The cross-hole acoustic method is the most commonly used method for acoustic testing of the surrounding rock. Acoustic waves are emitted in one borehole of the surrounding rock, and acoustic signals are received in another adjacent borehole. Information on the first arrival time and first wave amplitude and frequency of the transmitted acoustic waves are extracted, and the wave velocity of the surrounding rock between the two boreholes is determined by analytical calculations. In this study, the cross-hole acoustic method was used for acoustic testing of the retained rock mass after tunnel blasting excavation. Hole #1 was drilled at a depth of 500 cm on a flat surface of the tunnel sidewall. Holes 2# and 3# were kept parallel to 1#, and the distance between the center of the holes was 50 cm. The three holes formed an isosceles right triangle, and the residue in the holes was flushed away after the holes were formed to avoid any influence on the test results. During the test, the transmitting and receiving transducers were moved 20 cm toward the hole opening for each side of the sound wave obtained from the bottom of the hole at the beginning of the test. The field layout of the cross-hole sound wave method is shown in Fig. (4).

In order to obtain the damage characteristics of the surrounding rock of the bench method, blasting excavation and acoustic tests were conducted on different parts of the surrounding rock after tunnel blasting, and the test points are shown in Fig. (5). The test holes are distributed in four parts: A, B, C and D, corresponding to the shoulder part of the tunnel arch, the waist part of the tunnel arch (also the foot part of the upper bench), the foot part of the tunnel arch, and the bottom of the elevated arch of the tunnel.

Acoustic testing was performed on the surrounding rock after blasting in the Longnan tunnel. A typical acoustic wave train is shown in Fig. (2). For a part of the test acoustic wave train map, the borehole (depth of 0 m) of the surrounding rock acoustic wave velocity due to the test process of disturbance and difficult-to-fill water coupling and other reasons cannot be measured. In the acoustic waveform, 0 μs is the moment when the transmitting transducer emits the electrical signal, and the starting moment is the moment when the receiving transducer receives the electrical signal, and the difference between the two moments is the duration of the acoustic wave propagation in the surrounding rock medium. As shown in Fig. (6), the waveform onset moments at each test depth were found to be connected, and it has been observed that the sound time within 1 m near the excavation surface was significantly longer than that at the bottom of the test hole.

Fig. (4). Acoustic test scheme diagram.

Fig. (5). Distribution diagram of the field acoustic test holes.

Fig. (6). List of the curve.

Fig. (7). Field test of sound wave velocity distribution.

After automatic computer reading, the distribution of acoustic wave velocity of each part was calculated and plotted, as shown in Fig. (7). It has been observed that the acoustic wave velocity of the surrounding rock far from the excavation face was larger and relatively stable, and the acoustic wave velocity of the surrounding rock decreased to different degrees when it was closer to the excavation face, in which the maximum value of acoustic wave velocity of surrounding rock in parts A and D was reported to be 4.011 km/s, and the maximum value of acoustic wave velocity of surrounding rock in parts B and C was 4.294 km/s, with a difference of 6.59%, indicating that the surrounding rock was heterogeneous.

According to the reference information given in the “SL 47-2020 Technical Code for Rock Foundation Excavation of Hydraulic Structures”, whether blasting damage occurs in the rock body can be judged according to the rate of change of wave velocity η before and after blasting in the same part, and the rate of change η is calculated as:

(1)

Formula: is the wave velocity before blasting, and V_P is the wave velocity after blasting. When η is ≤ 10%, there is no damage or little damage to the rock mass; when 10% < η ≤ 15%, the rock mass is slightly damaged; when η is > 15%, the rock mass is damaged.

If the observation is made only after blasting, the wave velocity in the original state near the observation site can be used as the wave velocity before blasting, or it can be determined from the changing trend and characteristics of the observation data. In this test, according to the distribution law of acoustic wave velocity with the depth of surrounding rock, we determined the pre-burst wave velocity of 4.011 km/s in parts A and D and 4.294 km/s in parts B and C.

In rock engineering, the damage variable D is often used to characterize the attenuation of mechanical properties of a rock mass after disturbance, and the effective modulus of elasticity of material will decay linearly after damage, as shown in Formula (2).

(2)

Formula: and E_d are the dynamic modulus of elasticity before and after the damage, respectively.

In engineering practice, the damage variable of the rock mass can be characterized by the change in acoustic wave velocity. According to fluctuation theory, the wave velocity of a wave propagating in a continuous, homogeneous, isotropic elastic medium can be expressed as:

(3)

Formula: V_P is the longitudinal wave velocity of the rock mass, ρ is the density of the rock mass, and ν_d is the dynamic Poisson's ratio.

From formula (3), it can be seen that the propagation of elastic waves in the medium is only related to the medium density ρ and its dynamic deformation parameters E_d and ν_d. Assuming that the dynamic Poisson's ratio ν_d and the density ρ of the rock mass remain constant before and after blasting, substituting formula (2) into formula (3) yields:

(4)

Formula: is the longitudinal wave velocity after blasting.

From formula (4), the relationship between the damage variable of the rock and the acoustic wave velocity of the rock before and after the damage can be obtained as follows:

(5)

Using equation (5), the threshold value of the surrounding rock affected by blasting was calculated, and the damage variable was found to be 0.19 for a wave velocity change rate of 10%.

Fig. (8) shows the distribution pattern of different parts. Using the damage variable of 0.19 as the rock damage standard, the damage depths of the four test sites were 2.09 m at a, 1.20 m at b, 2.09 m at c, and 2.77 m at d. Using the damage variable of 0.28 as the rock damage, the damage depths of the four test sites were 1.84 m at a, 1.15 m at b, 1.80 m at c, and 1.96 m at d. Under the two standards, the depth of damage to the surrounding rock at the bottom of the tunnel was found to be the largest, followed by the arch waist of the two benches, and the depth of damage at the intersection of the two benches was the smallest. The depth of damage was determined by the two standards, the largest difference at d, and the remaining three differences were within 15%. For safety, the 0.19 damage variable was used as the damage standard for the rock mass in the subsequent analysis.

Further analysis was performed on the distribution curve characteristics of the damage variable by focusing on the depth of surrounding rock in each part of the tunnel section. It has been found that the damage variable of rock at the intersection of two benches at the excavation face was the largest at b, which exceeded 90%. Here, the wave velocity of the surrounding rock was only 797 m/s. Moreover, the density of rock mass hardly changed, and the wave impedance of the surrounding rock at the excavation face became smaller. The wave impedance matching between rock masses with different damage variables was found to be poor. As it was difficult for the blasting stress wave to propagate further through the severely damaged rock mass, the damage depth at this place was the smallest. Other parts of the excavation face with the damage variable were relatively small, and the wave impedance of the rock at different depths was better matched, which was conducive to the propagation of blasting stress waves. Hence, the depth of damage was relatively large.

LS-DYNA was used to establish the numerical model of tunnel blasting excavation [13-15]. In order to save computational resources, a 1/2 model was established, the symmetry plane of the model was set with normal displacement constraints, and the remaining five planes were set as transmission boundaries to simulate the infinite boundaries of the actual project. The model height, width, and thickness were 62.5 m, 40 m, and 69.2 m, respectively, as shown in Fig. (9).

The intrinsic model of the rock mass was used with a statistical damage softening model based on the Weibull distribution [16]. The physical and mechanical parameters of the rock masses used are shown in Table 3.

Table 3: ρ is the density of the rock mass, E is the elastic modulus, μ is the Poisson's ratio, R_t is the tensile strength, and R_c is the compressive strength.

The large number of blast holes is very complicated to model. Previous studies have shown [17, 18] that the use of equivalent blast loads to simulate the dynamic effects of the surrounding rock under the action of tunnel blasting can meet the required accuracy in engineering. In this study, a triangular load [19] was used as the equivalent blasting load, which was applied to the excavation boundary of the tunnel. The rise time of the triangular load, the time of positive pressure action, and the calculation of the peak load were already discussed in the literature [20]. The restart analysis function of LS-DYNA was used to realize the cyclic tunneling.

The numerical simulation of eight cycles of tunnel surrounding rock damage distribution cloud atlas is shown in Fig. (10). It can be seen that the surrounding rock damage caused by each cycle of blasting will be superimposed on the previous cycle of surrounding rock damage, resulting in deeper damage or greater damage to the surrounding rock. Overall, the damage to the surrounding rock at the arch footing of the upper bench is the most serious after the bench blasting excavation.

The distribution of the damage variable with the depth of the surrounding rock at the four locations that are statistically the same as the site acoustic test site is shown in Fig. (11). It has been observed that when the damage variable is 0.19, corresponding to A, B, C, and D for damage depths of 2.17m, 1.16m, 2.08m and 2.65m, respectively, and the numerical simulation of the surrounding rock damage depth and acoustic damage variable assessment of the damage depth are close to each other, the error is within 5%. As for the distribution characteristics of the surrounding rock damage, due to the non-homogeneity of the tunnel surrounding rock, the distribution characteristics of the damage variables obtained from numerical simulation and the distribution characteristics of the damage variable obtained from acoustic testing are somewhat different, but the overall distribution law is the same. When the damage at the excavation surface is serious, the damage depth of the corresponding part is small, such as the arch footing part of the upper bench; when the damage is relatively minor, the damage depth of the corresponding part is large, such as the inverted arch part. Compared to the above numerical simulation results and acoustic test results, the numerical simulation results are reliable.