3.1 Damage characteristics
3.1.1 Variation of porosity after impact on rock samples with different inclined faces
Rocks porosity reflects the ratio of internal defects, pores, and fractures to the total volume of rocks. The size of porosity directly affects the physical and mechanical properties of rocks. NMR technology enables a qualitative and quantitative description of the pore distribution characteristics in rocks by measuring the relaxation time of fluids in pores. Porosity measurements were carried out on rock samples after different numbers of impacts during the experiment. As shown in Fig. 6, the relationship curve between the porosity of sandstone samples at various angles and the number of impacts under the same impact energy is presented. Overall, the porosity decreases first and then increases with the increase in the number of impacts.
For rock samples with incline angles of 40° and 45°, the porosity is the lowest after the first impact and the highest after the fifth impact. The porosity slightly decreases after the sixth impact, and some damage is observed in the rock samples. For samples with incline angles of 55° and 60°, the variation characteristics of porosity curves after impact are similar, demonstrating an initial decrease followed by an increase. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. Following the initial impact, a decline in porosity is noted, suggesting compression of certain pores and a reduction in the overall pore volume.
Nevertheless, with successive impacts, the porosity gradually rises. This can be attributed to the multiple impact compression waves and reflected transmission waves causing ongoing alterations within the internal pores and fractures of the samples. Consequently, small pores expand into larger ones while new minor cracks emerge, leading to an increase in porosity.
By comparing the variation of porosity under different inclinations, it can be observed that the porosity change is greater in samples with smaller inclination angles under the same cyclic impact load. In other words, the rate of change of porosity decreases as the slope angle increases.
For a sample with a 40° inclined angle, the porosity was 10.21% before impact and increased to 10.92% after six impacts, resulting in a porosity change rate of 7.0%. In comparison, for a sample with a 60° inclined angle, the porosity before and after impacts were 8.25% and 8.80%, respectively, with a porosity change rate of 6.6%. A basic mechanical analysis indicates that as the slope angle increases, under the same impact force, the normal force component on the inclined surface decreases, resulting in reduced impact damage to the rock.
3.1.2 T2 distribution of the rock samples
The T2 spectrum curve is the transverse relaxation response of 1H protons in completely water-saturated rock samples under the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, reflecting the variation in the quantity of pores of different sizes. According to the transverse relaxation T2, the pores in rock samples can be classified into large pore size (T2>100ms), medium pore size (10ms<T2<100ms), and small pore size (T2<10ms) 13. Some scholars have also classified the pores in rocks into two main types based on the critical value of 10ms, namely macroscopic pores (T2>10ms) and microscopic pores (T2<10ms). This study primarily adopts the second type of classification method. According to empirical methods, a transverse relaxation time of 10 ms corresponds to a pore of approximately 300nm in size24.
Figure 7 illustrates the T2 spectrum curves of inclined plane samples with five different inclined angles under the same cyclic impact load. The horizontal axis in the figure is T2 relaxation time, with larger pores corresponding to greater values on the T2 spectrum curve. The vertical axis indicates the quantity of pores, with higher values representing more pores of that size.
The changing trends of each curve in the figure are similar. There are mainly two obvious spectrum peaks on the curve, and the signal amplitude of the first peak is significantly higher than that of the second peak. Compared with the T2 spectrum curve before impact (No.0), the peak values of both peaks decreased to varying degrees after the first two impacts, indicating a reduction in the number of internal pores in the sample and an overall decrease in porosity. From the third impact to the sixth impact, the curves shift to the left overall, suggesting a gradual decrease in pore size. In terms of peak changes, the peak value of the first peak increases significantly with the number of impacts, while the peak value of the second peak gradually decreases. This means that the number of small pores within the rock sample increases while the large pores are compacted and the number of large pores decreases. The overall porosity shows an increasing trend.
Taking the T2 spectrum curve of a rock sample with a 45° inclined plane as an example, there is no significant lateral displacement in the curve after the first two impacts, and the total relaxation time was within 1000ms. This means that there has been no significant change in pore size. After the first impact, the peak value of the first peak in the T2 spectrum curve remains unchanged, while the peak value of the second peak slightly decreases, indicating compaction of some large pores within the sample and no change in small pores. After the second impact, the first peak value decreases while the second peak value increases, indicating that some small pores have expanded into larger pores. The number of small pores decreases while the number of large pores increases. After the third impact, the curve undergoes the most significant changes, with both peaks shifting to the left, indicating an overall reduction in pore size. In addition, the first peak value significantly increased and the second peak value decreased, suggesting an increase in the number of small pores and a slight decrease in the number of large pores. After the fourth to sixth impacts, compared to after the third impact, there is no significant lateral shift in the two peaks, but their values fluctuate up and down, indicating a conversion between small and large pores. The overall change is not significant, and the total porosity gradually increases.
Therefore, as the number of impacts increases, the first peak mainly shows changes in the vertical direction, with only the third impact causing a leftward shift. The second peak exhibits both vertical and horizontal changes during the impact process, indicating that under cyclic impact loads, the changes in the number of small pores within sandstone are predominant. At the same time, both the size and quantity of large pores also undergo variations. Additionally, the larger the inclination angle of the plane, the greater the signal amplitude corresponding to the peak values in the T2 spectrum curve.
The area enclosed by the T2 spectral curve and the horizontal axis is referred to as the T2 spectrum area, which is directly proportional to the amount of fluid in the rock and can serve as an important parameter reflecting changes in rock pore structure16,24. The NMR spectral area and macroscopic pore ratio of sandstone samples with different inclined planes after 6 impacts were calculated, as shown in Table 2. The total spectral area of the sandstone samples ranges from 90000 to 30000, with small pore spectral areas accounting for more than 65% and large pore spectral areas accounting for below 35%. This indicates that smaller-sized pores are more prevalent within the sandstone samples, while large-sized pores are less numerous. It can be seen from the T2 spectrum curve that the signal values of small-sized pores are significantly higher. However, the overall trend of porosity changes aligns with variations in the spectrum areas of large-sized pores. Although there are many small-sized pores in the rock samples, large-sized pores are the main factor affecting porosity.
Table 2. T2 spectral area of rock samples with different angles under different impact frequency
Inclination angle α /°
|
Impact frequency
|
T2 spectral area
|
Microscopic porosity ratio /%
|
Macro porosity ratio /%
|
40
|
0
|
71064.12
|
66.27%
|
33.73%
|
1
|
67912.69
|
68.03%
|
31.97%
|
2
|
68917.37
|
67.47%
|
32.53%
|
3
|
75487.26
|
72.38%
|
27.62%
|
4
|
78139.86
|
72.41%
|
27.59%
|
5
|
80995.81
|
69.45%
|
30.55%
|
6
|
75905.19
|
73.54%
|
26.46%
|
45
|
0
|
73091.29
|
66.55%
|
33.45%
|
1
|
69220.40
|
68.17%
|
31.83%
|
2
|
70131.16
|
67.90%
|
32.10%
|
3
|
76396.46
|
73.54%
|
26.46%
|
4
|
79887.10
|
72.99%
|
27.01%
|
5
|
79414.97
|
73.01%
|
26.99%
|
6
|
78284.60
|
72.30%
|
27.70%
|
50
|
0
|
76463.04
|
68.27%
|
31.73%
|
1
|
73298.52
|
67.94%
|
32.06%
|
2
|
78592.57
|
70.84%
|
29.16%
|
3
|
83903.35
|
73.53%
|
26.47%
|
4
|
83699.35
|
73.46%
|
26.54%
|
5
|
82660.79
|
73.93%
|
26.07%
|
6
|
77644.57
|
72.40%
|
27.60%
|
55
|
0
|
75779.54
|
72.75%
|
27.25%
|
1
|
72609.12
|
72.06%
|
27.94%
|
2
|
74475.02
|
70.93%
|
29.07%
|
3
|
81043.59
|
76.57%
|
23.43%
|
4
|
84252.80
|
74.47%
|
25.53%
|
5
|
86304.48
|
75.02%
|
24.98%
|
6
|
84798.75
|
75.23%
|
24.77%
|
60
|
0
|
84607.31
|
71.21%
|
28.79%
|
1
|
80278.67
|
70.33%
|
29.67%
|
2
|
82366.63
|
69.94%
|
30.06%
|
3
|
84395.17
|
74.58%
|
25.42%
|
4
|
87590.64
|
72.94%
|
27.06%
|
5
|
87685.22
|
72.66%
|
27.34%
|
6
|
88250.83
|
70.92%
|
29.08%
|
Comparing the changes in macro and micro pore proportions after different numbers of impacts on samples of five types of rocks, it is found that the pore changes are more significant in samples with small inclinations, while samples with larger inclination angles show minor changes. Taking the change in micro-pore proportion as an example, after 6 impacts, the micro-pore proportion increased by 7.27% for the 40° inclined plane sample, and the maximum micro-pore proportion for the 60° inclined plane sample occurred after the third impact, with a 4.64% increase compared to the second impact.
3.1.3 NMR imaging
NMR imaging provides a visual representation of the spatial distribution and development status of internal pores in rock samples, which is crucial for studying rock damage. Figure 8 shows the NMR images of sandstone samples with inclination angles of 45 ° and 60 ° before and after six impacts. These images are cross-sectional images at a distance of 20mm from the bottom surface. The green spots in the images represent small-sized pores, while the yellow and red spots represent large-sized pores.
Taking the image of a 45 ° inclined plane rock sample as an example, the image of the sample before impact is mainly composed of relatively uniform distributed green spots, indicating that the pore size in the rock sample is small and uniform. After the first impact, the porosity is the smallest. The spots on the right edge of the cross-section were significantly reduced, and the distribution of the spots is mainly concentrated on the left side. At the same time, a small amount of yellow and red spots appear, indicating that some small pores have expanded into large pores. After the fifth impact, the porosity is the highest. The number of spots on the cross-section is significantly increased, and a large number of yellow and red spots appear, indicating an increase in the number of macro-pores.
After the sixth impact, the number of spots decreased slightly. However, there are obvious striped spots, indicating that some pores may have penetrated and formed a small number of cracks. Compared with the images of the 60 ° inclined plane rock sample, there is no obvious change in the number of spots on the cross-section during the impact process. The distribution of spots is relatively uniform, without obvious yellow, red, or striped spots appearing. It can be seen that if the inclination angle is too large, the damage degree to the rock sample caused by impact decreases.
3.2 Failure mechanism
3.2.1 Mechanical analysis of the inclined plane impact
As shown in Fig. 9, the impact surface of the sample is elliptical due to the slope influence. The size of the long semi-axis size gradually changes with the inclination angle of the inclined plane. Assuming that the major and minor axes of the inclined plane are a and b, respectively. According to the geometric relationship, it can be obtained that b=acosα=d/2, the inclined plane area A= πd 2/ 4cosα. Under the impact of a falling hammer, the rock sample experiences both vertical compression stress and horizontal shear force, with the vertical force having a greater impact on the sample. The impact force F of the falling hammer can be decomposed into normal force FN (Fτ = P) and tangential force Fτ. The stress on the inclined plane can be decomposed into
where, σx and σz are the horizontal stress and vertical stress on the inclined plane, Pa; P is the normal impact force on the inclined plane, N; F is The impact force of the falling hammer, N; d is the diameter of the sample, mm; α is the inclined angle. "K1" and "K2" are the component coefficients of horizontal and vertical directions, respectively. As shown in Fig. 10, as the angle of the inclined plane increases, the horizontal stress component first increases and then decreases, reaching its maximum value at an angle of 35°. The vertical stress component gradually decreases as the inclination angle increases. When the inclination angle is 45 °, the horizontal stress component and the vertical stress component are equal.
In summary, compared to traditional vertical impact, the impact of inclined plane loading on rock samples induces not only vertical compressive stress but also damage and deformation caused by horizontal forces. Both the damage and failure are influenced by the inclination angle. With increasing inclination angle, under the same drop height, the vertical stress decreases while the horizontal stress increases, resulting in reduced damage at the lower part of the sample.
3.2.2 Quantitative analysis of damage
To further investigate the internal damage and destruction of rock samples under different inclined plane impact frequencies, a damage variable D is introduced. The damage variable D is defined as a function of internal porosity as follows:
where, n0 represents the natural porosity of the rock sample, and nt represents the porosity of the rock sample after the t-th impact.
As shown in Table 3, the damage degree of samples with different inclined angles after 6 impacts was calculated.
Table 3. Statistical Table of damage variables
Impact frequency
|
40°
|
45°
|
50°
|
55°
|
60°
|
1
|
-0.51%
|
-0.58%
|
-0.44%
|
-0.89%
|
-0.48%
|
2
|
-0.40%
|
-0.09%
|
-0.06%
|
-0.87%
|
-0.51%
|
3
|
0.92%
|
1.26%
|
1.51%
|
0.06%
|
-0.05%
|
4
|
1.48%
|
1.77%
|
1.54%
|
0.46%
|
0.32%
|
5
|
1.89%
|
1.75%
|
1.38%
|
0.70%
|
0.31%
|
6
|
1.06%
|
1.55%
|
0.55%
|
0.52%
|
0.34%
|
According to the result in Table 3, it can be seen that when the number of impacts is less than 2, the damage variable is negative. This indicates that under the first two impacts, the interior of the sample shows a state of pore compression. Since the third impact, except for the 60° rock samples, the damage variables have been positive. The maximum value of the damage variable occurs in the fourth or fifth impact, and the order of the maximum values of the damage variables at each angle is 40° > 45° > 50° > 55° > 60°. The maximum value of the damage variable occurs in the 40° rock sample of the fifth impact, and the minimum value appears in the 60° rock sample of the third impact. Under the same number of impacts, the damage degree of the 45° rock sample is generally the highest, while the damage degree of the 60° rock sample is the lowest.
3.2.3 Failure mode
As shown in Fig. 11, after six cycles of inclined plane impact with the same energy, different types of cracks appeared in the upper part of the sample. The failure mode of the 45°~60° inclined plane sample is similar, with only one crack. However, the 40° inclined plane sample showed multiple cracks and a large amount of detachment at the bottom of the sample. The crack positions are all located within 20 mm of the upper end of the sample and parallel to the bottom surface of the sample. The failure type is a shear-tensile failure, as shown in Fig. 12. It is because the sharp corners of the sample are relatively thin, and the lateral force generated by the inclined plane impact causes the upper part of the rock sample to fail first. The impact damage and failure of rock samples on inclined planes are greatly affected by the angle of the inclined plane. The smaller the angle of the inclined plane, the smaller the transverse force and the larger the longitudinal force. The rock sample failure changes from a single transverse crack to multiple cracks. Therefore, the rock sample with a 40 ° inclined plane angle is the most severely damaged.