Study on Energy Dissipation Characteristics and Damage Law of Backfill under Cyclic Impact

0is research aims to study the damaging effect of underground blasting mining pillars on adjacent cemented filling bodies. 0e filling bodies were made by mixing ore rock with ash sand by the ratio of 1 : 4 and 1 : 6, respectively, which were subjected to cyclic impact tests with the split-Hopkinson pressure bar under the pressure of 0.2MPa and 0.24MPa to analyze the energy dissipation characteristics and damage law. 0e results showed that as the stress wave induced by the cyclic impact was transmitted to the composite specimen, the energy was absorbed for crack growth and development.0en, the energy reflection ratio increased while the energy dissipation ratio and transmission ratio decreased. For the combined specimen with the cement-sand ratio of 1 : 4, after five cycles of impact under the condition of Ip� 0.2MPa, the damage variables were 0.07, 0.11, 0.51, and 0.56, respectively, since the second time; under the condition of Ip� 0.24MPa, the damage variables were 0.17, 0.29, 0.55, and 0.66, respectively. After reaching the damage threshold of 0.63, the damage variable showed nonlinearity. Moreover, it was found that the mechanical properties of the filling body affect the whole combined specimen, and the dynamic strength of the combined specimen with the cement-sand ratio of 1 : 4 was higher than that of the cement-sand ratio of 1 : 6.0erefore, it can be concluded that during the twostep pillar recovery, the amount of blasting explosive can be appropriately reduced, and the number of blasting can be increased to reduce the damaging effect of blasting impact on the cemented pillar and reserved pillar to maintain stability.


Introduction
Subsequent filling mining method [1] is widely used in underground mining; in the second step of pillar mining, the explosion stress wave induced by blasting will enter the adjacent cemented filling body from ore rock, which usually causes damage to ore rock and filling body. e disturbance of blasting impact load to ore rock pillar and the artificial pillar can make the original microcracks inside the pillar expand and be connected to form a macrofault surface. Besides, the impact load has a significant influence on the deformation process and mechanical properties of the pillar. e failure of the ore rock and filling body involves a complex dynamic mechanical process [2][3][4][5], which seriously affects safety during mining.
Many studies have been conducted on the dynamic characteristics of rock, ore, or backfill [6][7][8][9][10][11][12][13]. Xie et al. [14] believed that energy dissipation would lead to lithology deterioration and strength reduction during the rock deformation and failure process. Zhu et al. [15] found a positive correlation between compressive strength and backfill with different proportions. Hou et al. [16] found the relationship between compressive strength and reinforcement factor of cemented backfill under different strain rates and concluded the variation law of compressive strength and dissipated energy density. Hu et al. [7]studied the cumulative damage effect of rock mass under blasting and revealed goaf's failure and instability mechanism. Zhu et al. [17] conducted an impact test on sandstone and analyzed the failure process of rock from the perspective of mesoscopic crack propagation and energy absorption. Literature [18][19][20][21][22][23] explored the damage evolution law of different rock masses under the cyclic impact and believed that cyclic impact and prestatic loading had nonlinear effects on the whole rock damage. Yang et al. [24] simulated blasting experiments for marble under different blasting conditions and analyzed the damage characteristics. Jin et al. [25] established a rock damage evolution model and explored the influence of static load on rock damage. Based on the deformation and failure characteristics of rock, Xiao et al. [26] proposed an inverted S-type damage evolution model and studied the influence of the initial damage degree on the mechanical fatigue properties of rock, such as stress amplitude and loading waveform changes and frequency.
rough the uniaxial compression test, Zhao et al. [27] studied the mechanical properties and cooperative deformation characteristics of cemented tailings filling materials with different cementsand ratios. Cao et al. [28]studied the variation rule and failure mode of mechanical characteristics of cemented filling with layered tailings. Liu et al. [29] proposed a new method of studying the rock deformation, failure, and instability of surrounding under load.
In terms of the dynamic characteristics of composite specimens, Yang et al. [30] conducted impact tests on composite rock samples with large wave impedance splicing of red sandstone and grey stone and summarized the stressstrain relationship and capacity dissipation law. Wang [31] carried out a quasi-triaxial loading test and analyzed the deformation evolution law of underground surrounding rock-filling body composition. Wang et al. [32] analyzed the rupture evolution law of cemented tailings cemented backfill. However, there is rarely any study about the adjacent structure of pillar and filling body and its response characteristics under the disturbance of blasting dynamic load in two-step pillar mining. In this study, the adjacent structure of pillar and filling body in an underground mine was simplified as the rock-filling combination specimen [33,34]. Under the effect of cycle blasting dynamic disturbance during stoping, the dynamic mechanical properties of the pillar can be considered as cyclic dynamic impact [35,36], which provides a basis for damage control of pillar stoping blasting construction in two steps.

One-Dimensional Dynamic and Static
Combination Loading Test  Figure 1; the preparation conditions met the impact test requirements in ISRM.  Figure 2. e main components include power wheel drive, elastic compression bar, damping absorption, signal collection, data storage, and processing. e elastic pressure rod is made of 40 Cr high-strength alloy steel, its diameter of is 50 mm, the elastic modulus is 210 GPa, and the density is 7810 kg/m 3 ; the p-wave velocity is 5100 m/s.

Experimental Principle.
In the SHPB test, there are two basic assumptions, including the one-dimensional stress wave propagation and stress uniformity. e "three-wave method" [37]was used to process the collected strain wave signal. e stress σ(t), strain ε(t), and strain rate _ ε(t) can be expressed as where A 0 is the cross-sectional area of the pressure rod; E 0 is the elastic modulus of the pressure rod system; A c is the cross-sectional area of the combined specimen; L is the length of the combined specimen; C 0 is the elastic wave velocity in the pressure bar; ε I (t) is the incident wave strain measured experimentally; ε R (t) is reflected wave strain; and ε T (t) is the transmitted wave strain. According to the stress wave propagation theory and energy conservation law, W I , W R , W T , and W D , which, respectively, represent the incident energy, can reflect the energy and transmitted energy in the experimental process, and the absorbed energy that causes the specimen to fail can be calculated as follows: e energy ratio _ W is calculated as in formula (4), where W I is the general name of reflected energy, transmitted energy and absorbed energy. Shock and Vibration

Test Scheme.
In this impact test, the combined specimens DM and CTB were, respectively, used as the incident end and the transmission end [38][39][40]. e impact pressure (replaced by Ip) was selected as 0.2 MPa and 0.24 MPa. Five cycles of impact tests were carried out on DM-CTB 1 : 4 and DM-CTB 1 : 6 specimens to simulate the cumulative damage and failure effect of multiple blasting stoping on adjacent cemented backfill.

Stress-Strain Curve Relationship. Figures 3(a) and 3(b)
, respectively, show the stress-strain curves of the combined specimens with the total ratio of beams under different air pressures after cyclic impact, and n represents the number of cyclic shocks [41,42].
(1) In the first impact cycle, for DM and CTB, the compressive springback process of pores or cracks was observed, and the stress-strain curve of the combined specimen was approximately a straight line. e impact contact surface is the DM end, and the material is dense and of high strength; therefore, the initial deformation was small, and the dynamic strength increased rapidly. Besides, as the CTB material was gradually compacted, the dynamic strength continued to increase. Because the load applied on the composite specimen was not enough to cause new cracks, they mainly show linear elastic characteristics.
(2) As the number of cycles increased, the stress-strain curves of the four groups of different combinations showed an upward convex trend. Compared with the previous stage, the growth rate and the slope of the curves were both gradually decreased. When the peak dynamic strength was reached, the stress-strain curves showed an obvious "inflexion point." e phenomenon of strain rebound was obvious. When Ip � 0.2 MPa and Ip � 0.24 MPa, the peak stress of DM-CTB 1 : 4 was greater than that of DM-CTB 1 : 6 . In the post-peak deformation and failure stage, the slope gradually slowed down, indicating that DM-CTB gradually transformed into the plastic zone.

MPa and
Ip � 0.24 MPa, in the process of cyclic impact, the stress-strain curve began to show the characteristics of ductile materials; because CTB has certain viscoelasticity, the microdefects inside the backfill were compacted to become closer during cyclic impact. After 5 cycles of impact, the overall mechanical properties of DM-CTB were weakened, showing the characteristics of ductile materials. When Ip � 0.2 MPa and strain rate was within a certain range, DM-CTB 1 : 6 showed strong viscoelastic characteristics during cyclic impact. When Ip � 0.24 MPa, as the strain rate increased, DM-CTB 1 : 6 showed brittle characteristics. erefore, brittle deformation characteristics were reflected in the stress-strain curve of DM-CTB. (4) It was analyzed that for DM-CTB, in the early stage of the cycle impact, cracks are easily spread through the filling body and the interface area, a microdefect in the CTB collapses, making the number of cracks increase with the increase of impact times; thus, internal cracks of CTB were developed, and the strength and deformation ability were decreased, making DM-CTB exhibit mechanical properties of ductile materials.

Energy Evolution Law under Cyclic Impact Load.
During the SHPB impact test, the incident energy is mainly closely related to the impact velocity of the bullet. However, the reflected energy, transmitted energy, and dissipated energy are mainly determined by the characteristics of DM-  transmission ratio T, and dissipation ratio H) and the energy ratio of the cyclic impact test can be calculated and recorded, as shown in Table 2, in which W R is reflected energy, W T is transmitted energy, and W L is the dissipated energy. It can be seen from Figure 4 that the energy reflection ratio of DM-CTB with different air pressure was greater than 60%; the reason is that the wave impedance of DM-CTB differs greatly from that of SHPB rod, and most of the energy was dissipated in the form of the reflected wave.
When the impact pressure Ip increased from 0.2 MPa to 0.24 MPa, the reflection ratio F of DM-CTB with different proportions increased; it was also found that when Ip of impingent pressure did not change, the transmission ratio T and dissipation ratio H of DM-CTB 1 : 6 were lower than those of DM-CTB 1 : 4 , except for the reflection amplitude F. To a certain extent, it is indicated that DM-CTB of low-ratio specimens has weak transmission performance and strong reflection ability; this can be explained as follows: the content of cement in the CTB part of DM-CTB 1 : 6 is low, the internal bond is weak, and the adhesion and cohesion between particles are relatively low, so the bond between mortar and tailings aggregate is poor, inducing a large number of original microdefects in the interior. When the stress wave propagates in the combined specimen, the incident energy is readily absorbed at the defect.
In the cyclic impact stage, DM-CTB experienced a transition from fatigue damage to failure stage. In the fatigue damage stage, the initial cyclic impact has a certain strengthening effect on the specimen structure and improves the impact resistance and deformation resistance of DM-CTB; with the increase of impact number n, the internal damage degree of DM-CTB was aggravated to activate more internal microcracks, increasing the number of defects. As the wave impedance of specimens was decreased and the ability to resist external loads was weakened, the combined specimens showed a decreasing trend in transmission ratio T, dissipation ratio H, and reflection ratio F.

Failure Modes of Composite Specimens under Cyclic
Impact. It can be seen from Figure 5 Shock and Vibration stage with no cracks or some internal microcracks produced, and the plastic deformation was incomplete. Moreover, the impact of low strain rate had a certain "reinforcing" effect on the specimen structure, and its impact resistance and deformation resistance were improved in the short term.
In conclusion, under the action of cyclic impact load, both ends of DM-CTB showed an end effect, which leads to stress concentration; at the same time, compression zones are formed at both ends of DM-CTB, resulting in cracks being parallel to the axial direction. With the increase of compressive stress, a potential shear failure surface is formed, and some cracks of the filling body in DM-CTB will further be expanded, finally forming a macroscopic failure surface. In the shear failure surface area, CTB samples will fall off due to the impact and exhibit compression shear failure. However, CTB will lose its bearing capacity and break into many small pieces when the dynamic load strength exceeds the residual strength of CTB.
For the same ratio, under the cyclic impact, the larger the impact pressure is, the more obvious the deformation failure of DM-CTB is. Under the same impact pressure, CTB in DM-CTB with a low ratio is more serious, and the mass of fragments increases accompanied by fine powder. e failure mode is mainly crushing failure, but the DM part is

Damage Rule of Composite Specimens under Cyclic
Impact. When Ip � 0.2 MPa and Ip � 0.24 MPa, each impact on DM-CTB will cause new damage on the original basis, which means the damage will be accumulated. Referring to the loading and unloading process, damage variable D is defined as follows: where E is the initial elastic modulus and E n is the elastic modulus after cycles of loading and unloading.
However, D is difficult to characterize the initial damage degree. In order to better reflect the damage change, the dynamic elastic modulus after the initial impact is taken as the benchmark, and the damage variable D after the initial impact is set as "0"; thus, the relationship between ratio, impact pressure duration, and cumulative damage variables can be established and shown in Figure 6.
It can be seen from Figure 6 that when Ip � 0.2 MPa, DM-CTB 1:4 had little influence on the finish before the damage threshold was reached. As the number of hits increases, damage variable D accumulates nonlinearly, but the rate was generally lower than the cyclic impact of higher impulse.
Taking DM-CTB 1:4 as an example, when Ip � 0.2 MPa, after 5 cycles of the impact, the damage variable D (counting from the second time) was 0.07, 0.11, 0.51, and 0.56, respectively. When Ip � 0.24 MPa, the damage variable D was 0.17, 0.29, 0.55, and 0.66; DM-CTB 1 : 6 also showed a similar  Shock and Vibration change. e results show that after being subjected to cyclic impact load, internal damage of DM-CTB accumulated continuously, and the internal structure was relatively stable and not easy to deform at the initial impact. With the increase of impact duration, its internal cracks and the damage variable D increased rapidly. e results show that although there was damage inside the retained pillar, it still had a certain bearing capacity. With the increase of cycle number and impact pressure, the cumulative damage variable increased gradually and tended to be flat when the rock sample was destroyed, indicating that with the progress of cyclic impact, the rock sample continuously absorbed energy for the expansion and development of cracks. As shown in Figures 5 and 6, under the condition of the same ratio and the same number of impacts, the growth rate of the damage variable D of the composite specimen was relatively low when the impact pressure was small. In the pillar recovery construction site, both the cemented pillar and the reserved pillar were affected by the impact. According to the test results, the explosive amount should be appropriately reduced, and increasing the number of blasting can reduce the damage of cemented pillars and reserved pillar caused by blasting disturbance to improve the stability of stope.

Conclusion
For DM-CTB 1:4 and DM-CTB 1:6 , under the pressure of 0.2 MPa and 0.24 MPa, cyclic impact tests were carried out to study the energy dissipation and damage law, and conclusions can be drawn as follows: (1) Under cyclic impact, the composite specimens experienced a transition from fatigue damage to failure stage. e structure of DM-CTB in the fatigue damage stage is "strengthened," and the impact resistance and deformation resistance are increased. After 5 cycles of shock, DM-CTB showed a decreasing trend of transmission ratio T and dissipation ratio H while increasing trend of reflection ratio F.
(2) Under the same impact pressure, as the strain rate increases and the dynamic load strength exceeds the residual strength of CTB, CTB will lose its bearing capacity and break into small pieces. In DM-CTB, the fragmentation degree of CTB increases, and the fracture is parallel to the length direction of the backfill sample, which is mostly transverse tensile failure. Tensile and shear damage degree of DM-CTB 1:6 is higher than that of DM-CTB 1:4 . (3) For DM-TCB 1:4 under the cyclic impact of Ip � 0.2 MPa, there is little influence on finishing when the damage threshold is not reached, and when the damage threshold exceeds 0.63, with the increase of impact times, the increase of impact times will make the damage variables appear nonlinear accumulation, but the cumulative rate is generally less than that of the damage variables with higher impulse cyclic impact.

Data Availability
e data used to support the findings of this study are included within the article.

Disclosure
XL and QZ are co-first authors.

Conflicts of Interest
e authors declare that they have no conflicts of interest.

Authors' Contributions
XL and QZ were responsible for conceptualization, methodology, validation, data curation, visualization, and original draft preparation. QZ was responsible for experimental guidance and data analysis. JW and WS were responsible for theoretical analysis. All authors were responsible for formal analysis and review and editing. All authors have read and agreed to the published version of the manuscript.