1 INTRODUCTION
The drilling and blasting (D&B) technique is widely used in tunnel construction and underground rock excavation (Cheng et al., 2022; Zhang, Liu, et al., 2023; Zhao et al., 2024, 2025). However, for deeply buried tunnels, the D&B process becomes more complex due to the limited free working face and the impact of high in situ stress (Xie et al., 2016). During the D&B process, cut blasting is especially critical, since the free face created by cut blasting directly affects the overall efficiency and cost of blasting operations (Singh, 1995; Wang et al., 2019; Xie et al., 2016; Zhang, Qiu, et al., 2023; Zhao et al., 2011). Therefore, studying cut blasting under high-ground stress conditions is essential for improving blasting efficiency.
Numerous factors influence the results of cut blasting, including the cutting model and cut-hole layouts. Traditional cut blasting methods typically consist of two types: parallel cutting and oblique cutting (Liu, Chang, et al., 2019; Tang et al., 2022). Due to limitations in drilling accuracy and the tunnel cross-section size, oblique hole cutting is mainly suitable for shallow hole excavation (Li, Yang, et al., 2023; Yang et al., 2020). In contrast, cut blasting using a single parallel hole is often less efficient (Li, Yang, et al., 2023). To address these challenges, researchers have developed advanced techniques aimed at enhancing cut blasting efficiency (Cheng et al., 2021; Li, Yang, et al., 2023; Zhang et al., 2021, 2022). Besides the cutting pattern, cut-hole layout substantially affects blasting performance, especially under high ground stress conditions. After detonation, the released blasting energy manifests as denotation gases and shock waves. The blast-induced damage to the rock mass can be viewed as a combined effect of denotation gases and shock waves (Wang et al., 2021). Cut-hole layout critically influences the propagation of stress waves and the evolution of damage, making it imperative to explore the mechanisms of blast-induced damage under various cut-hole configurations and high ground stress conditions to design an effective cut-hole layout.
In deep mining operations, the rock mass is exposed to a complicated dynamic–static coupling loading environment, making it challenging to reveal the blast-induced internal damage mechanisms through field tests. Numerical simulations have been proven to be an effective tool for studying blasting damage mechanisms and theoretical analysis (Ainalis et al., 2017; Li et al., 2015; Li et al., 2022; Li, Liu, Sha, Yang, Song, 2023; Wang et al., 2021; Xie et al., 2017; Zhang, Liu, et al., 2023). For instance, Xie et al. (2016) used LS-DYNA for numerical simulations to investigate the damage evolution mechanism in rock masses during deep cut blasting, highlighting the impact of ground stress on rock mass damage. Liu, Li, et al. (2018) used LS-DYNA to explore blast-induced damage zones in rock masses, identifying the optimal hole spacing parameter. Xie et al. (2017) conducted numerical simulations using LS-DYNA to enhance cut blasting design, providing valuable references for rock excavation in deep underground mines. Chen et al. (2016) analyzed the effects of hole spacing on the propagation of blast-induced fractures through laboratory experiments, revealing that the direction of crack extension could be effectively controlled when empty holes were located within the fracture zone. Ding et al. (2021) emphasized that an appropriate decoupling coefficient can concentrate the energy carried by blast-induced cracks, thereby increasing crack propagation length and expanding the fracture zone range, ultimately improving rock fragmentation effectiveness.
Additionally, numerous scholars have focused on the study of empty holes' effects on blast-induced damage. Lü et al. (2022) demonstrated that empty holes serve as effective guides for crack extension. Li, Liu, et al. (2018) simulated the relationships between cut-hole parameters and rock damage, identifying optimal hole spacing and suggesting that large-diameter empty holes are more favorable for cut blasting. Zhang et al. (2021) underscored the importance of optimizing hole spacing to enhance rock breakage efficiency, noting that large-diameter empty holes play a crucial role in directing blast crack propagation and improving fragmentation. Zhang et al. (2020) conducted a comprehensive analysis of the impacts of empty hole configurations on rock fracture mechanism, developing formulas to calculate optimal hole spacing. In another study, Li, Zhu, et al. (2018) performed numerical simulations to investigate the effects of empty hole spacing on crack extension patterns, finding that smaller spacing between empty holes significantly inhibits crack propagation. Yang et al. (2021) investigated the relationship between blast hole arrangement and ground stress under different deep confining pressures, concluding that the orientation of the maximum principal stress should ideally align with the direction of the blast hole connecting line.
Based on the reviewed literature, few studies have simultaneously investigated the effects of charge hole decoupling coefficients, empty hole diameters, and hole spacing on blast-induced rock damage under high in situ stress conditions. This gap is particularly critical for cut blasting in complex high-ground stress environments. Therefore, this study aims to use numerical simulations to comprehensively assess the impact of cut-hole parameters on the rock damage mechanisms induced by blasting, determine the optimal parameter values, and validate their effectiveness through field experiments. First, the calibration of numerical model parameters is conducted. The influence of decoupling coefficients under both hydrostatic and non-hydrostatic stress conditions is then analyzed. Next, the effects of empty hole diameter and hole spacing under non-hydrostatic stress conditions are evaluated. Finally, field tests are conducted to confirm the effectiveness of the recommended cut-hole parameters.
2 ENGINEERING BACKGROUND
An underground mine located in southwestern China served as the case study for this study. The mine uses the D&B method for tunnel excavation and stope blasting, with a maximum mining depth exceeding 1500 m. The field uses the “1+6” cutting mode, which consists of one charge hole and six empty holes. The tunnel cross-section size is 4.20 m × 3.45 m (width × height), as shown in Figure 1. As mining depth increases, the mining environment and the ground stress become increasingly complex. Table 1 presents the field measurements of ground stress at different mining depths. The maximum principal stress in this mine is nearly horizontal and aligns with the strike of the ore body. Notably, as mining depth increases, the in situ ground stress gradually increases; at the 924 level, the maximum horizontal principal stress (
) reaches 48.83 MPa, approximately to 50 MPa. The horizontal ground stress perpendicular to the tunnel axis (the minimum horizontal principal stress,
) increases to 30 MPa. Therefore, ensuring efficient and safe production under high in situ ground stress conditions has become a critical issue for the mine.
Schematic diagram of on-site tunnel excavation.
Table 1. Results of on-site ground stress measurements.
| Location |
Depth (m) |
In situ ground stress |
| Maximum horizontal principal stress
(MPa) |
Vertical principal stress
(MPa) |
Minimum horizontal principal stress
(MPa) |
| 1584 level |
846 |
27.02 |
23.87 |
19.95 |
| 1046 level |
1104 |
40.15 |
32.92 |
26.12 |
| 1151 level |
1209 |
38.29 |
34.49 |
24.16 |
| 1274 level |
1270 |
36.17 |
31.79 |
23.68 |
| 1104 level |
1276 |
39.25 |
35.21 |
25.87 |
| 1214 level |
1276 |
38.78 |
34.32 |
25.56 |
| 1104 level |
1426 |
39.14 |
34.64 |
29.49 |
| 924 level |
1612 |
48.83 |
42.35 |
30.42 |
3 METHODS
3.1 Material model for numerical simulation
3.1.1 Rock material model
The Riedel Hiermaier Thoma (RHT) model is widely used in LS-DYNA to simulate the fracturing behavior of rock materials under initial stress conditions (Hashemi & Katsabanis, 2021; Huo et al., 2020; Katsabanis, 2020; Leng et al., 2021; Saadatmand & Katsabanis, 2020). This model comprehensively incorporates critical factors such as confining pressure, high strain rates, strain hardening, and damage softening to characterize the material responses under dynamic loading conditions. Additionally, the
compaction equation is used to describe the mechanical behavior of rocks under varying stress conditions.
In the RHT model, 38 parameters need to be defined. The basic physical and mechanical properties of rock material are obtained from laboratory experiments. For this study, the primary parameters are as follows: rock density (
2757 kg/m3), uniaxial compressive strength (
= 97.65 MPa),
-wave velocity (
= 4047 m/s), Young's modulus (
= 32.56 GPa), and the Poisson's ratio (
= 0.21). The shear modulus is calculated as
13.45 GPa, and the static uniaxial tensile strength is (
9.77 MPa). The remaining variables are obtained from theoretical calculations or reference values (Borrvall & Riedel, 2011; Brannon & Leelavanichkul, 2009; Liu, Li, et al., 2018; Neithalath et al., 2006; Yavuz et al., 2010), and are adopted in this study. All the parameters are detailed in Table 2.
Table 2. Rock material parameters in the RHT model.
3.1.2 Material model for explosive and air
In LS-DYNA, the *MAT_HIGH_EXPLOSIVE_BURN material model is used to characterize explosive materials utilizing the Jones–Wilkens–Lee (JWL) equation of state (EOS) to illustrate the relationship among explosion pressure, energy, and volume (Liu, Yang, et al.,
2018; Liu, Li, et al.,
2019; Wei et al.,
2009). The formula is expressed as
(1)
where
represents the pressure of explosive detonation wave;
,
,
,
, and
are material-specific constants;
denotes the relative volume; and
indicates the internal energy per unit explosive volume.
Pentaerythritol tetranitrate (PETN) is utilized in the simulation process; the parameters are from the validated results reported by Tawadrous (2011): the explosive density
150 kg/m3; the detonation velocity is 7450 m/s;
625 GPa,
23.3 GPa;
= 5.25;
= 1.6;
= 0.28; and
8.56 GPa.
Furthermore, the air medium in LS-DYNA is represented using the
material model, which incorporates a linear polynomial equation of state
to establish the relationship between pressure, density, and internal energy (L. S. T. C,
2015):
(2)
where
indicates the dynamic viscosity coefficient and
denotes the air material constant; normally,
0, and
0.4. Air density
= 1.255 kg/m
3 and
is 2.5 × 10
5 J/m
3 (Wang et al.,
2007).
3.2 Model parameter validation
To validate the model parameters, an extensive analysis was conducted between the simulation results and theoretical calculations. The comparative analysis focused on damage patterns, crack propagation, and shock wave attenuation. For this purpose, a two-dimensional plane model with an uncoupled charge was constructed, as shown in Figure 2. The rock and air sections have radii of 250 and 125 cm, respectively; the explosive and blast hole have radii of 6 and 10 cm, respectively. The rock section is modeled as the solid material using the Lagrange algorithm, whereas the air and explosive sections are treated as fluid materials using the Arbitrary Lagrange Eulerian (ALE) algorithm (Wang et al., 2021).
Two-dimensional plane model.
R
r,
R
b,
R
e, and
R
a denote the radius of the rock, the borehole, the explosive, and the air portion in the numerical model, respectively (cm).
3.2.1 Failure criteria
Under decoupled charge conditions, the initial pressure of the explosion shock wave (Dai,
2013):
(3)
where
P indicates the initial shock wave pressure;
is the uncoupled charging coefficient;
is the expansion adiabatic factor of the denotation products, set to 3;
is the axial charge coefficient,
1; and
n is the pressure amplification factor, generally set as
n = 10.
The stress intensity at any point within the rock:
(4)
where
indicates the rock radial stress,
,
,
represents the distance between the calculation point and the center of the explosive,
is the radius of the blast hole,
indicates the wave decay index,
,
is the lateral stress coefficient of the rock mass,
,
is the rock dynamic Poisson's ratio,
,
is the tangential stress in the rock mass,
, and
is the plane stress,
.
According to the Mises criteria, rock damage occurs if
satisfies the following condition:
(5)
where
is the uniaxial failure strength;
and
are the rock uniaxial dynamic compressive/tensile strength, forming the crushing zone and the fracture zone, respectively.
Following the numerical modeling, the simulation results for the two-dimensional plane model are presented in Figure 3b. When the pressure of the explosion shock wave exceeds the rock dynamic compressive strength, the rock near the borehole is instantly fractured, creating a compression–shear crushing zone (Zone I), as depicted in Figure 3b. During the explosion, besides the blast shock wave, numerous explosive gases penetrate deep into the rock through the fissure. At the tip of these fissures, the combined effects of the tensile stress wave component and the pressure from the explosive gas lead to propagation of the cracks, forming a tensile–shear damage zone, referred to as the fracture zone (Zone II). Subsequently, the stress wave continues to propagate toward the free surface, causing the radial cracks to further propagate along the fracture tips, ultimately leading to the development of an elastic vibration zone (Zone III).
Rock damage diagrams. (a) Theoretical rock damage schematic (Whittaker et al.,
1992) and (b) numerical simulation results of the rock damage.
However, it is important to note that in the continuum-based finite element modeling (FEM), no actual cracks are generated; thus, the flow of explosive gases through these cracks is not represented in the model. This limitation may affect the accuracy of capturing the full dynamics of the explosive effects on the rock. Nonetheless, the simulation results indicate that the damage distribution and crack extension characteristics (at a damage threshold of 0.4) are highly consistent with the theoretical results (Whittaker et al.,1992), as shown in Figure 3a.
3.2.2 Theoretical analysis of damage scope
To further validate the reliability and the reasonability of the model, the damage radii of the crushing and fractured zones obtained from numerical simulation were measured and compared to the results obtained from theoretical calculations (Dai,
2013):
(6)
(7)
(8)
(9)
(10)
(11)
(12)
where
and
denote the damage radii of the crushing and fracture zone, respectively;
and
are wave decay indices;
B is a constant;
is the radius stress; and
signifies the denotation velocity.
Based on previous research (Dai, 2013; Hanukayev, 1980), the area of the crushing zone is typically 2–3 times the blast hole radius, while the radius of the fracture zone area is approximately 10–15 times the blast hole radius. Figure 4 displays the numerical simulation results; the measured radii of the crushing and fracture zones are 48.5 and 128.2 cm, respectively. The comparison with theoretical calculations, summarized in Table 3, reveals that the numerical simulation results closely align with theoretical results. Furthermore, both the simulation outcomes and theoretical calculations are consistent with the findings from earlier studies (Dai, 2013; Hanukayev, 1980). This alignment further confirms the reliability of the simulation model.
Results of the crushing and fracture zone obtained from numerical simulation.
Table 3. Comparison of the radii of the crushing and fractured zones obtained from theoretical calculations and simulation results.
| Type |
Crushing zone |
Fracture zone |
|
|
|
| Theoretical calculations |
3.03 |
11.77 |
| Numerical simulation results |
4.85 |
12.82 |
In addition, the attenuation principle of the peak pressure at various locations from the borehole is discussed. Following the explosion, the rock undergoes substantial impact loading, and the shock wave pressure propagating in the rock under an uncoupled charge can be described as follows (Dai,
2013):
(13)
(14)
where
indicates the initial shock wave pressure;
represents the denotation pressure.
The values of peak pressure at different locations around the borehole can be calculated as follows (Dai,
2013):
(15)
where
represents the pressure of the shock wave;
is the charge hole radius.
The peak pressure at various points can be calculated using Equations (13-15). Figure 5 illustrates the comparison between the theoretical calculations and the simulation results. Seven observation points were selected, ranging from the vicinity of the borehole to the model boundary. It could be found that the decay trend of peak pressure obtained from numerical simulations matched the theoretical calculation results.
Peak pressure comparison between theoretical calculations and simulation measurements.
In conclusion, the analysis of rock damage, crack extension, and shock wave attenuation characteristics, along with comparison with theoretical calculations, demonstrates that the model is both reasonable and well suited for the research presented in this article.
3.3 Indicators for evaluating blast-induced rock damage based on simulations
Two evaluation indexes: relative damage area (RDA) and peak particle velocity (PPV) were proposed in this paper to quantitatively evaluate blast-induced rock damage under different conditions.
3.3.1 RDA
Numerous scholars have explored different methods to quantify the rock damage patterns under initial stress. Ai et al. (
2014) and Li, Liu, Sha, Yang, Ma, et al. (
2023) utilized fractal dimension and fractal damage to characterize crack's behaviors under varying static stresses, and they concluded that both fractal dimension and fractal damage decrease with increasing static pressure. Zhai et al. (
2018) quantitatively analyzed the number and the distribution of cracks using fractal dimensions. Guo et al. (
2015) proposed leveraging the fractal dimension of core surface traces to quantify cracks. In addition, Qiao et al. (
2023) developed an image processing method to quantify the rock damage areas, demonstrating superior performance in capturing rock damage units compared to ImageJ software, and this method is used in this study; the formula is as follows:
(16)
where
indicates the RDA rate,
is the damage area, equivalent to the sum of damaged pixels on the image, and
is the sum of the total pixels of the image.
3.3.2 PPV
It is widely recognized that the energy produced by blasting is partially utilized for rock fragmentation, while the remaining portion is transformed into various forms, including vibration waves, flying rocks, air shock waves, heat energy, and other energy types. Among these, vibration waves are often quantified by PPV, which serves as a key parameter for assessing the intensity of blasting-induced vibrations near the borehole (Lurka et al., 2021). In the simulation, the PPV value can be obtained using LS-PrePost post-processing software.
4 NUMERICAL SIMULATION RESULTS' ANALYSIS AND DISCUSSION
Based on the blasting scheme utilized at the mine site, this article presents a series of numerical simulations with various cut-hole layouts under different ground stress conditions. As indicated in Table 1, the field ground stresses are anisotropic. Consequently, the numerical models incorporate two types of ground stress conditions: hydrostatic and nonhydrostatic, as illustrated in Figure 6. For the hydrostatic stress analysis, four groups are considered: 0, 10, 20, and 30 MPa. In the non-hydrostatic stress models, the horizontal stress is maintained at 30 MPa, while the vertical stress varies from 10 to 20, 30, 40, and 70 MPa. The cut blasting parameters optimized in this study include the uncoupling coefficient of the charge hole (
), the empty hole diameter (
), and the spacing between the charge hole and the empty hole (
).
(a) Hydrostatic stress and (b) nonhydrostatic stress numerical models.
4.1 Effects of uncoupling coefficients on rock damage under hydrostatic stress
First, the effect of the uncoupling coefficient
on blast-induced rock damage under various hydrostatic stress conditions was analyzed. The coefficient
, defined as the ratio of the charge hole diameter to the explosive diameter, was varied from 1.00 to 1.15, 1.25, 1.50, and 1.75. Notably, these specific values were chosen based on practical field operations.
Figure 7 presents the simulation results of rock damage under different uncoupling coefficients and hydrostatic pressures. As shown, three distinct damage zones were identified across all conditions, and the overall damage scope decreased with increases of uncoupling coefficients and ground stresses. Figure 8 shows the RDA calculation results for all simulations. Consistent with the observations in Figure 7, as the decoupling coefficient increases, the RDA shows a decreasing trend when K exceeds 1.15. This indicates that the air-coupled medium dissipates the energy of the blasting shock wave, thereby reducing the explosion pressure on the borehole wall and weakening the blasting-induced damage. Notably, in the absence of in situ stress, the RDA does not decrease monotonically; instead, it first increases and then decreases as the uncoupling coefficient K increases, reaching a maximum value at K = 1.15. This phenomenon might be influenced by two factors: first, limitations in the numerical model, including simplifications and assumptions related to material behavior and boundary conditions, could lead to deviations. Second, the process of analyzing damage contours and counting damage pixels in damage diagrams may involve subjective judgment, leading to potential errors. Nevertheless, the overall trend remains reasonable and reliable. Additionally, as the in situ stress increases, the RDA decreases, with the reduction rate gradually slowing down. In conclusion, the uncoupling coefficient significantly impacts rock breakage and damage, while ground stress shows a restraining effect on overall damage.
Blast-induced rock damage with different uncoupling coefficients under hydrostatic stress conditions.
Relative damage area rate of different uncoupling coefficients
K under hydrostatic stress.
Moreover, significant differences in crack propagation behavior are observed under different ground stress conditions and with different uncoupling coefficients. In the absence of ground stress, both the number and the length of cracks in Zone III remain relatively unaffected by changes in the uncoupling coefficients. However, under the influence of ground stress, as illustrated in Figure 7, the length of the primary cracks decreases with increasing ground stress. Additionally, when the uncoupling coefficient
is less than 1.50, the number of primary cracks shows minimal variation across different hydrostatic pressure conditions. Conversely, when
exceeds 1.50, the number of primary cracks begins to decrease. For instance, at
= 1.75, the number of primary cracks reduces to 6 under hydrostatic pressures of 10, 20, and 30 MPa. These results are consistent with the findings from a previous study (Xie et al., 2017).
Moreover, the PPV values around the charge hole were calculated. Due to the symmetry of the 2D plane strain model, two points, A and B, along the charge hole wall were selected as the measurement points, as depicted in Figure 9a. These points were used to obtain an average PPV for evaluating the blast vibrations at the hole wall. Figure 9b illustrates the PPV results under different uncoupling coefficients and hydrostatic stress conditions. When the uncoupling coefficient K is less than 1.50, the PPV values under no ground stress are significantly higher than those under hydrostatic stress, indicating that ground stress plays a critical role in suppressing the blast-induced vibrations. This observation aligns with previous findings reported by Zhang, Liu, et al. (2023). Specifically, in the case of coupled charging (K = 1.00), PPV increases with increasing in situ stress. This occurs because the blast-induced energy intended for rock damage is impeded by the in situ stress, causing more explosion energy to be diverted into rock vibrations, aligning with the conclusion of a previous study (Li et al., 2020). However, for uncoupled charge (K > 1.00), the PPV no longer shows an obvious upward trend as in situ stress increases, suggesting that the influence of in situ stress on vibration is less pronounced under uncoupled charge conditions. On the other hand, PPV shows a clear decreasing trend with increasing uncoupling coefficients under both no-stress and stressed conditions. Notably, when K exceeds 1.25, there is a significant decrease in PPV, indicating that the air-coupled media dissipate a substantial portion of the blast energy, reducing shock wave transmission and consequently lowering blast-induced vibrations. This behavior highlights the effectiveness of uncoupled charging in minimizing vibration effects, particularly at higher uncoupling coefficients.
Peak particle velocity (PPV) calculation results with different uncoupling coefficients
K under hydrostatic stress. (a) Schematic diagram of the observation points and (b) PPV results.
4.2 Effects of uncoupling coefficients on rock damage under nonhydrostatic stress
The rock damage behavior under non-hydrostatic stress was systematically analyzed. In this study, the horizontal stress was maintained at 30 MPa, while the vertical stress was varied from 10 to 20, 30, 40, and 70 MPa, respectively. Figure 10 shows the results of rock damage and crack propagation under these nonhydrostatic stress conditions. It was observed that when ground stress and uncoupling coefficients increased, the extent of rock damage decreased. This contrasts with the behavior under hydrostatic stress conditions, where rock damage is uniformly distributed around the blast hole, forming a circular damage zone with evenly distributed cracks. In contrast, under nonhydrostatic stress conditions, rock damage and crack propagation show anisotropy, with cracks predominantly extending in the direction of maximum horizontal principal stress. This highlights the significant influence of stress anisotropy on rock damage behavior.
Rock damage results of different uncoupling coefficients under nonhydrostatic stress.
As shown in Figure 10, the horizontal crack length is significantly greater than the vertical crack length when the horizontal stress is 30 MPa and the vertical stress is 10 MPa. As the vertical stress increases, the development of rock damage and crack propagation shifts toward the vertical direction. The greater the disparity between horizontal and vertical stresses, the more pronounced the anisotropy in rock damage and crack propagation. This indicates that ground stress has a strong directional influence on crack extension. Higher ground stress amplifies this guiding effect, leading to cracks predominantly extending along the direction of the maximum principal stress.
Similarly, the RDA and PPV results were also calculated. As illustrated in Figure 11a, the maximum RDA is observed at a nonhydrostatic pressure of 30–10 MPa, followed by a rapid decrease as the vertical stress increases to 20 MPa. When the vertical stress ranges from 20 to 40 MPa, the RDA declines more gradually. However, a sharp reduction is noted again when the vertical stress increases to 70 MPa. Overall, under non-hydrostatic stress conditions, the RDA tends to decrease with increasing vertical stress, with the rate of reduction initially increasing, then slowing down, and accelerating again. This behavior is primarily attributed to the significant difference between horizontal and vertical stresses at 30–10 MPa and 30–70 MPa, respectively, highlighting the pronounced anisotropic characteristics of rock damage and crack propagation. Finally, as shown in Figure 11, both the RDA and PPV decrease with increasing uncoupling coefficients under non-hydrostatic stress conditions, indicating that a coupled charge is more effective for rock breakage in cut blasting.
Results of the rock mass relative damage area and peak particle velocity (PPV) under nonhydrostatic stress. (a) Relative damage area calculation results and (b) PPV results.
4.3 Effects of empty hole diameter and hole spacing under nonhydrostatic stress
Subsequently, simulations were conducted with varying empty hole diameters and hole spacings. The empty hole diameters
were set to 4, 6, 8, and 10 cm, while the hole spacings
were set to 14, 16, and 18 cm, respectively. The simulation results are presented in Figure 12, which were cropped from the original numerical model size (Figure 6) to provide a clearer and more focused view of the damage patterns.
Rock damage results from different empty hole diameters and hole spacing under non-hydrostatic stress. (a)
14 cm, (b)
16 cm, and (c)
18 cm.
4.3.1 Empty hole diameter
In Figure 12, significant damage differences are observed in simulations across all configurations of empty hole diameters (
) and hole spacings (
). For example, when the empty hole diameter is small (e.g., 4 cm), a non-penetration zone forms along the connection line between the blast hole and the empty hole across all hole spacing configurations. As the empty hole diameter increases, this non-penetration zone gradually disappears, resulting in a large damage zone. To further illustrate the effects of the empty hole, the radii of the crushing zone and the fracture zone for all simulations with various empty hole diameters and hole spacings were calculated and compared. Figure 13a–c shows the statistical results of the damage zones size at different empty hole diameters and under different in situ stress conditions for hole spacings of 14, 16, and 18 cm, respectively. The solid lines represent the fracture zone results, while the dashed lines indicate the crushing zone results. It can be observed that the crushing zone increases with increasing empty hole diameter for all three hole spacing configurations. As shown in Figure 12, when the hole spacing is 14 cm, the rock mass within the cut cavity is nearly fractured at an empty hole diameter of 6 cm and becomes fully damaged at diameters of 8 and 10 cm. For a hole spacing of 16 cm, the damage is nearly penetrated at an 8 cm diameter and fully damaged at 10 cm. When the hole spacing is 18 cm, the rock mass within the cavity is fully damaged at an empty hole diameter of 10 cm. This indicates that increasing empty holes diameter facilitates effective rock fragmentation within the cut cavity. In contrast, the size of the fracture zone shows a decreasing trend with an increase in the empty hole diameter. This suggests that the air medium in larger diameter empty holes impedes the propagation of explosive energy outside the cut cavity. When the diameter of the empty hole exceeds a certain range, it weakens the formation and extension of secondary cracks near the cavity, as illustrated in Figure 12.
Radii of crushing and fracture zones. (a), (b), and (c) damage zones' sizes at different empty hole diameters and under different in situ stress conditions for hole spacings of 14, 16, and 18 cm, respectively.
After the explosive detonates within the rock medium, the explosive energy is released in the form of stress waves that propagate through the surrounding rock mass. These shock waves generate a dynamic stress field in the rock, leading to significant stress redistribution around the empty hole. This often results in stress concentration phenomena, which are critical for understanding the rock's response to blasting. The stress distribution in the vicinity of the empty hole has been thoroughly described in detail by Lin (
2006):
(17)
(18)
(19)
where
and
denote the radial stress and the tangential stress, respectively;
indicates the shear stress; and
, where
is the empty hole radius.
According to Equations (17-19), when
1,
= 0, and
= 0,
reaches its maximum value at
. This indicates that the tensile stress is the strongest at the intersection point of the line connecting the blast hole and the empty hole. Figure 14 displays the effective plastic strain at five measurement points in the vicinity of the empty hole. It is evident that under different ground stress conditions, point A shows the highest level of damage and the largest effective plastic strain.
(a) Measurement points and (b) results of the effective plastic strain at different measurement points with
= 14 cm and
= 8 cm.
4.3.2 Hole spacing
Following the analysis of the empty hole diameter, this section investigates the effect of hole spacing on blast-induced rock damage. Five points (A, B, C, D, and E) were selected near the empty hole to capture variations in stress and damage patterns, as illustrated in Figure 14a. The effective plastic strain results for these observation points under different hole spacing and empty hole diameter configurations are presented in Figures 15 and 16. In Figure 15, at the empty hole diameter
= 8 cm, it can be seen that when the hole spacing is small (14 cm), point A, located on the wall of the empty hole along the connection line between the blast hole and the empty hole, shows the highest effective plastic strain. As the hole spacing increases to 16 and 18 cm, the maximum effective plastic strain tends to shift toward the sides, reaching its maximum at points B and C, as shown in Figure 15b,c. However, the overall effective plastic strain decreases with increasing hole spacing. When the empty hole diameter increases to 10 cm, the maximum effective plastic strain is primarily located on the wall of the empty hole along the connection line between the blast hole and the empty hole for all hole spacing configurations. Similarly, the effective plastic strain diminishes as the hole spacing increases. Moreover, the effective plastic strain for each hole spacing is higher than that for the empty hole with diameter of
= 8 cm. This indicates that larger empty hole diameters yield higher effective plastic strain, while increasing hole spacing results in reduced overall strain levels.
Effective plastic strain results for five measurement points with
= 8 cm, (a)
= 14 cm, (b)
= 16 cm, and (c)
= 18 cm, respectively.
Effective plastic strain results for five measurement points with
= 10 cm. (a)
= 14 cm, (b)
= 16 cm, and (c)
= 18 cm, respectively.
Figures 17 and 18 present the peak pressure results at five measurement points for empty hole diameters of 8 and 10 cm, respectively. In Figure 17, the peak pressure reached a maximum at point A when
= 8 cm and
= 14 cm, gradually decreasing toward both sides. As the hole spacing increased to 16 and 18 cm, the pressure initially increases and then decreases from point A to the sides, with maximum values observed at points B and C, located at approximately 45° on both sides. Conversely, when the empty hole diameter
increases to 10 cm, as shown in Figure 18, the peak pressure first increases and then decreases from point A to both sides for all hole spacing configurations (14, 16, and 18 cm).
Peak pressure results for five measurement points with
= 8 cm. (a)
= 14 cm, (b)
= 16 cm, and (c)
= 18 cm, respectively.
Peak pressure results for five measurement points with
= 10 cm. (a)
= 14 cm, (b)
= 16 cm, and (c)
= 18 cm, respectively.
Additionally, the distribution of maximum crack length outside the fracture zone, as shown in Figure 12, for all hole configurations is illustrated in Figure 19. Figure 19a–c shows the configurations of hole spacing of 14, 16, and 18 cm, respectively. The bars with black lines represent the crack length results in the X direction, while those without black lines represent the crack length in the Y direction. As the vertical stress increases from 10 to 20, 30, 40, and 70 MPa, the maximum crack length in the X direction gradually decreases, while the maximum crack length in the Y direction increases for all configurations (e.g., for a hole spacing and empty hole diameter of 14 and 4 cm, respectively). This indicates that the propagation of cracks aligns with the direction of the maximum in situ stress. Subsequently, when the empty hole diameter
≤ 8 cm and the hole spacing is 14, 16, or 18 cm, the maximum crack lengths in both the X and Y directions are comparable. However, when the empty hole diameter is 10 cm, the maximum crack lengths in both directions at a hole spacing of 18 cm are greater than those at spacings of 14 and 16 cm.
Distribution of the maximum crack length in
X and
Y directions. (a), (b), and (c) Maximum crack lengths in
X and
Y directions at different empty hole diameters and under different in situ stress conditions for hole spacings of 14, 16, and 18 cm, respectively.
In conclusion, at a hole spacing of 14 cm and an empty hole diameter of 8 cm, the rock within the cavity shows complete damage, and the extents of the crushed and fracture zones are expanded, resulting in maximum crack lengths in both the X and Y directions outside the cavity. For a hole spacing of 16 cm and a diameter of 8 cm, the rock also sustains complete damage, with further expansion of the crushed and fracture zones; however, the maximum crack lengths outside the cavity in the X and Y directions are less than those observed with a diameter of 6 cm. When the hole spacing is 18 cm, complete damage within the cavity occurs only at an empty hole diameter of 10 cm. It is important to note that the cost associated with large-diameter drilling is also a crucial consideration on-site. Thus, the optimal cut-hole layout is
8 or 10 cm,
14 cm. This finding aligns with the previous study carried out by Xie et al. (2017), which suggested that under high-ground stress conditions, cut blasting is most effective when
is 1.5 times the
. In this study, with
is set at either 8 or 10 cm, the recommended
range is 12 to 15 cm. Consequently, the chosen hole spacing of 14 cm in this study is deemed reasonable.
5 FIELD EXPERIMENTS
Additionally, to evaluate the superiority of the optimized parameters, field comparison tests were conducted at two different mining sites to evaluate the overall blasting performance against the original cut blasting scheme. The original method utilized configurations with a central charge hole diameter of 4 cm, an empty hole diameter of 4 cm, and a hole spacing of 12 cm. Based on the numerical simulation analysis, the recommended cut blasting parameters are summarized in Table 4. Given the on-site drilling equipment, the diameter of the drill rod is fixed at 4 cm, which is close to a coupling charge configuration. In both field tests, apart from the differences in the cut-hole layout, as shown in Figure 20, the design of auxiliary holes, relief holes, and perimeter holes as well as the charging, inter timing, and detonation sequences, remained consistent. Both tests utilized #2 rock emulsion explosives, detonated from the bottom of the holes. Figure 21 presents the complete process of drilling, charging, and blasting.
Table 4. Optimal cut blasting parameters. (cm)
|
Charge hole diameter |
Empty hole diameter |
Hole spacing |
| Values |
4 |
8 or 10 |
14 |
Field blasting test design scheme.
Field blasting experiment. (a) Pre-process, marking the hole location, (b) hole drilling, (c) charging, (d) detonation network, and (e) blasting pile.
The field blasting results for both the original method and the optimized scheme are summarized in Table 5. Following the application of the newly recommended cut-hole parameters, significant improvements in blasting performance were achieved. As detailed in Table 5, the powder factor (PF) was reduced by 27.4%, the advance rate increased by 9.3%, and the blast hole utilization improved by 12.0%. The implementation of the new cut-hole layouts enhanced the tunneling efficiency by approximately 30%. Overall, the simulation findings presented in this study provide valuable guidance and practical significance for field operations.
Table 5. Comparison of blasting results for both the original method and the optimized scheme.
| Blasting effect |
Evaluation indexes |
|
(kg/m3) |
Advancement (m) |
Blast hole utilization (%) |
| Original design |
3.32 |
2.58 |
83.3 |
| Optimized design |
2.41 |
2.82 |
93.3 |
| Differences (%) |
↓ 27.4 |
↑ 9.3 |
↑ 12.0 |
6 CONCLUSIONS
The D&B method is widely utilized for underground resource excavation. However, undesirable blasting designs and complex ground stress environments often affect the blasting results. To address these challenges, this paper performed detailed numerical simulations to investigate the rock damage mechanisms after blasting under various ground stress conditions and optimize the cut-hole layout. The main conclusions are as follows:
1.
The developed numerical model accurately simulates rock damage, crack propagation, and shock wave attenuation, aligning well with theoretical results. The validation confirms the model's reliability and suitability for this study.
2.
Analysis reveals that uncoupling coefficients significantly influence rock damage and crack propagation under varying stress conditions. Higher uncoupling coefficients reduce damage and vibrations, particularly under hydrostatic stress, while anisotropic behavior is observed under non-hydrostatic stress. A coupled charge is more effective for rock breakage in cut blasting.
3.
A large-sized empty hole shows a strong free surface effect on the facing-blasting side, significantly enhancing both the extent of rock damage and rock fragmentation. Additionally, it also facilitates crack propagation on the back-blasting side of the empty hole, although higher drilling costs for larger size holes must be considered.
4.
Simulation results indicate that hole spacing plays a critical role in cut blasting. Increasing hole spacing within a certain range improves excavation efficiency. However, exceeding this range leads to a shift in the effective plastic strain distribution toward the sides of the empty hole while reducing overall strain levels. Cut blasting is most effective when the hole spacing is 1.5 times the empty hole diameter.
Field blasting tests confirmed that the suggested cut-hole layout significantly enhanced the cycle advance rate and improved blast hole utilization by 9.3% and 12.0%, respectively, while reducing the powder factor by 27.4%. The simulation findings offer valuable insights for cut blasting in deep underground engineering.
AUTHOR CONTRIBUTIONS
Junjie Zhao: Conceptualization; formal analysis; writing—original draft. Diyuan Li: Supervision; writing—review and editing; funding acquisition. P. G. Ranjith: Writing—review and editing. Xiaoli Su and Xinxin Lü: Validation. Yanliang Li: Writing—review and editing.
ACKNOWLEDGMENTS
The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No.: 52374153). In addition, we are grateful for the technical support from the High Performance Computing Center of Central South University.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
Biography
Diyuan Li is a professor and doctoral supervisor at Central South University (CSU). He received his PhD degree in geotechnical engineering in 2010 from Central South University, with 2 years of overseas joint study in the Norwegian University of Science and Technology from 2007 to 2009. He was selected for the National Youth Talent Program, and is currently the vice dean of the School of Resources and Safety Engineering at Central South University. He is a director of the Chinese Society of Rock Mechanics and Engineering and Executive Committee Member of the Rock Dynamics and Rock Mechanics Testing Committees. He is mainly engaged in teaching and research work in rock mechanics and rock engineering, and has achieved some innovative results in testing techniques and characterization of rock crack propagation characteristics, rock fracture mechanics behavior and testing, and slabbing failure mechanism and criteria of hard rocks. He has presided over four National Natural Science Foundation projects and two Hunan Provincial Natural Science Foundation projects (including the Outstanding Youth Project). He has already published over 200 academic papers, including 127 indexed by SCI with an H-index of 36. Over the past 3 years, he has been selected as one of the “Highly Cited Scholars in China” by Elsevier. He has been granted 18 national invention patents and has received eight provincial-level and industry association science and technology awards.
