Effects of Confining Stress on Blast-Induced Damage Distribution of Rock with Discontinuity

Abstract

Discontinuous rock mass, such as joints and fractures, have a great influence on the blasting quality and sometimes induce additional damage at the discontinuity. In deep rock engineering, high in situ stress makes the damage mechanism of rock with discontinuity under blasting loading more complicated. Quantitative analysis of blast-induced damage in discontinuous rock under high in situ stress is of great importance in guiding the fine blast design. In this paper, a series of numerical models have been established to quantitatively investigate the effect of confining stress and inclination angle on blast-induced damage of rock with discontinuity. The numerical results show that the discontinuity obviously changes the distribution mode of blast-induced damage, and there is more damage near the discontinuity. The blast-induced damage crack length of discontinuous rock decreases as hydrostatic stress rises. Under non-hydrostatic stress, the damage crack propagation appears to have a higher tendency in the higher confining stress direction. In addition, the inclination angle of discontinuity will affect the damage distribution of rock with discontinuity. The fragmentation degree is greatest when the discontinuity is perpendicular to the direction of higher confining stress. Due to the presence of discontinuity, the guiding effect of higher confining stress on damaged cracks is weakened. The results provide a reference for the tunnel fine-blasting design of rock with discontinuity.

1. Introduction

As the demand for resources and space increases, the scale and amount of deep rock engineering gradually increase [1,2,3,4]. Drilling and blasting technology is widely used in rock engineering, such as tunneling and underground chamber excavation, due to low cost and high efficiency [5,6]. With the increasing of the in situ stress in rock engineering projects, the drilling and blasting are faced with severe challenges, such as unmanageable blast-induced damage cracking and insufficient fragmenting, so sustainable development of deep rock engineering is limited [7,8,9,10]. Therefore, it is essential to enrich the understanding of blast-induced damage cracking of high-stress rock mass for improving blasting efficiency in deep projects.

In recent years, many researchers have focused their attention on the blasting damage mechanism of rocks under high confining stress. Rossmanith et al. [11] carried out the blasting experiment on PMMA models with high prestress. They found that the crack induced by blasting is obviously affected by prestressing. Kutter and Fairhurst [12] indicated that the crack induced by blasting propagated preferably in the direction of maximum principal stress. Jung et al. [13] also proved in their experiment that the crack induced by blasting would be aligned in the direction of the maximum principal stress. Yi et al. [14] simulated the fracturing of rock by blasting under different confining stresses in LS-DYNA. They pointed out that the damage evolution in rock is affected by confining stress. In particular, the effect of confining stress on the development of far-field cracks induced by blasting is more significant. Li et al. [15] studied the influence of in situ stress on rock blasting crushed zone and cracked zone. Xie et al. [16] studied the damage mechanism of rock in cutting blasting under high in situ stress by using LS-DYNA. They observed that the damage range of rock gradually decreased with the increasing of in situ stress. The limit effect of in situ stress and the difference between horizontal and vertical stresses are the main reasons resulting in the trouble of cutting blasting in deep rock. Tao et al. [17] also reached a similar conclusion that with the increase in the difference between horizontal and vertical stresses, radial cracks clustered more near the maximum principal stress. Moreover, Li et al. [18,19] studied the influence of in situ stress on smooth and presplitting blasting. The above-mentioned research is mainly focused on the damage mechanism of the rock with continuity under the confining stress. However, due to the heterogeneity and anisotropy of rock, discontinuities like joints and fractures generally exist in rock engineering projects [20,21]. These weak structures deteriorate under the combined action of blasting loading and in situ stress, which may lead to poor expected blasting effect and even induce disaster.

So far, much research has investigated the damage mechanism of rock with discontinuity under dynamic loads or combined static and dynamic loads by using the SHPB equipment [22,23,24,25]. However, the dynamic loading generated by the SHPB test cannot fully simulate the actual blasting loading. To date, there has been limited research into the damage mechanism of rock with discontinuity under confining stress and blast loading. For instance, by using the SPH-FEM approach, Jayasinghe et al. [26] analyzed the influence of in situ stress and discontinuity on rock blasting damage. They pointed out that the joint persistence and the location of the rock bridges control the distribution of blasting damage. Ma and An [27] also discussed the influence of in situ stress and restored joints on the blasting damage distribution of rock in LS-DYNA. Wang and Konietzky [28] used LS-DYNA and UDEC coupling numerical methods to study the dynamic fracture process of jointed rock mass under three cases of confining stress. The results show that the propagation of cracks induced by blasting in jointed rock mass is strongly restricted in the direction of minimum principal stress. Jiang et al. [29] established a series of numerical models to study the dynamic response and damage mechanism of discontinuous rocks under four cases of confining stresses. They reported that the damage of rock with discontinuity under confining stress and blasting loading becomes more complicated. In addition, Dong et al. [30,31] studied the effect of in situ stress on energy transmission of blasting stress waves in jointed rock mass based on model tests. Tian et al. [32] proposed a distance calculation method for peripheral boreholes under the combined action of in situ stress and joints. The above research shows that more and more scholars have begun to focus on the influence of confining pressure and discontinuity on the dynamic behavior of rock mass. However, the quantitative relationship between damage distribution and confining stress and discontinuity angle is still lacking under blasting loading and confining stress.

In this study, the finite element software LS-DYNA R8.1.0 is used to focus on the blasting damage distribution of rock with discontinuity under different confining stresses. Firstly, on the basis of a small explosion test, the parameters of the numerical model are calibrated. Furthermore, the blasting damage characteristics of rock with discontinuity and continuity under high confining stress are compared. Then, the effects of confining stress and inclination angle on blasting damage characteristic of rock with discontinuity are analyzed. Finally, according to the numerical calculation results, the field optimization test of the tunnel blasting parameters is carried out.

2. Numerical Model Development and Material Models

2.1. Finite Element Model

In this study, a single-hole numerical model was established in LS-DYNA to investigate the blasting damage and dynamic response of rock with discontinuity under confining stress, as shown in Figure 1. This model is a square with a length of 5 m, in which a discontinuous surface is prefabricated. In accordance with the specifications of the drilling equipment commonly used in tunneling, the borehole with a diameter of 42 mm is located in the center of the model. Decoupled charges were used, with a cartridge diameter of 32 mm. The discontinuity with a length of 1 m is set 0.5 m away from the center of the borehole. The inclination angle α of the discontinuity is defined as the angle between the discontinuity and the horizontal direction, including five inclination cases (i.e., 0°, 30°, 45°, 60° and 90°) in this paper. To simulate the infinite rock around the borehole in deep engineering, non-reflective boundaries are placed on the surrounding surfaces (i.e., the left, right, upper, and lower surfaces) of the model. A large number of published studies have shown that a non-reflective boundary can greatly reduce the reflection of stress waves at the boundary [33,34,35]. As the numerical results are strongly influenced by the mesh size, the mesh size is strictly necessary for the numerical calculation of the blasting process. To improve the validity of numerical results, it is usually recommended that the mesh size does not exceed 1/6–1/12 of the wavelength; the mesh size should be shorter than 23 mm by calculation [33]. Then, the convergence test is carried out by halving the element size until the difference in numerical results is lower than 5%. Finally, the mesh size of the explosive and rock around the borehole is approximately 2.5 mm, and the mesh size at the boundary of the rock is also determined to be 10 mm to improve the accuracy of numerical calculation. The number of elements and nodes are 284,428 and 571,636, respectively. Moreover, the Arbitrary–Lagrange–Euler (ALE) coupling algorithm is used to avoid mesh distortion. It is generally believed that the coupling area radius must be bigger than ten times the explosive radius to ensure the convergence of numerical calculation results [36]. For this, the air size is determined to be 2 m × 2 m.

In order to study the damage and dynamic response of rock with discontinuity under different confining stresses, different cases of confining stresses are designed. The hydrostatic and non-hydrostatic stresses are considered, as shown in

Table 1. Cases of confining stress and inclination angle in simulations.

Case	Vertical Stress σV/MPa	Horizontal Stress σH/MPa	Inclination Angle
Without confining stress	0	0	0°
Hydrostatic stress	10	10
	20	20
	30	30
	40	40
	50	50
Non-hydrostatic stress	30	10	0°
		20
		40
		50
Non-hydrostatic stress	10	30	30°
			45°
			60°
			90°
	50	30	30°
			45°
			60°
			90°

. The quasi-static loading method [37] was used to apply vertical confining stress to the top and bottom boundary of the numerical model and horizontal confining stress to the left and right sides. The keyword *DEFINE_CURVE is used to apply the time history of confining stress to the model boundary. The application time of the pre-confining stress was determined to be 80 ms so as to reduce the vibration caused by inertia force and kinetic energy. The explosive detonates at 90 ms.

2.2. Material Models and Parameters

Among the many material models of rock, the RHT model (*MAT_272) in LS-DYNA is selected in this study. Compared with other material models for rock, the RHT model considers the influences of confining pressure, strain rate, strain hardening, and damage softening on the failure strength of rock materials, which can effectively simulate the blasting process of deep rock mass. Therefore, the RHT model will be applied to the numerical analysis. The RHT model uses three stress limit surfaces to represent the strength criteria, i.e., the initial elastic yield surface, the failure surface, and the residual friction surface [38]. The damage of rock in the RHT model is defined as the ratio of cumulative plastic strain to failure strain. If the rock is completely damaged, D = 1. If the rock is not damaged at all, then D = 0. The greater the degree of rock damage, the greater the D. The RHT model can use the damage variable D to describe the blast-induced damage crack propagation. There is a total of 38 parameters in the RHT model, some of which can be determined by rock basic mechanics parameters and empirical formulas [16], while the rest of the parameters can be referenced from the existing literature [15]. The RHT model parameters used in rock modeling in this paper are shown in

Table 2. The RHT parameters of rock.

Parameter	Value	Parameter	Value
Mass density (kg/m3)	2660	Break compressive strain rate	3 × 1025
Elastic shear modulus (GPa)	21.9	Break tensile strain rate	3 × 1025
Relative shear strength	0.18	Lode angle dependence factor Q0	0.68
Relative tensile strength	0.04	Lode angle dependence factor B	0.01
Parameter for polynomial EOS T1 (GPa)	35.27	Compressive yield surface parameter	0.53
Parameter for polynomial EOS T2 (GPa)	0	Tensile yield surface parameter	0.70
Damage parameter D1	0.04	Crush pressure (MPa)	125
Damage parameter D2	1.0	Compaction pressure (GPa)	6
Hugoniot polynomial coefficient A1 (GPa)	35.27	Shear modulus reduction factor	0.5
Hugoniot polynomial coefficient A2 (GPa)	39.58	Eroding plastic strain	2.0
Hugoniot polynomial coefficient A3 (GPa)	9.04	Minimum damaged residual strain	0.01
Failure surface parameter A	1.60	Porosity exponent	3.0
Failure surface parameter N	0.61	Initial porosity	1.0
Residual surface parameter AF	1.60	Pressure influence on plastic flow in tension	0.001
Residual surface parameter NF	0.61	Tensile strain rate dependence exponent	0.036
Parameter for polynomial EOS B0	1.22	Compressive strength (MPa)	167.80
Parameter for polynomial EOS B1	1.22	Compressive strain rate dependence exponent	0.032
Reference compressive strain rate	3 × 10−5	Gruneisen gamma	0
Reference tensile strain rate	3 × 10−6

[15].

The explosive material is modeled by *MAT_HIGH_EXPLOSIVE_BUREN in LS-DYNA. JWL EOS can predict explosion pressure comprehensively and is widely used in explosion simulation. The relationship between the pressure and the relative volume of the rock during the blasting process is determined by *EOS_JWL calculation.

$$P=A\left(1-\frac{\omega }{R_{1}V}\right)e^{-R_{1}V}+B\left(1-\frac{\omega }{R_{2}V}\right)e^{-R_{2}V}+\frac{\omega E_0}{V}$$

(1)

where P is the detonation pressure; V is the relative volume; E₀ is the energy per unit volume of the explosive; A, B, R₁, R₂, ω are the material parameters. *EOS_JWL parameters are mainly derived from the literature [39] and are A = 586 GPa, B = 21.6 GPa, R₁ = 5.81, R₂ = 1.77, ω = 0.282, and E₀ = 7.38 GPa. Explosive parameter density ρ = 1320 kg·m⁻³; velocity of detonation d = 6690 m·s⁻¹; P_cj = 16 GPa.

Material models *MAT_NULL and *EOS_LINEAR_POLYNOMIAL are used to describe the mechanical behavior of air inside the borehole after the explosive explosion. Air pressure is given by EOS

$$\begin{array}{l}P=C_0+C_1\mu +C_2\mu +C_3\mu +\left(C_4+C_5+C_6\mu \right)E\\ \mu =\frac{\rho }{{\rho }_0}-1\end{array}$$

(2)

where P is the gas pressure; μ is the dynamic viscosity coefficient; E is the internal energy per unit volume; μ can be determined by ρ and ρ₀; ρ and ρ₀ are the density and initial density of the material respectively. C₀, C₁, C₂, C₃, C₄, C₅ and C₆ are constants; C₀ = C₁ = C₂ = C₃ = C₆ = 0; C₄ = C₅ = γ−1; γ is specific heat coefficient 1.4. The air density and initial internal energy are 1.290 kg·m⁻³ and 250,000 J·m⁻³, respectively.

2.3. Comparison between Numerical and Experimental Results

In this paper, the RHT model is used to simulate Banadaki’s experiment [40], which verifies the accuracy of the rock material parameters. Banadaki prepared a series of cylindrical granite samples with a diameter of 144 mm and a height of 150 mm. A blasthole with a diameter of 6.45 mm was drilled in the center of the specimen. The sample is composed of five materials from the inside to the outside: PETN explosive, polyethylene, air, copper, and granite, as shown in Figure 2a. The results of the laboratory single-hole blasting test are shown in Figure 2b. A planar numerical model with the same size as the experiment was established and the numerical simulation results were compared with the physical experiment phenomena to verify the RHT model parameters. The simulation results of single-hole blasting based on the RHT model are shown in Figure 2c. It can be seen from Figure 2 that the damage area shown by the numerical simulation is similar to the results of the test carried out by Banadaki. Simultaneously, the simulation showed that the number of explosion cracks was basically the same as the test result. Therefore, the blasting damage simulation results are in good agreement with the test results, and the model can simulate crack growth more accurately.

Due to the damage mechanism of discontinuous rock being different from that of continuous rock, the reliability of the RHT model for blast-induced damage simulation of discontinuous rock is verified by the test of Li et al. [41]. The test was performed on a PMMA circular plate with a diameter of 400 mm and a thickness of 10 mm. An empty hole with a diameter of 5 mm is arranged in the center of the circular plate. Three pre-discontinuities are evenly distributed on the circular plate, with an angle of 120° between adjacent pre-discontinuities. The pre-discontinuity length is 30 mm, the width is 0.2 mm, and the discontinuity tip is 30 mm away from the center of the empty hole. The basic parameters of PMMA are derived from Li et al. [41] and Jeong et al. [42], and the RHT parameters are obtained through the empirical formulas [16] and the literature references [15]. Hexogen with a charge diameter of 7 mm is used for initiation, the parameters are derived from Li et al. [41]. Figure 3a,b show the distribution of blast-induced damage cracks obtained by test result and numerical calculation result, respectively. Obviously, there is a good correlation between the test and the numerical calculation result. Therefore, the RHT model can be used to simulate the blast-induced damage distribution of rock with continuity and discontinuity.

3. Results and Discussion

3.1. Comparison of Dynamic Response and Damage Evolution between Rock with Discontinuity and Continuity under High Confining Stress

Based on the verified numerical model, the dynamic response and damage evolution process between rock with discontinuity and continuity is compared under 30 MPa hydrostatic stress. In an effort to highlight the influence of confining stress on the damage distribution of discontinuous rock, the angle of discontinuous rock is determined to be 0°. Figure 4 provides the pressure propagation after blasting in rock with discontinuity and continuity under 30 MPa hydrostatic stress. A pressure wave with high strength was formed around the borehole at the initial phase of the cartridge explosion (at 50 μs). In discontinuous rock, the pressure wave propagates away from the borehole and reaches the discontinuity at 100 μs. Along with this, stress concentration is found at both ends of the discontinuity. Subsequently, the pressure wave underwent complex changes in the discontinuity, including the reflection of the wave and so on. In continuous rock, the pressure wave propagates outward and decays. It can be concluded that the pressure wave propagation in rock with discontinuity and continuity is very different.

In order to quantitatively compare the dynamic response between rock with discontinuity and continuity, two observation points were respectively placed between the borehole and the discontinuity and directly below the discontinuity, as shown in Figure 5. Two observation points, called S1 and S2, in turn, were used to evenly divide the distance between the borehole and the discontinuity. Two observation points with the same distance, named S3 and S4, are arranged below the discontinuity. The pressure and velocity-time curves at observation points of rock with discontinuity and continuity under 30 MPa hydrostatic stress are shown in Figure 6 and Figure 7. As can be seen from Figure 6a and Figure 7a, the pressure and velocity-time curves at points S1 and S2 (between the borehole and the discontinuity) show different characteristics compared with points S3 and S4 (below the discontinuity). The discontinuities hinder most of the pressure wave, resulting in a significant decrease in the pressure and vibration in the rock directly below the discontinuity. With the attenuation of the stress wave in continuous rock, the peak values of the pressure and velocity curve decrease gradually (as seen in Figure 6b and Figure 7b). Figure 6c and Figure 7c compare the maximum pressure and peak particle velocity (PPV) at the four observation points. The maximum pressure and PPV of rock with discontinuity and continuity are similar from the observation points S1 and S2 (between the borehole and the discontinuity). However, the maximum pressure and PPV of the discontinuous rock are significantly smaller than that of the continuous rock from the observation points S3 and S4 (below the discontinuity). This is because the reflection of the stress wave and the deformation of the discontinuous medium occurs at the discontinuity when the stress wave passes through the discontinuity. More energy carried by stress waves cannot enter the rock below the discontinuity. Based on this principle, pre-splitting blasting is widely used in rock engineering projects to reduce blasting vibration and maintain the stability of the remaining rock mass [43]. For instance, a series of blasting tests with and without the pre-splitting technique were carried out at the Rampura Agucha mine by P.K. Singh et al. [44]. The results showed that blast-induced vibrations were significantly reduced in the pre-splitting blasting tests as compared to the tests without the pre-splitting blasting technique. Zhou et al. [45] compared the differences in ground vibrations induced by the blasting excavations of shafts with the pre-splitting and smooth techniques. The results showed that at the same monitoring locations and directions, the peak particle velocities in the case with the pre-splitting blasting technique were significantly lower than those in the case with the smooth blasting technique.

Figure 8 shows the damage evolution process of rock with discontinuity and continuity under hydrostatic stress of 30 MPa. Damage distributions at several typical moments (i.e., 50 μs, 100 μs, 150 μs, 200 μs, 300 μs, 500 μs, and 700 μs) are given. As can be seen from Figure 8, regardless of the discontinuity of the rock, the damage induced by blasting presents isotropy under hydrostatic stress (at 100 μs). Figure 8 shows that the damage cracks are dense and distributed in the vicinity of the borehole (i.e., the crushed zone), and there are fewer explosion cracks distribution in the far area (i.e., the cracked zone). In the crushed zone, the rock is crushed because the shock wave generated by the explosion is stronger than the dynamic compressive strength of the rock. When moving away from the borehole, the strength of the shock wave decreases. Until its strength is lower than the dynamic compressive strength of the rock, the rock escapes being crushed. However, the tensile strength of the rock is much lower, resulting in a cracked zone appearing due to the stress wave [15]. When a discontinuity appears below the borehole, the damage distribution of rock around the borehole shows a significant change. It seems that the discontinuity causes more damage in the rock mass between the borehole and the discontinuity after blasting. A damaged area with a triangular shape developed above the discontinuity (on the side close to the borehole). It is because the stretch wave reflected at the discontinuity forms denser damage of rock near the discontinuity. In addition, some damage cracks appear below the discontinuity through the discontinuity (after 300 μs). The reason may be that the discontinuity is gradually closed under the blasting pressure, resulting in more energy generated by the explosion into the rock mass below the discontinuity. It can be seen that the existence of discontinuities changes the damage distribution around boreholes under the 30 MPa hydrostatic stress. Therefore, under the combined action of confining stress and discontinuity, rock damage characteristics are more complex than those of rock with continuity.

3.2. Effects of Confining Stress on Damage Characteristic of Rock with Discontinuity

In an effort to study the damage characteristics of the rock with discontinuity under different hydrostatic stresses, six cases of hydrostatic stresses are designed, i.e., 0 MPa, 10 MPa, 20 MPa, 30 MPa, 40 MPa and 50 MPa. Figure 9 shows rock damage under these six cases of hydrostatic stresses. As the hydrostatic stress changes, the distribution of damage also shows a difference. It can be seen from Figure 9 that the damage between the borehole and the discontinuity is almost triangular in shape. However, with the increase in hydrostatic stress, the damage around the borehole decreases gradually in the other three zones (i.e., the damage along the horizontal direction, the damage above the borehole, and the damage behind the discontinuity). Concretely, without confining stress, damage spreads more strongly from the borehole to the model boundary. There are several major damage cracks at the horizontal and above the borehole. It is also observed that many damage cracks are formed on both ends and below the discontinuity. When the hydrostatic stress increases to 10 MPa, the number of damage cracks in the horizontal direction and above the borehole decreases intuitively from the simulation results. In this case, the length of damage cracks at both ends of the discontinuity is obviously inhibited, and the length and number of cracks are lower than those without confining stress. It is noteworthy that at a hydrostatic pressure of 20 MPa, the damage cracks at both ends of the discontinuity almost disappear. An interesting observation was that under 50 MPa hydrostatic stress, almost without damage was observed above the borehole, but there was still damage between the borehole and disconnection. Theoretically, under hydrostatic stress, damage should be distributed almost evenly around the borehole in continuous rock. However, based on such observation under 50 MPa hydrostatic stress, it can be assumed that the discontinuity weakens the barrier caused by the confining stress.

In order to obtain more quantitative results, the maximum damage lengths and fragmentation degree of rock (i.e., the ratio of the volume of broken rock to the entire volume of rock) in different zones were identified in the post-processing software, as shown in Figure 10 and Figure 11. In the RHT model, the rock-breaking simulation can be realized by removing the damage element of the rock. In this paper, the damage threshold of rock elements is set at 0.4, and the elements of rock whose damage degree exceeds 0.4 are deleted. When calculating the broken rock volume in different areas, the volume of rock in the crushed zone is not included. As observed, the maximum damage length and fragmentation degree along the horizontal direction and above the borehole decrease with the increase in hydrostatic stress. This is because the confining stress has a resistance effect on the propagation of damage cracks induced by blasting [46]. This phenomenon is found in common studies [16,47,48]. According to the numerical results, the damage length above the borehole changes almost linearly with the hydrostatic stress. However, with the increase in hydrostatic stress, the damage length in the horizontal direction gradually decreases while the number of changes also falls. In Figure 10, the damage length behind the discontinuity is obviously limited by the confining stress. Meanwhile, the damage volume ratio behind the discontinuity gradually shrinks with the increases of hydrostatic stress from 0 MPa to 50 MPa, as seen in Figure 11.

Due to the tectonic stress in the underground deep rock, the in situ stress showed anisotropy in horizontal and vertical directions. Thus, four cases of non-hydrostatic stresses were set. The horizontal confining stress was fixed without change, and the vertical confining stress was determined to be 10 MPa, 20 MPa, 40 MPa, and 50 MPa. The damage of rock with discontinuity was compared between four cases of non-hydrostatic stress and hydrostatic stress, as shown in Figure 12. It can be seen from Figure 12 that, compared with hydrostatic stress, the damage distribution of rock with discontinuity appears to have stronger anisotropy under non-hydrostatic stress. When the vertical stress is lower than or equal to 30 MPa, the length of the damage crack in the horizontal direction increases obviously with the decrease in the vertical stress. When the vertical stress is greater than 30 MPa, the length of the damage crack in the vertical direction has no significant change. Meanwhile, the damage along the vertical direction increases between the borehole and discontinuity with the increase in vertical stress. The damage crack from the borehole is more inclined to connect with the discontinuous ends. As the vertical stress increases, so does the area of damage below the discontinuity. The results show that the damage cracks will preferentially propagate in the direction of high stress.

Figure 13 and Figure 14 show the maximum damage length and fragmentation degree in different zones under four cases of non-hydrostatic stress and hydrostatic stress. Figure 13 and Figure 14 show that, as the vertical confining stress increases, the damage length and damage area along the horizontal direction decrease gradually, while the damage length above the borehole shows an increasing trend. In addition, the change rate of damage length in the horizontal direction with vertical stress is greater than that above the borehole. When the vertical stress is lower than 30 MPa (i.e., maximum principal stress along the horizontal direction), the damage length in the horizontal direction increases gradually with the decrease in vertical stress. On the contrary, when the vertical stress is greater than 30 MPa (i.e., maximum principal stress along the vertical direction), the damage length and area of the direction of high stress increase with the increase in vertical stress. The results show that the damage cracks will be inhibited in the direction of low confining stress, and damage cracks are prone to develop towards the direction of high confining stress.

3.3. Effects of Discontinuity Inclination Angle on Damage Characteristic of Rock with Discontinuity under High Non-Hydrostatic Stress

In Section 3.2, the damage distribution of rock with horizontal discontinuity under hydrostatic and non-hydrostatic stresses is analyzed. The difference between horizontal and vertical stress has a serious effect on the damage distribution of rock with horizontal discontinuity under non-hydrostatic stress. In order to further investigate the influence of inclination angle on the damage distribution of discontinuous rocks under non-hydrostatic stress, the discontinuous rock with five cases of inclination angle (i.e., 0°, 30°, 45°, 60°, and 90°) is designed under non-hydrostatic stress. According to the results in Section 3.2, the horizontal stress is fixed at 30 MPa, and the vertical stress is determined at 10 MPa and 50 MPa. Figure 15 gives the damage distribution of discontinuous rocks with different inclination angles under horizontal stress of 30 MPa and vertical stress of 10 MPa. It can be seen that the inclination angles of discontinuity change the damage distribution under the same confining stress. Firstly, the damages along the horizontal direction on the left side of the borehole and the vertical direction above the borehole are less affected by the inclination angles of discontinuity. This is because, on the side away from the discontinuity, the damage distribution is mainly determined by the confining stress and blasting loading. It can be seen more clearly from Figure 16 that the maximum damage length on the left side of the borehole first increases and then decreases as the inclination angle increases. On the contrary, above the borehole, the damage length first decreases and then increases as the inclination angle increases. Then, more differences in the damage distribution were shown in the zone between the borehole and discontinuity and the zone behind discontinuity. Some blasting-induced damage originating from the borehole connects the borehole to the ends of discontinuity, ruling out the case of the angle being 0°. It may be caused by the anisotropy of the confining stress and change in discontinuous inclination. Meanwhile, with the increase in inclination angle, more and longer blasting-induced damage appears behind the discontinuity (as seen in Figure 15 and Figure 17). When the inclination angle of discontinuity is 90°, the number of damage cracks behind the discontinuity is the largest. It may be because when the discontinuity angle changes from 0° to 90°, the horizontal high confining stress could lead to the discontinuity closure more easily so that more blasting energy crosses the discontinuity.

The damage characteristics under horizontal stress of 30 MPa and vertical stress of 50 MPa are shown in Figure 18, Figure 19 and Figure 20, respectively. Figure 18 shows that, under 50 MPa vertical stress, the damage characteristics are significantly different from those under vertical stress of 10 MPa, although at the same angle. Firstly, with the discontinuity away from the left zone of the borehole, the maximum damage length and fragmentation degree in this zone decreases gradually until it does not change. It is probably due to the resistance action of the confining stress in the smaller stress direction limiting the damage. And the effect of discontinuity on this zone is reduced. The damage length above the borehole does not change greatly with the inclination angle. With the increase in inclination angle, the damage between the borehole and the ends of discontinuity is weakened. When the inclination angle is 90°, it is impossible to induce damage between the discontinuous ends and the borehole. However, there is still a large amount of damage near the discontinuity, even if the maximum stress is in the vertical direction. Therefore, it can be proved that discontinuity will weaken the guiding effect of high confining stress on damage.

4. Tunneling Field Test

The field test site is determined to be Bailongtan Tunnel, Guangxi, China, which is a two-hole separated highway tunnel, as shown in Figure 21a. The design length of the left line is 2780 m, and the maximum depth is about 358.724 m. The design length of the right line is 2789 m, and the maximum depth is about 336.710 m. The rock in the test site is medium-weathered limestone, and the average saturation uniaxial compressive strength is 51.9 MPa. The test site has a medium-thick to super-thick layered formation, as shown in Figure 21b.

Smooth blasting (original scheme) was used to excavate the upper bench of the tunnel, and the borehole layouts are shown in Figure 22a. It should be noted that 1#, 3#, etc., represent the detonation sequence of the boreholes. A total of 100 boreholes with diameters of 42 mm are set, and the spacing between the peripheral boreholes is 60 cm. An emulsion explosive with a diameter of 32 mm was used. As can be seen from Figure 22b, half-boreholes were not found on the side of the tunnel after blasting. By analyzing the test results, it can be seen that there are three possible reasons, including the tunnel working area passing through the layered formation, the joint within rock mass, and the excessive damage to discontinuity caused by centralized charging of peripheral boreholes.

In order to overcome the influence of discontinuity on tunnel contour quality, the original blasting scheme is optimized. An innovative blasting method is proposed so as to achieve high-quality contour in the discontinuous rock mass. In detail, 11 boreholes with spacing of 30 cm are arranged at the side of the tunnel to initiate detonation before the other boreholes, as shown in Figure 23a. The air deck charge is adopted for these boreholes. There are three benefits to this model. Firstly, the boreholes arranged vertically along the side walls can easily form connected slots under in situ stress in mountain tunnels. Then, the preferentially formed slots can reduce the damage at discontinuity caused by main boreholes. Finally, the air deck charge could reduce the peak pressure acting on the borehole wall, reducing the damage at discontinuity. The tunnel contour quality of the optimized scheme is shown in Figure 23b. Obviously, there are half-boreholes at the side of the tunnel, and the tunnel contour quality is obviously improved.

5. Conclusions

Based on the verified numerical model, the effects of confining stress and discontinuity inclination angle on the damage distribution of rock with discontinuity have been investigated. The damage evolution and dynamic response of rock with continuity and discontinuity under high confining stresses have been compared. Then, the effects of confining stress and inclination angle on the damage distribution characteristics of rock with discontinuity have been analyzed. According to these results, the following conclusions can be drawn:

(1)

There are obvious differences in blast-induced damage distribution between discontinuous rock and intact rock under the same high confining stress. Discontinuity induces a non-uniform distribution of blasting damage, and more damage accumulates near the discontinuity;

(2)

The magnitude and direction of confining stress have a great influence on the blast-induced damage distribution of rock with discontinuity. High hydrostatic stress limits the damage crack propagation. With the increase in hydrostatic stress, the blast-induced damage crack length of discontinuous rock decreases. The direction of higher confining stress shows a higher tendency for damage crack propagation;

(3)

Under the same non-hydrostatic stress, the change in discontinuity inclination angle results in the different blast-induced damage distribution of rock with discontinuity. When the discontinuity is perpendicular to the higher confining stress, the damage fracture degree of the rock is the largest. In addition, discontinuity weakens the guiding effect of non-hydrostatic confining stress on blast-induced damage.