Analysis of Cumulative Damage for Shared Rock in a Neighborhood Tunnel under Cyclic Blasting Loading Using the Ultrasonic Test

In blasting excavation of neighborhood tunnels, damage accumulation process in surrounding rock is inevitable. To explore the influence of damage accumulation of rock mass under multiple blasting loads, we analyzed the vibration damage accumulation process of ultrasonic wave velocity of rock mass in shared rock of Liuyuetian neighborhood tunnel through ultrasonic test. Moreover, the effects of cyclic blasting loads on damage to the shared rock in the neighborhood tunnel were discussed and reported. *e results demonstrate that the damage accumulation to the shared rock in the neighborhood tunnel is generated after multicycle progressive blasting operations. Influenced by cyclic blasting loads during the posterior excavating tunnel, the damage range of shared rock at the anterior excavating tunnel is 1.2 to 1.4m, and the damage range of shared rock at the posterior excavating tunnel is 2.2 to 2.4m. *e damage range of shared rock in the posterior excavating tunnel is about 1.71 to 1.83 times that in the anterior excavating tunnel. Under blasting load, the stress concentration zone of shared rock is close to the blasting excavating face and is mainly within 2m along the longitudinal axis of the tunnel. With continuous advancement of the blasting excavating face, the stress concentration zone moves forward continuously, and a striped stress concentration zone, which is approximately 2m deep, is formed gradually. *us, a method was proposed to determine the damage range of shared rock in the neighborhood tunnel during blasting excavation, as well as the variation law of damage. *e experiences and conclusions presented can be used as references in the design and construction of similar engineering projects in the future.


Introduction
Drilling and blasting method has been widely used in mining, hydropower, transportation, and other industries due to its advantages such as low cost, simple construction technology, and possibility to deal with various shapes and sizes of openings [1][2][3][4][5]. When the drilling and blasting method is used to excavate the rock mass in the neighborhood tunnel, the blasting vibration may influence the surrounding rock, support system, and lining structure of the tunnel significantly [6][7][8][9][10]. How to ensure the stability of the lining structure, support system, and shared rock of the tunnel, and relieving adverse effects of blasting vibration is the challenge in tunnel engineering construction. As the major load-carrying structure of the neighborhood tunnel, the shared rock is not only an essential support system but also the weak position of the tunnel structure [11][12][13][14]. For the rock mass of the neighborhood tunnel, the changing clear spacing and complex stress structure may influence the stability of the surrounding rock [15][16][17][18][19]. In particular, the rock masses of the tunnel are often excavated by cyclic progressive blasting method. Multiple disturbances to the same position in remaining rock and even in shared rock can easily cause propagation of microcracks, thereby resulting in continuous deterioration of mechanical properties, continuous reduction of material strength, and gradual deterioration of stability [20][21][22].
is condition causes instability of the tunnel support system. Owing to the unique construction technology, complex structural form, and stress state, as well as frequent blasting vibration, the vibration effects and damage features of surrounding rock are highly complicated [23,24]. erefore, studying the damage mechanism and evolution process of shared rock in the neighborhood tunnel is an important task.
Over the years, abundant studies on rock damage caused by blasting have been reported, mostly based on field investigations and laboratory experiments [25][26][27][28]. e damage of rock mass in underground mining and tunneling has been described in terms of blast-induced rock mass damage, rock mass damage area, excavation damage area, blasting vibration damage accumulation, and other factors [29][30][31][32]. For instance, Chaboche [33] defined the concept of damage variables by using an indirect measurement program, then obtained different damage growth equations such as creep, ductile, and brittle damage. Using continuum mechanics and statistical fracture mechanics, Liu and Katsabanis [34] determined the minimum damage value under the crack density obtained by integrating the crack density function over time and then verified the feasibility and reliability of the model by field blasting test and numerical simulation. Concerning the evolutionary damage law of rock mass, Hao et al. [35] proposed an anisotropic damage model by analyzing the dynamic response of a granite site under blasting loads based on the theory of continuous damage mechanics. Other researchers also agree that the two main factors affecting rock mass damage are strain rate and rock dynamic fracture parameters. e damage of rock mass is mainly affected by explosive force, stress redistribution, and weathering. Ramulu et al. [36] discussed the influence of repeated blast loading on the damage of rock mass during tunnel blasting excavation and established an on-site damage model by using peak particle velocity and plastic deformation. Malmgren et al. [37] studied the damage distribution range in the construction process of mining and damage evolutionary characteristics of rock mass using digital imaging techniques. Ling et al. [38] constructed a multivariate discriminant analysis model for rock damage caused by blasting vibration. Liu et al. [39] studied the fracture process of rock mass by acoustic emission and microseismic monitoring under multihorizontal uniaxial load aimed at guiding the working time and working area of field personnel. e damage to blast-induced vibration can lead to the generation, expansion, and transfixion of microcracks or macrocracks during rock mass excavation by blasting, and in severe cases, it may result in spalling and collapse from the excavated surface [40][41][42]. In recent years, with the rapid development of computer technology, numerical simulation methods have been adopted to study the influence of blasting vibration on rock mass [43][44][45][46][47][48][49].
We can observe from the aforementioned references that significant efforts have been exerted to investigate rock damage according to the monitoring data obtained from field investigations. However, few studies have been conducted on the damage shape and size of shared rock in the neighborhood tunnel under cyclic blasting loads, and it lacks a principle to determine the sphere of influence of blasting. In the present study, the influences of surrounding rock at different levels and thickness of the shared rock on the lining structure of anterior excavating tunnel under blasting load of posterior excavating tunnel were analyzed by ultrasonic test. e engineering characteristics of the Liuyuetian neighborhood tunnel were considered. Furthermore, the spatiotemporal sphere of influence of cyclic blasting in shared rock as well as its variation law was characterized. e remainder of this paper is structured as follows. Section 2 introduces the principle of rock mass damage. Section 3 describes engineering background, test principles and equipment, and monitoring schemes. en the ultrasonic test results of two typical sections are analyzed in Section 4, and the ultrasonic wave velocity distribution of shared rock in Section 5. Finally, the paper is concluded in Section 6.

Principle of Rock Mass Damage
Macroscopically, rock mass is considered as a continuous material with original defects in the damage mechanics theory; that is, rock mass is a continuum with many cracks [50][51][52]. e damage can be regarded as the opening and expansion of the original cracks due to the propagation, reflection, and interaction of the explosion stress wave, resulting in the deterioration of the rock mechanical properties such as elasticity modulus, wave velocity, damping, and frequency [53][54][55]. According to the change of elasticity modulus, Kawmaoto et al. [56] got the classic definition of damage variable D: where E 0 is the elasticity modulus of rock mass before blasting (MPa) and E is the equivalent elasticity modulus of rock mass after blasting (MPa). According to the elastic wave theory, the elasticity moduli of rock mass before and after blasting are, respectively, where ρ 0 and ρ are the densities of the bedrock before and after blasting, respectively; μ 0 and μ are Poisson's ratios of the bedrock before and after blasting, respectively; ] 0 is the wave velocity of rock mass before blasting (m/s); and ] is the wave velocity of rock mass corresponding to the same test position after blasting (m/s). When the tunnel is excavated by smooth blasting or presplitting blasting, the property of the reserved surrounding rock will not change qualitatively before and after blasting.
Assuming that the density and Poisson's ratio of rock mass before and after blasting are approximately equal, that is, ρ 0 � ρ and μ 0 � μ, then equations (1)∼ (3) give erefore, the damage variable of rock mass can be approximately expressed by the changes of wave velocity of rock mass before and after blasting. In the field of blasting engineering, the allowable change rate of wave velocity before and after blasting can be determined according to the different damage control standards. For example, the change rate η of wave velocity before and after blasting is used to determine the damage degree of rock mass under the action of blasting load in the literature [57][58][59]: When the change rate η > 15% before and after blasting, it can be judged that the rock mass is damaged. erefore, the damage variable D can be expressed as At this moment, the damage threshold of rock mass is D cr � 0.28. e damage threshold can be used to judge the sphere of influence of blasting to surrounding rock.

Engineering Background.
e Liuyuetian tunnel from Yongshun County to Jishou City is located in Yongshun, China. e entrance of the tunnel in Jishou City is connected to the Mengdonghe bridge. According to the standard of the International Tunnel Association, the Liuyuetian tunnel is a long tunnel with a length of 1010 m (ZK10 + 445-ZK11 + 455) on the left and 1015 m (YK10 + 440-YK11 + 455) on the right. e geography of this project is characterized by denudation and corrosion of low-mountain landscape. e natural slope of mountains in the portal section is 30°to 35°, accompanied with great topographic relief. According to highway tunnel design data, weak weathering limestone is the dominant rock in the tunnel range. e neighborhood tunnel is a structural form that connects a separated tunnel and a multiarch tunnel. Unlike the Sandwich wall of the multiarch tunnel, which is made of concrete, there is a reserved rock mass between the two holes of the neighborhood tunnel. e total length of the neighborhood tunnel is 77 m and the buried depth is 25 to 46 m. e clear spacing of shared rock is 3 to 6 m. e surrounding rock in the tunnel is mainly at level IV. e plan view of the neighborhood tunnel is shown in Figure 1, and the profile view of 1-1 is shown in Figure 2.
e Liuyuetian tunnel was designed and constructed based on the New Austrian tunneling method. e rock mass of the neighborhood tunnel was excavated by upper and lower benches to relieve any influence of blasting vibration on the remaining rock. Preliminary support is applied in a timely manner after completion of the excavation. e excavation of the upper bench adopts the blasting technique of wedge cut and the diameter of the blast hole is 42 mm. Smooth blasting was applied on periphery holes using #2 rock emulsion explosives. e blast holes are located at intervals of 50 cm.

Test Principle and Equipment.
As an effective nondestructive method, ultrasonic testing has been widely used to detect and evaluate crack detection [60,61], bolt looseness monitoring [62], corrosion detection [63], void detection [64,65], rock mass damage [66], and others [67,68]. e ultrasonic test aims to analyze the stress state and integrity of rock mass according to the propagation law of the ultrasonic wave velocity in rock mass. Influenced by structural surfaces with different mechanical properties, the ultrasonic wave may develop refraction, scattering, and thermal loss during propagation in rock mass, thereby resulting in geometric and physical attenuation. In practical engineering, different shapes and numbers of cracks and cavities exist in rock mass, which may affect the propagation velocity of the ultrasonic wave. When the distances of refraction, scattering, or diffraction of the ultrasonic wave are relatively long, the ultrasonic wave velocity declines greatly. Moreover, the velocities of the ultrasonic wave vary at different properties of rock masses. As the tunnel advances continuously, the stress equilibrium state of protolith is destroyed such that stresses in the rock mass are redistributed or form local stress concentration. e stress state and integrity of rock mass change greatly when frequent blasting loads are applied onto rock mass, thereby resulting in continuous reduction of the ultrasonic wave velocity.
In this test, single-hole ultrasonic test method is applied at the side wall of the tunnel, as shown in Figure 3. e monitoring apparatus is RSM-SY5 (T) nonmetallic ultrasonic wave apparatus that was made by the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, and consisted of a transmitting transducer and two receiving transducers. In ultrasonic testing, the one-transmittingdouble-receiving probe is placed in the test hole, and water is used as a coupling agent. e entrance of hole is plugged with an air bag, and then the test hole is filled with water. e ultrasonic test site is presented in Figure 4.

On-Site Monitoring Schemes.
According to the spatial layout of the neighborhood tunnel and mechanical properties of the rock mass, the shared rock on the side of the anterior excavating tunnel was selected as the monitoring position. Ultrasonic test holes were set in the level IV surrounding rock. Specifically, holes L1 and L2 were intended to monitor sections K11 + 390 and K11 + 395. Figure 5 shows the layout of the ultrasonic test hole. e diameter of the ultrasonic test hole is 50 mm. Drilling depths of L1 and L2 are 5.4 m and 5.8 m, respectively. A 50 cm space is reserved between the bottom of the ultrasonic test hole and the side wall of the shared rock in the posterior excavating tunnel. All ultrasonic test holes tilt down by 5°with consideration of the coupling effect between the sensor and the hole wall. Fresh water is applied as the coupling agent in the test. e one-transmitting-doublereceiving probe starts from the bottom to the entrance of the ultrasonic test hole at a sampling distance of 20 cm. is test Shock and Vibration 3 300~600 996 Central line    Figure 6. According to the test results in Figure 6, the ultrasonic wave velocity decreases continuously with the increase in the number of blasts, indicating that the damage to the surrounding rock is intensified continuously. When the hole depth is in the range of 1.4 to 3.4 m, the ultrasonic wave velocity at the test hole before blasting is higher than 4200 m/s, which agrees with the longitudinal wave velocity described by Ling et al. [38]. is condition reflects that the surrounding rock in this section is close to protolith and the integrity degree is relatively high, along with a low damage degree. However, the ultrasonic wave velocity drops dramatically by 42.6% from 5226 m/s at the hole depth of 1.4 m to 3050 m/s at 0.4 m. is condition proves that the integrity of the rock mass decreased and the load-bearing performance of the rock mass declines continuously. e ultrasonic wave velocity presents a monotone decreasing trend when the test hole is close to the anterior excavating tunnel, which is due to the blasting-induced damage to local shared rock. In the hole depth range of 3.4 to 5.8 m, the ultrasonic wave velocity in shared rock continues to decrease with the increase in the number of blasting in the posterior excavating tunnel. is condition demonstrates the occurrence of crack expansion in the shared rock in this section, which decreases the mechanical properties of rock mass significantly and forms a stress concentration zone.

Ultrasonic Test Results Analysis
To analyze the effects of the number of blasting on the damage accumulation degree of the shared rock, we formulate equation (1), which expresses the relationship between the hole depth and the damage variable. e relation curves are presented in Figure 7. Figure 7 shows that, within the hole depth of 3.4 to 5.8 m, the mean D in five tests is 0.043, 0.044, 0.163, 0.051, and 0.045. Specifically, the D of the surrounding rock reaches the maximum (0.163) during the third blasting. According to damage judgment theory, the damage failure of rocks occurs when the D is higher than 0.28. In view of the relationship between D and hole depth, D is less than 0.28 in the first and second blasting excavations, indicating no damage to rocks. However, continuous blasting vibration still might cause deterioration to the physical and mechanical properties of the surrounding rock within a certain range, and cracks propagate continuously. e damage failure of rock mass initiates from the 4.6 m hole depth at the third blasting. According to the damage criterion of rock mass in Section 2, the damage range is determined at 2.2 m. e critical depth for rock failure at test holes is 4.2 m during the fourth blasting,

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indicating that the damage range expands to a certain extent. e damage range remains the same at the fifth blasting, but the damage degree increases to a maximum of 0.61. e relation curves between relative ultrasonic wave velocity in the shared rock and hole depth are shown in Figure 8. e relative ultrasonic wave velocity refers to the variation of the ultrasonic wave velocity in rock mass during one blasting compared with that in the previous blasting. Figure 8 shows that the ultrasonic wave velocity attenuates slightly during the first blasting due to the long distance from the explosive source to the test hole. e relative ultrasonic wave velocity is controlled within 162 m/s. However, the relative ultrasonic wave velocity increases slightly during the second blasting, and the maximum value reaches 193 m/s. e relative ultrasonic wave velocity increases during the third blasting, reaching as high as 876 m/s. is result is related to the distance between the blasting hole and the surrounding rock at the test point. In addition, the damage degree of the surrounding rock increases quickly when the ultrasonic wave velocity attenuates significantly, and the region with high attenuation rates mainly concentrates in the depth range of 3.6 to 5.8 m.
e boundary lines are obvious. e maximum relative ultrasonic wave velocities during the fourth and fifth blasting are 398 m/s and 415 m/s, respectively. e attenuation amplitudes are smaller than those in the third blasting. Given a similar distance between the explosive source and the test hole, the relative ultrasonic wave velocity in the fifth blasting is significantly higher than that in the first blasting. To sum up, the resistance of the shared rock to explosive loads drops dramatically with the increase in the number of blasting.

Ultrasonic Test Results of K11 + 395.
e ultrasonic wave velocity in one test before blasting and the ultrasonic wave velocity in five tests after blasting were collected from the anterior excavating tunnel section K11 + 395. Five blasting excavation faces of the posterior excavating tunnel existed, namely, K11 + 403, K11 + 399, K11 + 396, K11 + 391, and K11 + 388. e relation curves of ultrasonic wave velocity, damage variable, and relative ultrasonic wave velocity with hole depth are shown in Figures 9-11.
In Figure 9, the ultrasonic wave velocity within 1.2 to 5.4 m of the test hole before blasting is higher than 4300 m/s, which is consistent with the test results of L1. e ultrasonic wave velocity within 0.6 to 1.2 m drops significantly due to the damage of shared rock during the blasting excavation of the anterior excavating tunnel. e ultrasonic wave velocity decreases to different extents after multiple blasting of the posterior excavating tunnel. In particular, the ultrasonic wave velocity in the rock mass within 3.0 to 5.8 m of the hole depth decreases greatly at the third blasting, and the average reduction rate of the ultrasonic wave velocity reaches 13.4%. Figure 10 shows that when the hole depth ranges from 3.0 to 5.4 m, the average damage variables of the ultrasonic wave velocity in five tests after blasting are 0.029, 0.082, 0.233, 0.066, and 0.063. Specifically, the damage variable of the surrounding rock reaches the maximum (0.233) during the third blasting, which is consistent with the ultrasonic wave velocity test results at L1. According to the damage criterion in Section 2, we can calculate that the damage accumulation range of the shared rock caused by the blasting of the posterior excavating tunnel is 2.4 m.
As shown in Figure 11, the maximum relative ultrasonic wave velocities in the five tests after blasting are 95, 403, 1100, 327, and 337 m/s. Similarly, the maximum relative ultrasonic wave velocity is also achieved in the third blasting. High values of the relative ultrasonic wave velocity mainly concentrate in the depth range of 3.0 to 5.4 m, indicating the serious damage of the surrounding rock in this section.
In other words, the attenuation laws of ultrasonic wave velocities at L1 and L2 are consistent. e damage range of shared rock under explosive loads is approximately 1.2 to

Distribution Law of Ultrasonic Wave
Velocity of Shared Rock

Effects of Relative Ultrasonic Wave Velocity on Shared
Rock. e region between L1 and L2 was set as the test region to analyze the effects of single blasting on the ultrasonic wave velocity (Figure 12). e variation laws of the ultrasonic wave velocity in shared rock in the test region can be concluded by testing the ultrasonic wave velocity in blasting holes in the posterior excavating tunnel.
A widely accepted view is that cyclic blasting excavation may cause damage accumulation to shared rocks. us, the effects of each blasting on shared rock in the test region were analyzed by relative ultrasonic wave velocity. e posterior excavating tunnel had four blasting excavation faces, namely, K11 + 399, K11 + 396, K11 + 391, and K11 + 388. e variations of relative ultrasonic wave velocity in the test region under each blasting condition are presented in Figure 13. e monitoring section K11 + 395 is 0 m away from the vertical coordinate and K11 + 390 is 5 m away from the vertical coordinate. Figure 13 shows that the relative ultrasonic wave velocity in shared rock in the test region changes greatly after each blasting. e excavation face during the first blasting is K11 + 399, and the maximum relative ultrasonic wave velocity difference is − 492 m/s. e region with great attenuation amplitude of ultrasonic wave velocity is mainly in the area that is 0 to 2 m away from the side wall of the posterior excavating tunnel and has a hole depth of 5.0 to 5.4 m. e maximum relative ultrasonic wave velocity difference reaches − 1220 m/s during the second blasting. e region with great attenuation amplitude is mainly located in the area that is 0-1.5 m away from the side wall of the posterior excavating tunnel and has a hole depth of 4 to 5 m. e reason is that this region is close to L1 and shows serious damage to the surrounding rock. e maximum relative ultrasonic wave velocity difference is − 876 m/s during the third blasting. e region with great attenuation amplitude is mainly in the area that is 3 to 5 m away from the side wall of the posterior excavating tunnel and has a hole depth of 3.8 to 4.6 m. e excavation face is close to L2 during the third blasting, so the ultrasonic wave velocity at L2 attenuates quickly. e maximum relative ultrasonic wave velocity difference decreases to − 398 m/s in the fourth blasting. e region with great attenuation amplitude is mainly located in the area that is 1 to 5 m away from the side wall of the posterior excavating tunnel and has a hole depth of 4.2 to 4.6 m.
Based on the preceding analysis, the maximum attenuation amplitude of the relative ultrasonic wave velocity is detected during the second blasting. e region with great attenuation amplitude is mainly located in the area that is 0 to 1.5 m and 4 to 5 m away from the side wall of the   Figure 12: Layout of test region (unit: cm). Shock and Vibration 7 posterior excavating tunnel and has a hole depth of 3.8 to 5.0 m. us, stresses are relatively concentrated in local shared rock, thereby resulting in serious damage to the surrounding rock and significant attenuation of the ultrasonic wave velocity.

Effects of Absolute Ultrasonic Wave Velocity on Shared
Rock. Figure 14 shows nephograms of the change process of the ultrasonic wave velocity in the test region after each blasting relative to the absolute ultrasonic wave velocity before blasting.
In ultrasonic wave velocity tests, the ultrasonic wave monitoring instrument cannot collect ultrasonic wave velocity due to serious damage to some shared rock, which decreases the hole depth after several numbers of blasting. Figure 14 shows the obvious attenuation region of the ultrasonic wave velocity of the rock mass. e attenuation rate is high when the hole depth is in the range of 3.5 to 5.4 m, and the absolute variation is higher than 1000 m/s. e maximum absolute variation (1355 m/s) of the ultrasonic wave velocity is in the region with 3.7 to 4.0 m depth and 3 to 5 m distance from the monitoring position. Based on the preceding analysis, the stress concentration region of the shared rock is close to the excavation face under explosive loads of the posterior excavating tunnel.
is region mainly distributes within 2 m along the longitudinal axis of the tunnel. is stress concentration region moves forward continuously as the excavation face advances. Finally, a strip stress concentration region that is approximately 2 m deep is formed.
In other words, determining the sphere of influence of cyclic explosive loads is important to support and protect the shared rock in the neighborhood tunnel. Crack expansion on surrounding rock stops after the dividing point is determined, accompanied by decelerating growth of the bulking force. e safe construction of the project can be ensured by strengthening supports to the surrounding rock and adjusting the sphere of influence of dynamic disturbances, including explosion.  Shock and Vibration

Conclusions
e main objective of this study is to determine the damage range of the shared rock in the neighborhood tunnel during blasting excavation. Based on the field ultrasonic test presented in this study, the following conclusions can be drawn: (1) Compared with single blasting, progressive cyclic explosions may cause damage accumulation to the shared rock in the neighborhood tunnel and the damage intensifies continuously. erefore, the effects of damage accumulation have to be considered to evaluate the influences of explosive loads on the shared rock. (3) e stress concentration region of the shared rock is close to the excavation face under explosive loads of the posterior excavating tunnel and is mainly within 2 m along the longitudinal axis of the tunnel. e stress concentration region moves forward continuously as the excavation face advances. A strip stress concentration region that is approximately 2 m deep is formed gradually. (4) A method to determine the sphere of influence of cyclic explosive loads on the shared rock is proposed. Variation law of the ultrasonic wave velocity in the shared rock under cyclic explosive loads is disclosed by analyzing the relative and absolute ultrasonic wave velocities.

Data Availability
All data used to support the findings of this study are included within the article. ere are not any restrictions on data access.

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Conflicts of Interest e authors declare no conflicts of interest.