3.1. Strength and Deformation Properties
Based on the recorded data from uniaxial compression tests, the curves of stress versus strain of these rock samples can be easily plotted, which are presented in Figure 4
a. It is observed that these curves were concave-upward at the initial loading stage, indicating the gradual shut of native cracks and pores in the samples under the action of compressive loads. When the elastic deformation stage was reached, the curves turned into straight lines; that is, the stress increased linearly with the increase of the axial strain. Afterwards, the curves became convex. This suggests the specimens experienced plastic deformation resulting from the initiation and development of cracks. After the peak point, the specimens lose their bearing capacity quickly, showing significant brittleness. Therefore, the whole deformation process contains four typical phases: native defects closure, elastic deformation, plastic deformation and post-peak failure. Besides, it can be seen that the curves of the pre-holed specimens fluctuate when approaching the peak point. This is caused by the sudden occurrence of cracks, which will be interpreted at length in the next section.
Details of the physical dimensions and mechanical parameters of all the samples are shown in Table 3
. In which, σp
denote the uniaxial compressive strength, peak strain and Young’s modulus, respectively. Note that the Young’s modulus was defined as the slope of the elastic deformation portion of the stress–strain curve, which can be obtained by linear fitting. As seen in Table 3
, the peak strength of the three intact specimens was 100.9 MPa, 105.6 MPa and 101.3 MPa, respectively, with the coefficient of variation of 2.49%. Moreover, the corresponding three values of the Young’s modulus were also very close. This manifests that the sandstone possessed a relatively high degree of homogeneity. However, compared with the specimens CS-1 and CS-2, the axial strain of the specimen C-3 at the initial loading stage was large (see Figure 4
a), which may result from the poor parallelism of the specimen ends or the loose contact between the LVDT and compression platens.
b illustrates the average mechanical parameter values of different groups of samples. It was found that the mechanical properties of the samples with openings, including the σp
, were much lower than those of the intact samples, and the degree of weakening was closely associated with the configuration of openings. For the uniaxial compressive strength, the reduction rate ranged from 15.80% to 29.94%, and the values of these groups could be ordered from large to small as: C (102.60 MPa) > V (86.39 MPa) > S (81.89 MPa) > H (78.15 MPa) > D (71.88 MPa). Interestingly, observations demonstrate that the average strength of Group V was even higher than that of Group S. This behavior was attributed to different stress distributions round the openings, which would be detailedly illustrated in the numerical study section. In terms of the Young’s modulus, the average value of Group C was the largest, followed by Groups H, V, D and S, with a decrease extent of 14.76%–24.93%. Besides, compared with the intact rock samples, the peak strains of the holed samples were also reduced to varying degrees. Among them, Group S had the largest peak strain (6.11‰), while the strain of Group D was the smallest. In conclusion, both the quantity and configuration of the openings exerted a significant influence on the strength and deformation properties.
3.2. Fracture Development and Failure Patterns
Generally, under the action of loads, the compressive stress or tensile stress will concentrate around the opening. As the applied load increases, the stress concentration factor rises accordingly. As a consequence, tensile or shear cracks will occur when the tensile strength or cohesion is surpassed. Meanwhile, strain localization is gradually formed at the stress concentration zones. Therefore, the DIC technology was used to monitor the fracture process of samples under uniaxial loading. By importing the recorded speckle photos into GOM Correlate software, both the real-time strain and displacement distributions of each sample can be visualized. Figure 5
shows the principal strain contours of five representative samples during uniaxial loading. In the figure, the numbers 1, 2, 3, 4 and 5 marked represent the elementary tensile cracks, posterior tensile cracks, sidewall slabbing cracks, shear cracks and surface spalling cracks, respectively. For the lowercase letters that located on the upper-right corner of the number, they denote the occurrence sequence of the same pattern of cracks.
(1) Sample C-3
In Figure 5
a, the fracture growth of the sample C-3 in uniaxial compression is clearly shown. At 8 MPa, plenty of yellow and red spots with high strain appeared on the surface of the sample because of the shut of the native micro defects under compression. When the applied stress increased to 30 MPa, it was found that the quantity of these spots went up accordingly. This is because some new micro cracks emerged near the native defects in the elastic deformation stage. At a stress level of 60 MPa, the high strain spots were observed to distribute in the vicinity of the main diagonal of the sample. As the axial stress mounted further, high strain areas gradually gathered along the principal diagonal and the right end. At 95 MPa, a tensile crack 1a
emanating from the lower-right corner of the sample grows along the loading direction. When reaching the peak stress, the other tensile crack 1b
symmetric with the crack 1a
appeared in the upper-right corner of the sample. These two cracks propagated towards each other, and finally get coalesced at the post-peak failure stage. Besides, it could be seen that a shear band 4 occurred in the center of the sample. It would develop into a shear crack along the counter diagonal and intersect with the connected two tensile cracks at the end of the test.
(2) Sample S-2
b illustrates the principal strain distributions of the sample S-2 at six representative stress levels. Based on that, the fracture process can be summarized as follows. At the first loading stage, the strain distribution was similar to that of the sample C-3. When the elastic deformation stage was approached, only a few spots appeared, indicating the quantities of the formed micro cracks were relatively small. After that, an elementary tensile crack 1a
initiated from the floor of the opening and propagated slowly towards the direction of the maximum compression. When the axial stress was 65 MPa, it was found that the sidewall slabbing cracks 3a
occurred on the two sides of the opening, resulting in the appearance of V-shaped notches. Two posterior tensile cracks 2a
were also gradually formed at the upper-left and lower-left corners of the opening in turn. However, compared to the situation at 40 MPa, the length of the crack 1a
was shortened. At the peak point, the cracks 1a
disappeared completely, while the crack 2b
was getting longer. Additionally, another posterior tensile crack 2c
at the upper-right corner of the opening was observed, and some surface spalling cracks 5 appeared on the right side of the opening because of the high level of concentrated compressive stress. At 78 MPa after the peak, the spalling area enlarges and a shear crack 4a
emerged in the upper-right corner of the sample. This shear crack would continue propagating along the counter diagonal until it merged with the right V-shaped notch. After that, the other shear crack 4b
appeared in the lower-left corner of the sample and intersects with the left V-shaped notch, leading to the sample instability.
(3) Sample H-3
The variation of the principal strain field in the sample H-3 with the axial stress is given in Figure 5
c. At the first two loading stages, the strain change laws were consistent with those of the samples C-3 and S-2. In the plastic deformation stage, two elementary tensile cracks 1a
first occurred on the bottom of the opening simultaneously. Then the V-shaped notches occurred one by one on both sides of the two openings owing to the emergence of sidewall slabbing cracks (3a
). Afterwards, two vertical posterior tensile cracks 2a
appeared at the lower-left corner of the left opening and the lower-right corner of the right opening, respectively. Note that, in this period, the cracks 1a
gradually disappeared as the posterior tensile cracks grew. When the stress rose to the peak, the other four posterior tensile cracks (2c
) emerged at the corners of the openings and propagated in parallel with the compression direction. When the stress dropped from the peak to 68 MPa, the two openings coalesced due to the connection between the two adjacent V-shaped notches, then the sample failed when the shear crack emerging at the lower-left corner of the sample reached to the left opening and the crack 2c
propagated to the upper end of the sample.
(4) Sample D-1
As shown in Figure 5
d, the fracture development around the two openings in the sample D-1 subjected to uniaxial compression was distinctly reproduced. Likewise, the primary pores and fine fissures in the sample would close under the action of a small load. Correspondingly, numerous yellow spots occurred in the sample at the start of the test. During the elastic deformation, some micro cracks might be formed round these defects owing to stress concentration. At 40 MPa, two elementary tensile cracks 1a
emerged at the floors of the two openings, but the crack 1a
initiated first. As the stress continued increasing, the slabbing failure happened on the sides of the openings and the V-shaped notches came into being. Next, a posterior tensile crack 2a
parallel to the orientation of the load appeared at the lower-right corner of the lower-left opening. With the growing of the stress to the maximum stress, the length of the crack 2a
increased, and the other two posterior tensile cracks 2b
were formed round the upper-right corner opening. After the peak, the two openings got linked via an initiated shear crack 4a
. Additionally, the other shear crack 4d
occurred in the upper-right corner of the sample and would link with the V-shaped notch on the right side of the upper-right opening at last.
(5) Sample V-3
e displays the principal strain states of the observation surface of the sample V-3 in the process of uniaxial loading. Similarly, several types of cracks appeared sequentially at the periphery of the two openings during sample loading. In other words, firstly, two elementary tensile cracks 1a
occurred on the bottom of the lower and upper openings, respectively. Secondly, a posterior tensile crack 2a
initiated from the lower-left corner of the upper opening and propagated straight to the opening below with the increasing stress. At the peak stress, it was observed that the other two posterior tensile cracks 2c
had emerged at the upper-right corners of the two openings. During the propagation of these posterior tensile cracks, the slabbing cracks were found to appear on the opening sides. At the post-peak failure stage, a shear crack appeared in the upper-left corner of the specimen. Once it gets connected with the crack 2a
and the new formed posterior tensile crack 2d
at the lower-right corner of the lower opening, the failure would take place.
Based on the DIC experimental technique, we could also visualize the displacement contours of these samples at different loading times. Figure 6
presents the horizontal displacement states of the above samples at the same stresses. The displacement symbol is defined as: if rock particles move to the right, the displacement is positive. Otherwise, the displacement is negative. In Figure 6
a, the displacement of the left blue part of the sample C-3 was negative at the early loading stages, suggesting that this part of rock moved towards the left. As the stress grows, a yellow curved area with positive displacement was gradually formed near the right border. It was symmetrically distributed with the blue curved area near the left end. Due to the end friction, the displacements of regions near the loading ends were basically zero. As a result, the shear band 4 would be formed on the diagonal and the right yellow part would be split when the two cracks 1a
get connected. For the sample S-2, first, a triangular cyan area with negative displacement on the left side of the opening gradually appeared as the stress rose. At 40 MPa, it could be seen that there was a short dividing line between the green and cyan areas on the floor of the opening. This formed boundary was the crack 1a
. At 65 MPa, the cyan area evolved into a trapezoidal blue area. Obviously, the right boundary of this area represents the cracks 2a
. Meanwhile, a triangular yellow area with positive displacement appears on the right side of the opening. At the maximum stress, it was found that the boundary of the cyan area at the upper-left corner of the opening disappeared, while that at the lower-left corner prolongs. This proved that the crack 2b
lengthened. Besides, at the upper-right corner, a vertical line representing the crack 2c
emerged as well. At 78 MPa after the peak, a yellow shear band appeared in the upper-right corner of the sample. Similarly, according to the displacement distributions of the rest samples in Figure 6
b–e, it can be summarized that the displacement variation during the loading was agreeable with the fracture development. That is to say, the dividing lines between two different color areas on the sample surface would occur at the places where the cracks appear.
From the above description, we could reach a conclusion that five sorts of cracks, namely, elementary tensile crack, posterior tensile crack, sidewall slabbing crack, shear crack and surface spalling crack, were formed in the samples containing inverted U-shaped openings during uniaxial compression. For the samples containing two openings, three categories of hole coalescence were observed in this research: the slabbing coalescence, the shear coalescence and the tensile coalescence. The final failure modes of the above five samples are shown in Figure 7
. In the figure, the red line means the failure path, and the black dotted line denotes the appeared crack, which is not easy to identify using the naked eye. To sum up, the failure mode of the samples S-2 and D-1 was shear-dominated failure, while that of the other three samples belonged to tensile-shear failure. To put it differently, the instability of the sample S-2 was attributed to the intersection of the shear cracks (4a
) and the V-shaped notches, while that of the sample D-1 was induced by the coalescence of the shear cracks 4a
. For the intact sample C-3, the failure resulted from the connection between the shear crack 4 and the merged tensile cracks 1a
. With regard to the samples H-3 and V-3, the coalescence of the shear cracks and the posterior tensile cracks gives rise to the final instability. Since the brittleness of the rock was extremely remarkable, the failure of these samples was violent and rapid. As a result, the collected photos of the samples after the peak were relatively few, and the post-peak failure behavior was hard to monitor. Besides, at the end of the tests, it was found that partial posterior tensile cracks propagated further toward the upper or lower ends. However, when approaching the loading ends of the sample, the propagation direction of the posterior tensile cracks was deflected because of the end friction. The other shear cracks also appeared on the diagonal and propagated towards the opening sidewalls. It is noted that some unmarked cracks are observed in Figure 7
, which were formed after failure, and did not take charge of the eventual failure.
3.3. AE Activity and Threshold Stress
In AE tests, the ringing count represents the number of signal oscillations that cross the detection threshold. It can be used for reflecting both the frequency and intensity of the AE signal. Thus, in this study, the ringing count and cumulative ringing count were selected as the evaluation indexes of the AE activity. The curves of the applied stress, AE count and cumulative AE count versus the loading time are plotted in Figure 8
Based on the crack development of the samples under uniaxial compression, the corresponding AE activity can be classified into five stages. The characteristics of the stages are described as follows:
Stage I: At this stage, the native defects slowly shut under the action of loads, which will not generate a great amount of strain energy. As a consequence, the AE activity is not very active. Thus, the quantity of detected AE count is relatively small and the cumulative AE count grows nonlinearly.
Stage II: As the stress rises, the samples deform elastically in this stage. Moreover, some micro cracks occur round the tips or corners of the natural defects. This gives rise to the growing increase of the released strain energy. Therefore, both the AE count and the cumulative AE count increase to varying degrees. In terms of the sample D-1, the reason why the AE signals are not remarkable at this stage may be that the coupling between the sensor and the rock sample is not very good during loading.
Stage III: In this stage, the AE count of the sample remains basically the same and the cumulative AE count increases linearly. This is because the elementary tensile cracks appear and propagate stably along the loading direction under increasing loads. Therefore, this stage can be named the stable crack growth stage.
Stage IV: During this stage, the slabbing crack and posterior tensile crack occur rapidly. Consequently, the AE activity is extremely active, accompanying by several significant jump of AE count. This is induced by the rapid appearance of cracks or coalescence between cracks. It is noted that when the posterior tensile crack propagates to the V-shaped notch, the stress fluctuation is corresponded. Hence this stage is unstable cracking stage.
Stage V: At the last stage, the shear cracks are formed and then intersect with the V-shaped notch or the posterior tensile crack. This triggers the instability of rock samples. Accordingly, the AE count increases drastically and the axial stress decreases to zero in a short time.
Clearly, the variation of AE signals was agreeable with the crack development shown in Figure 6
. Besides, according to the divided stages, it was obvious that several stress thresholds were related between the adjacent stages, namely, the crack closure stress (σc
) between the stages I and II, the crack initiation stress (σi
) between the stages II and III and the crack damage stress (σd
) between the stages III and IV as well as the peak stress (σp
) between the stages IV and V. For the σc
, it corresponds to the axial stress when the stress–strain curve turns from nonlinearity to linearity. In regard to the rest stress thresholds, they can be determined by combining the crack development and AE signals; that is, if the strain localization and significant AE count occur simultaneously, new crack initiates or crack coalescence occurs. Table 4
lists the threshold stress values of the above five samples subjected to uniaxial compression.
As shown in Table 4
, the σc
of the sample C-3 was 23.89% of the σp
, whilst that of the samples containing inverted U-shaped openings was within the range of (12.50%–17.83%)σp
. The reason may be that the excavation of the openings at the center of the samples gives rise to the decrease in the numbers of natural defects. In respect of the σi
, it corresponded to the axial stress when the crack 1a
started to initiate. The value of the sample C-3 was 0.44σp
. In contrast, the values of the other samples ranged from 0.27σp
. The order of the initiation stress of the samples with openings could be ranked as: sample V-3 > sample H-3 > sample S-2 > sample D-1. This is because the tensile cracks occurred more easily around the openings than in the intact sample, and the crack initiation stress was attributed to the stress state of the roof or floor of the opening, which would be illustrated in detail in the next section. With regard to the σd
, for the samples with openings, it corresponded to the stress when the slabbing crack or the posterior tensile crack emerged, and their values were 0.65–0.78 times the peak stresses. This would also be deeply analyzed in Section 4