The Baizhushan Tunnel is a separate extra-long tunnel. The left length of the tunnel is 4,358 m, and the maximum buried depth is 318 m. The right length of the tunnel is 4,404 m, and the maximum buried depth is 323 m. The distance between the left and right lines of the tunnel is 16–41 m. The tunnel is a Renzipo tunnel. The longitudinal slopes of the left and right tunnels are 2.0% and −1.35%, respectively. The ZK20-770∼ZK21-215 section was selected as the research section. The roof depth of this section is 54.6 ∼ 195.48 m. The surrounding rock is medium-weathered thin-to-medium-thick-layered tuffaceous slate, and the joint fissure is developed. The rock mass R c = 25   M P a , (BQ) = 265, and the surrounding rock grade is IV, as shown in Figure 1.

There are two main problems in the construction process of the Baizhushan Tunnel. First, the traditional tunnel blasting method caused a large number of holes. The layout of traditional blast holes is estimated according to the tunnel section area and rock hardness coefficient: N = 3.3 f S 2 . 3 (1)

In this article, the cross-section area of the upper bench of the tunnel in the test section is S = 120   m 2 , and the rock firmness coefficient is f = F c / 10 = 4.2 ; thus, the whole cross-section needs 131 holes, a heavy drilling workload, and a long drilling time, which are contrary to the demands of a rapid tunneling process for a large cross-section tunnel.

Second, according to the traditional blasting scheme, the over-excavation of the Baizhushan Tunnel is significant, and five field blasting tests have been carried out. The over-excavation and under-excavation data are shown in Table 1, with the maximum over-excavation being 60.0 cm and the average over-excavation thickness being 36.70 cm. The code stipulates that the maximum allowable value of over-excavation (National standard of the People 's Republic of China GB50299, 1999) is 15 cm, and the traditional design scheme is significantly over-excavated, which seriously increases the construction cost.

In order to obtain the static and dynamic parameters of surrounding rock in this section, drilling core sampling obtained the standard slate samples. As shown in Figure 2, the uniaxial compression test, triaxial compression test, and Brazilian splitting test were carried out on a TAJW-2000 rock triaxial testing machine controlled using a microcomputer. Six cylindrical rock samples with a diameter of 50 mm and height of 100 mm were prepared for the uniaxial compression test and triaxial compression test; three cylindrical rock samples with a diameter of 50 mm and height of 50 mm were prepared for the Brazilian splitting test; and three cylindrical rock samples with a diameter of 50 mm and height of 25 mm were prepared for the SHPB test, as shown in Figure 3. The sample size was measured using a Vernier caliper and weighed using the electronic balance. The average density of the sample was 2,721 kg/m³.

The purpose of the uniaxial compression test was to obtain the uniaxial compressive strength, elastic modulus, and Poisson’s ratio of the rock samples. When carrying out the uniaxial compression test, the preloading of 0.2 KN was applied first; after the instrument was stabilized, it was converted to displacement loading. The loading rate was 0.12 mm/min, and the uniaxial compression process is shown in Figure 3A. According to σ c = P / A , the uniaxial compressive strengths of the three rock samples were 53.77, 50.20, and 36.78 MPa, respectively, and the average uniaxial compressive strength was 46.91 MPa. By calculating the ratio of lateral and axial displacement of the sample, the average Poisson’s ratio of the rock samples was found to be 0.24. The stress–strain curve of the uniaxial compression test was drawn, as shown in Figure 4, and the average elastic modulus of 39.69 GPa was calculated.

The main purpose of the triaxial compression test was to obtain the strength parameters B and N of the HJC constitutive model. Three groups of tests were carried out, and the confining pressures of 5, 10, and 15 MPa were applied to the samples, respectively. The test process is shown in Figure 3C. According to σ 1 = P / A , the triaxial compressive strengths under different lateral stresses were 41.06, 49.56, and 58.30 MPa, respectively. The cohesion c = 19 MPa was calculated by axial stress and lateral stress.

The Brazilian splitting test was carried out to obtain the tensile strength of rock samples. The linear load was applied in the diameter direction of the cylindrical specimen, and the loading rate was 0.15 mm/min until the rock sample was destroyed. The Brazilian splitting test process is shown in Figure 3B. The tensile strength of the rock sample was determined as σ t = 2 P / π D L . The tensile strengths of the three rock samples were calculated to be 12.23, 12.30, and 12.58 MPa, respectively, and the average tensile strength was 12.37 MPa.

The purpose of the SHPB test was to calculate the strain rate influence coefficient C of the HJC constitutive model. The SHPB test was carried out through the separate Hopkinson compression bar test system ALT100 developed by Archimedes Industrial Technology Co., Ltd. The experimental process is shown in Figure 3D. Based on the impact experimental data of slate processed by the two-wave method and three-wave method, it was concluded that, when the impact pressures were 0.1, 0.2, and 0.3 MPa, the average peak stresses of rock failure were 89.5, 95.2, and 101.8 MPa, respectively, and the corresponding average strain rates were 103.50, 180.21, and 201.42 s. It was found that the greater the impact load, the greater the peak stress of the rock. Since the strain sensitivity under loading had little effect on the rock dynamic tensile strength, it was considered that the rock uniaxial tensile strength and dynamic tensile strength were the same. The mechanical parameters of slate are shown in Table 2.

The parameters of field use of 2# emulsion explosive were as follows: density ρ 0 = 1.24   g / c m 3 , detonation velocity D = 4200   m / s , charge diameter d c = 32   m m , hole diameter d b = 42   m m , charge length l c = 2.4   m , and hole length l b = 3.5   m . The initial impact pressure P = 1371   M P a on the rock wall of the hole was calculated according to Eq. 1. According to Eq. 2, the safe distance d from No. 13 and No. 14 cut holes to the tunnel design contour was 2.81 m. According to the rock breaking theory of wedge-shaped cutting holes, the optimal hole arrangement angle of a wedge-shaped cutting hole was 60°.

There were 131 blasting holes in the upper steps of the original blasting scheme, including 18 cutting holes, 59 auxiliary holes, 35 peripheral holes, and 19 bottom holes. The scheme was subjected to three-stage compound wedge cutting. The first-stage cutting was inclined to the tunnel center angle of 69°, and the blast hole length was 1.5 m. The second-stage cutting was 72°, and the blast hole length was 2.3 m. The third-stage cutting was 73°, and the blast hole length was 3.8 m. The other blast hole lengths were 3.5 m. The blasting parameters are shown in Table 5. There were 105 blasting holes in the upper steps of the reduced-hole layout scheme, including 12 cutting holes of 4.2 m blasting hole length, 41 auxiliary holes, 39 periphery holes, and 11 bottom holes. The blast hole lengths were 3.5 m. Two blast holes with low charge were arranged in the center of the heading face to decompose the large chunks of rock (these are collectively referred to as the unloading hole), and the blasting hole length was 3 m. The blasting parameters are shown in Table 6.

ANSYS/LS-DYNA software can better simulate complex structure calculations, especially for solving nonlinear problems, such as high-speed collision and explosion shock. LS-DYNA software was used to establish the blasting model of the reduced-hole layout with the size of 20 m × 20 m × 3.5 m (X × Y × Z) and the original blasting model. The schematic diagram of the two models is shown in Figure 8. Figure 8A is a schematic diagram of the original blasting scheme model. Figure 8B is a schematic diagram of the reduced-hole layout blasting scheme model. The charge structure adopted was an uncoupled charge, the cartridge diameter was 32 mm, and the blast hole diameter was 42 mm. In a study, for conducting a more realistic simulation of on-site blasting and rock selection using HJC material (Banadaki, 2010; Xie et al., 2017; Dong, 2019; Li et al., 2022), the authors defined the keyword initial-detonation to delay initiation and added the keyword mat_add_erosion as the erosion failure criterion to control the failure of the unit. The minimum tensile stress was defined as the failure criterion of the surrounding rock. The finite element mesh was the SOLID164 element, which was divided into about 800,000 grids. The model adopted a cm∼g∼μs unit system. In order to avoid the influence of the reflection wave caused by the artificial boundary on the calculation results, the heading face was set at the free boundary, and the other five surfaces were set at the non-reflection boundary. The hole-bottom initiation blasting method was adopted, and the total simulation initiation time was 4,000 µs. The calculation used the fluid–solid coupling algorithm.

According to Hu (2019), when wedge-cutting blasting is used, the position of the cutting hole should not exceed half of the distance from the central axis of the tunnel to the side wall. Otherwise, drilling is difficult. With cutting hole spacing a ≤ B/2, where B is the width of the tunnel section, so the maximum distance between cutting holes is 6 m. To meet the cutting hole angle of 60°, the minimum distance between two rows of cutting holes is set at 4.2 m. To verify whether the safety distance d = 2.81 m from No. 13 and No. 14 cutting holes to the tunnel contour line was the optimal distance, in other words, to determine whether the cutting-hole spacing of 5 m was optimal, two numerical models, both with a cutting angle of 60° and with cutting-hole spacings of 4.2 (safe distance d = 3.10 m) and 6 m (safe distance d = 2.37 m), respectively, were established. As shown in Figure 15A, at the safe distance of 3.10 m, the damage value of the rock mass in the center of the heading face was close to 1; at the distance of Z = 1.8 m (Z = 0 in the center of the heading face), the rock mass was fully broken, but the damage value of the rock mass between the cutting hole and the auxiliary hole was small; at 3.3 m, the damage value of the rock mass between the cutting hole and the auxiliary hole was about 0.3, which caused the large fragmentation rate of the rock mass to be too high. The cutting hole could not provide a better freeing surface for the auxiliary hole, the clamping effect of the rock was significant, and the damage range of the peripheral hole was small after initiation, which led to under-excavation.

When the safe distance was 2.37 m as shown in Figure 15B, the cutting hole was close to the auxiliary hole, and the effective stress superposition effect was more obvious when the cutting hole was detonated. The damage around the peripheral hole was obviously larger than that when the safe distance was 3.10 m, especially in Z = 1.8 m, the damage to the rock mass around the tunnel profile was very large, resulting in serious over-excavation of the tunnel.

The angle for wedge-cut blasting is between 60° and 80°. The optimal hole-layout angle β of the proposed hole-reduction layout scheme was 60°, and the safe distance from the No. 13 and 14 cutting holes to the tunnel profile was 2.81 m. To verify that 60° was the optimal angle, two numerical models were established, in which the safety distance was 2.81 m and the cutting angle was 70 °and 80°, respectively, and the damage of the two models was analyzed, as shown in Figure 16. When the cutting hole angle was 70° at Z = 0.6 m as shown in Figure 16A, the central damage of the heading face was small, the damage value was about 0.2, and this part of the rock mass showed fine cracks. At Z = 1.6 m, the damage value in the center of the palm face was about 0.5, and there were rough cracks in this part of the rock mass. At Z = 2.6 m, the damage value in the center of the palm face was close to 1, and the rock mass in this part was completely broken, indicating that the cracks at the bottom of the cutting hole were penetrated and the rock was prone to collapse. The cutting hole can provide a freeing surface for the auxiliary hole. However, before Z = 2.6 m from the heading face, this part of the rock mass only had cracks, and it collapsed with the collapse of the rock mass at the bottom of the cutting hole, which can lead to oversized thrown rock blocks.

When the angle of the cutting hole was 80° as shown in Figure 16B, the damage value was about 0.15 at Z = 0.6 m, and the damage at the center of the heading face was less. At Z = 1.6 m, the damage value at the center of the heading face was about 0.4, and cracks appeared in this part of the rock mass. At Z = 2.6 m, the damage value of the center of the palm face was about 0.6. At Z = 3.0 m, the damage value was close to 0.7. The rock mass at the bottom of the cutting hole could not be collapsed, and the cutting angle was too large to provide a freeing face for the auxiliary hole.

The original blasting scheme adopted three-stage compound cutting blasting. The cutting angles β were 69°, 72°, and 73°, respectively. The total number of holes was 131. The hole network layout is shown in Figure 17A. The blasting scheme of the reduced-hole layout extrapolated the wedge-shaped cutting hole to the maximum extent. The horizontal spacing of the cutting hole was 5 m, and the longitudinal distance was 0.6 m. The distance from the No. 13 and No. 14 cutting hole to the tunnel contour was 2.81 m. The cutting angle β was 60°, and the number of holes in the upper bench section was 105. The hole network layout is shown in Figure 17B.

Based on the aforementioned numerical simulation results, the article carried out the millisecond-delay blasting excavation method in the test section of the Baizhushan Tunnel. When the original blasting scheme was carried out, the average utilization rate of the blast hole was 78.3%, the unit consumption of explosives was 0.79 kg/m³, the average over-excavation thickness was 36.70 cm, the maximum over-excavation thickness was 60 cm, and there was no under-excavation as shown in Figure 18A. The authors applied the blasting scheme of the reduced-hole layout to the site for a total of five tests and counted the utilization rate of the blast hole. As shown in Table 7, the average utilization rate of wedge-cut holes was 81.9%, the average utilization rate of other blast holes was 91.2%, and the average explosive consumption was 0.72 kg/m³. The total station instrument was used to measure the over-/under-excavation in each part of the upper step as shown in Figure 18D, and the survey results are shown in Figure 18B. It was found that all of them were over-excavated, and there was no under-excavation. The reduced-hole blasting design scheme for the large-span section tunnel as proposed in this article can control the average over-excavation thickness within 20 cm, and the smooth surface-blasting effect is superior as shown in Figure 18C.