental study on deformation, peak strength and crack damage behavior of hollow sandstone under conventional triaxial compression. Eng. Geol. 213: 11-24. compression. Eng. Geol. 199, 74–90.

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specimens under dynamic and quasi-static loadings. Eng. Geol. 201(4), 71–84.

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ACCEPTED MANUSCRIPT Research Highlights

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Analyze the effect of the coplanar flaw angle on mechanical parameters of sandstone containing two coplanar oval flaws; Construct the relationship between the ligament angle and mechanical parameters of sandstone containing two non-coplanar oval flaws; Reveal the crack evolution mechanism of sandstone containing two oval flaws by photographic monitoring and AE techniques.

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