The Vibration Response to the High-Pressure Gas Expansion Method: A Case Study of a Hard Rock Tunnel in China

Abstract

The vibration of rock breaking in tunnel excavation may cause serious damage to nearby buildings if it is not controlled properly. With reference to a hard rock tunnel in China, the vibration response to the high-pressure gas expansion method (HPGEM), an emerging rock-breaking approach, was investigated with field tests, theoretical derivations, and numerical simulations, then comparisons with the traditional dynamite blast were performed. Firstly, the vibration velocity prediction formulas of the two methods were fitted based on the field tests. Subsequently, the accuracy of the formula was verified by numerical simulation, and the vibration attenuation law of the HPGEM was explored. Comparisons were made between the blast and HPGEM, particularly the differences in peak particle velocity (PPV) for different agent qualities, distance from the blasting center, and engineering conditions. Furthermore, this study also analyzed the relationship between the agent qualities and the rock-breaking volume under different cases, finding that the HPGEM has slight vibration and good rock-breaking effect. The HPGEM is thus fully capable of replacing dynamite blasting to carry out rock-breaking operations in certain special areas.

1. Introduction

The vibration generated by the rock-breaking process in tunnel excavation is one of the key factors that jeopardize the safety of adjacent important buildings (structures). Currently, dynamite blasting is still one of the most commonly used rock-breaking methods [1,2]. However, it inevitably produces high vibration velocity due to its own principle of action; thus, it is no longer applicable in some special construction environments. To solve this problem, some new methods such as the tunnel boring machine (TBM) [3], mechanical excavation [4,5], and gas blasting [6,7], etc., have emerged (Figure 1). Nevertheless, these methods still have some shortcomings. TBM equipment is costly and requires a large construction area [5]. Mechanical excavation is inefficient and has a limited scope of application [6]. Gas blasting has high requirements for equipment and operation, and high requirements for the environment [7]. The above problems bring challenges to the safe excavation of hard rock tunnels near important buildings or facilities in urban development.

The “High-Pressure Gas Expansion Method” (HPGEM) [8,9] was proposed to address the above-mentioned shortcomings. This method involves the simultaneous chemical and physical reactions of the gas generator in the expansion pipe as the active ingredients under sealed conditions. In an extremely short period of time, a large number of high-temperature and high-pressure gases are released to expand and affect the surrounding media, thus achieving rock breaking (Figure 2 and Figure 3). Existing studies have shown that the rock fragmentation morphologies found after HPGEM and traditional explosive blasting are quite different. The fragmentation of rock slag after HPGEM is obviously larger than that from the drilling and blasting method, and the failure surface of the rock slag basically retains the original structural plane, while the failure surface of rock slag produced by the drilling and blasting method is mostly a fresh fracture surface. More specific HPGEM principles can be found in the authors’ previously published literature [10].

As an emerging rock-breaking method, there are few studies on HPGEM. Peng et al. [9] applied HPGEM to a tunnel excavation to find the optimal blasting design parameters. In addition, they constructed a set of rock mass classification methods applicable to HPGEM [10]. Based on a tunnel in Hangzhou, Liu et al. [11] proposed a set of safe and efficient solutions for urban hard rock excavation by analyzing the rock-breaking effect and vibration effects of the HPGEM on the surrounding buildings. Subsequently, to investigate the applicability of HPGEM in hard rock tunnels near historical sites, Liu et al. [12] obtained suitable rock-breaking parameters for tunnel excavation by means of theoretical analyses, on-site experiments, and vibration monitoring. They found that if the plugging holes were of high quality and not drilled, HPGEM could have the advantages of low vibration, low noise, and fewer flying rocks, which provided a solution for hard rock tunnel excavation near ancient buildings and historical sites.

There have been many studies on the hazards caused by blasting vibration. As early as the 1970s, standards were issued for the control of blasting vibration damage to buildings [13]. Singh [14] carried out dynamic monitoring of the stratum before and after the explosion to obtain the maximum peak particle velocity, and then investigated the influence of blasting in open-cast coal mines on the stability of an adjacent underground coal mine roadway. Zhou et al. [15] assessed the damage to residential structures induced by blasting vibration in open pit mines by developing a gradient hoist model, and damage categories were more accurately investigated. Noren-Cosgriff et al. [16] evaluated the damage to residential structures caused by blasting vibration in a quarry. The test results confirmed that the limits of the standards in most countries were too conservative. Yue et al. [17] used ANSYS/LS-DYNA software to study the effects of borehole arrangement, delay time and decoupling charge on the rock damage and vibration attenuation of multi-hole blasting, and then optimized the blasting design to improve the blasting effect. Wang et al. [18] discussed the propagation characteristics and attenuation prediction equations for blasting vibration in rock tunnels by on-site monitoring and numerical simulation. They also improved the empirical equations of scalar distance to predict the peak mass vibration in the whole space of the rock tunnel, and finally proposed a new equation for predicting the peak mass vibration of the adjacent tubes in the plane of the center of blasting. Lv et al. [19] obtained the propagation mechanism and the damage distribution characteristics of blasting vibration along the elevation direction of the high sidewall of a deep underground cavern. The propagation mechanism of blasting vibration in the direction of blasting vibration was analyzed, and the prediction formula of particle vibration velocity along the elevation direction under the blasting vibration condition was derived. Aiming at problems such as the lack of comprehensive stage analysis in the field of blasting vibration, Zhang et al. [20] elucidated the research progress of blasting vibration, clarified the research frontiers, and discussed in depth the social significance of the intelligent blasting system in the context of artificial intelligence. Based on a tunnel project in Shenzhen, Wu et al. [21] proposed a four-part excavation method with a vibration buffer rock layer. Numerical simulation was utilized to model the damage prevention mechanism of the vibration buffer rock layer to understand the propagation of cracks in the interbedded rock. Finally, combined micro-vibration control blasting technology was realized by combining different loading structures and blasting equipment designed according to the change in the thickness of the interbedded rock.

In summary, as an emerging rock-breaking method, the application effect and vibration response law of HPGEM in practical engineering still need to be studied. In view of this, based on a hard rock tunnel in China, this paper analyzed the vibration velocity and rock-breaking capacity of the dynamite blasting method and HPGEM. The forces and vibrations of the buildings near the excavated tunnel under different scenarios were identified by means of numerical simulation and on-site monitoring. The vibration attenuation law during rock-breaking by the HPGEM was explored, and the relevant fitting equations were proposed. Finally, engineering recommendations were made for the adoption of these two methods.

2. Project Overview

This study is based on the background of a double-hole tunnel of a highway in China, which is close to underground pipelines and a high-speed rail line; therefore, there are strict restrictions on construction vibration in this project. An overview of the study area is presented in Figure 4. The Quaternary overburden in the study area is mainly Pleistocene diluvial silty clay (Q_P^d1), and the underlying is the upper Jurassic C-1 member (J₃^c-1) tuff. The surrounding rock is hard, the development degree of joints and fissures is different, there is a dripping phenomenon, and the weathering degree is from never weathered to slightly weathered. There is no obvious surface water in the tunnel site. The groundwater is mainly bedrock fissure water. The connectivity of joint fissures is general. It is the main storage space of groundwater and mainly depends on atmospheric precipitation. The low-lying parts are discharged in the form of underground runoff, while the slope parts are discharged from the surface through seepage along fissures or terrain cutting. Therefore, the project has a strict restriction on construction vibration. According to the previous design and construction experience and the seismic intensity table in the blasting safety regulations, as well as the requirements of the project specification documents, the safety seismic standards for the underground pipelines and high-speed rail line were formulated to require that the vibration velocity should be controlled within 7.0 cm/s. The vibration velocity of the high-speed rail line should be controlled within 1.0 cm/s. This brings great challenges to tunnel boring work. Meanwhile, the geological survey demonstrates a mean compressive strength of 69.8 MPa for the rock mass, but the actual strength of the rock mass is more than 140.0 MPa. Overall, the tunnel is a hard rock tunnel, and blasting operations with explosives are extremely difficult in these circumstances. Meanwhile, the use of other blasting methods is either costly or inefficient. Therefore, there is an urgent need for a new rock-breaking technique with good rock-breaking effect and tiny vibration velocity to ensure the safety and efficiency of the construction project.

3. Rock Breaking Design Program

3.1. Dynamite Blasting

3.1.1. Schematic Design

Since HPGEM is an emerging rock-breaking method with little engineering experience to draw on, this study first carried out the design of the rock-breaking scheme by explosive blasting (No. 2 rock emulsion explosive), to provide a reference point for the subsequent design of the HPGEM. Due to the constraints of the construction project’s environment, dynamite blasting cannot be performed in the case study tunnel. Therefore, all blasting tests in this study were conducted in another tunnel about 1 km away from the case study tunnel (with almost the same geological conditions as in the study area). The blasting vibration velocities in three directions are monitored during the blasting operation. The peak particle velocity [22,23] is usually taken as the key factor for determining the impact of blasting vibration. Determination of the PPV is the basis for measuring whether the blasting operation causes damage to adjacent buildings (structures), which the Sadowski formula is commonly used to predict [24,25] (Equation (1)).

$$PPV=K{\left({\displaystyle \frac{\sqrt[3]{Q}}{R}}\right)}^{\alpha }$$

(1)

where the characteristic coefficient $K$ and $\alpha$ are the coefficients related to the site topography (geological conditions and other factors are shown in

Table 1. Relationship between the values of $K$, $\alpha$, and lithology.

Lithology	$\mathit{K}$	$\mathit{\alpha }$
Hard rock	50~150	1.3~1.5
Medium hard rock	150~250	1.5~1.8
Soft rock	250~350	1.8~2.0

). PPV is the peak particle velocity (cm/s), $R$ is the distance from the blasting center (m), $Q$ is the maximum explosive charge in all sections (kg).

Taking the logarithm of both sides of Equation (1) gives the following:

$$\mathit{lg}PPV=\mathit{lg}K+\alpha \mathit{lg}\left({\displaystyle \frac{\sqrt[3]{Q}}{R}}\right)$$

(2)

$$\mathrm{Let}y=\mathit{lg}PPV;x=\mathit{lg}\left({\displaystyle \frac{\sqrt[3]{Q}}{R}}\right);b=\mathit{lg}K;k=\alpha$$

Then:

$$y=kx+b$$

(3)

The regression calculation yields the following:

$$k={\displaystyle \frac{n{\sum }_{i=1}^n{x}_i{y}_i-{\sum }_{i=1}^n{x}_i{\sum }_{i=1}^n{y}_i}{n{\sum }_{i=1}^n{x_i}^2-{\left({\sum }_{i=1}^n{x}_i\right)}^2}}$$

(4)

$$b={\displaystyle \frac{1}{n}}\left(\sum _{i=1}^n{y}_i-\alpha \sum _{i=1}^n{x}_i\right)$$

(5)

The correlation coefficient can be expressed as:

$$\gamma ={\displaystyle \frac{{\sum }_{i=1}^n\left(x-\overline{x}\right)\cdot \left(y-\overline{y}\right)}{\sqrt{{\sum }_{i=1}^n{\left(x-\overline{x}\right)}^2\cdot {\sum }_{i=1}^n{\left(y-\overline{y}\right)}^2}}}$$

(6)

where $n$ is the total number of monitoring; and, each $x_i$ and $y_i$ represents the size of a particular experiment $x$ and $y$.

If the full section excavation is used, the PPV will exceed the specified limit. Therefore, the proposed tunnel is divided into a drilling and blasting excavation area and a mechanical and drilling and blasting excavation area, according to the distance from the highway and underground pipelines. Excavation operations are carried out in the areas within 34 m from the left and right sides of the highway centerline, and drilling and blasting excavation is performed outside the area. Since the PPV is the direct cause of damage to buildings (structures), the analysis is conducted on vibration monitoring and the blasting effect of the drilling and blasting method. In this blasting design, the wedge cutting technique was applied to blast excavate a section of the upper and lower benches. The spacing of the cut holes was 0.9 m, with a plum-shaped arrangement and a row spacing of 0.7 m. Each hole was charged with 0.4 kg of explosives (calculated based on the design of the drilling and blasting excavation). The first section of the charge was slightly larger, with a charge of 0.6 kg per hole, and an advance of 1.0 m per cycle. Refuge blasting is used at the center of the empty hole by spiral hollowing, with a maximum charge of 0.6 kg per hollowing hole. Each cut and peripheral hole is charged with 0.2 kg of explosives, and the guide mine for each advance cycle is 0.8 m long. Sections are divided according to the distribution of drilling and blasting holes, and the detonator section is shown in Figure 5.

3.1.2. Monitoring and Fitting

An attempt is first made to obtain the blasting vibration fitting equations for the study area. The TC-4850 blast vibrometer (Zhongke Electric, Yueyang, China), TC-3850 blast vibrometer (Zhongke Electric, Yueyang, China), CDJ-1 type velocity sensor (China Sichuan Chengdu Zhongke measurement and Control Co., LTD, Chengdu, China), and three-direction velocity sensor (China Sichuan Chengdu Zhongke measurement and Control Co., LTD, Chengdu, China) were utilized to perform on-site PPV monitoring. The obtained PPV monitoring results were divided into three velocity directions: vertical, radial, and tangential. Since the PPV mainly occurs in the vertical direction [26,27], only the vibration velocity in the vertical direction is regressed and analyzed in this study. The vibration test results and vertical vibration velocity are shown in

Table 2. Vibration test results.

Monitoring Point No.	R (m)	Q (kg)	PPV (cm/s)	Main Vibration Frequency (Hz)
1	26	20	4.52	108.108
2	28	22	4.25	98.199
3	35	18	2.93	116.280
4	42	24	2.64	166.166
5	31	15	2.98	85.107
6	39	18	2.69	109.863
7	28	17	3.67	94.933
8	13	17	11.78	88.889
9	53	14	1.56	200.911
10	50	12	1.39	192.667
11	40	11	1.96	145.752
12	24	12	3.79	90.909
13	35	12	2.47	100.122

.

Based on Table 2 and Equations (1)–(6), the relevant parameters can be determined as: $K$ = 103.02, $\alpha$ = 1.377. It can be found from Table 1 that the K is in the range of 50–150 and the $\alpha$ is in the range of 1.3–1.5 for hard rock, which is in line with the actual rock mass conditions. The fitting equation for the vibration velocity of the explosive blasting currently is as follows:

$$PPV=103.02\times {\left({\displaystyle \frac{\sqrt[3]{Q}}{R}}\right)}^{1.377}$$

(7)

Then based on Equation (7), for the inverse highway roadbed (HR), underground pipeline (UP), and high-speed rail line (HSRT) to reach the PPV control value at the nearest distance to the maximum section of the explosive charge, that is, the limit cases of the maximum section of the explosive charge without considering the possibility of practical operation, the values are, specifically, as shown in

Table 3. Maximum section explosive charge in limit cases.

Location	PPV Control Value (cm/s)	R at Minimum PPV (m)	Q (kg)
HR	7	5.70	0.53
UP	7	4.64	0.29
HSRT	1	50.00	5.15

.

(1) Drilling and blasting

Based on the tunnel segmentation schematic, the PPV in the upper bench blasting will occur in the 13th segment at the tunnel face of section YK9+082. The Q of the 13th section, the explosive charge per hole, and the charge of other segments is calculated according to Table 3 and Equation (7). Finally, the vibration velocity of the highway roadbed, underground pipelines and high-speed rail line caused by blasting with explosives in each section is back-calculated to verify whether the PPV control value is exceeded, and the calculated seismic wave propagation distance is taken as the average value of the distances of each section of the gun holes. The results show that, for the upper bench blasting at the tunnel face at section YK9+082 in the 13th section (Q is 6.8 kg), the PPV for the highway roadbed, underground pipelines and high-speed rail line are calculated to be 6.95 cm/s, 6.36 cm/s and 0.97 cm/s, respectively, which are close to but less than the limit of the specified PPV. Similarly, the PPV of each section at the lower bench of the tunnel face at section YK9+082 during blasting are calculated. Since the underground pipeline is closer to the tunnel lower bench, it is not necessary to calculate the PPV of each section of Q for the highway roadbed during blasting of the lower bench. For the upper bench blasting of the tunnel face at section YK9+082, the calculated PPVs for the underground pipelines and high-speed rail line are found in the first segment (with a Q of 4 kg), which are 6.33 cm/s and 0.76 cm/s, respectively, which are less than the specified PPV control value. Therefore, the settings of the blasting parameters for the upper and lower benches are reasonable. Their specific calculation results are shown in Figure 6.

(2) Collaborative dredging

The project overview confirms that the minimum clear distance of the underground pipeline from the tunnel bottom at the highway central divider is only 4.64 m. Therefore, in this blasting design, it is assumed in the limit case that the highway central divider, the blasting tunnel face and the underground pipeline are in the same plane. Theoretically the maximum PPV will occur in this section. If the PPV at the tunnel face satisfies the vibration velocity provisions, the PPV at the section between the YK9+082 and YK9+150 should be within the safety limit. The calculation method is the same as the previous drilling and blasting method, and the calculation results are shown in Figure 7. It can be seen that when the underground pipeline is located directly above the guided blasting, the PPV of the highway roadbed, underground pipeline and high-speed rail line are in the 15th segment (with Q of 1 kg), the 13th segment (with Q of 0.6 kg), as well as in the 13th and 15th segments (with Q of 1 kg), respectively, which are 4.83 cm/s, 6.10 cm/s and 0.47 cm/s, respectively, which are less than the specified PPV limit, indicating that the blasting parameters of the lower bench meet the safety requirements.

(3) Numerical simulation of explosive blasting under three operating conditions

Conventional blasting for the proposed tunnel is a design based on the protection of adjacent projects. The highway in operation, the fully enclosed high-speed railway line, and the inaccessible underground pipeline make it impossible to carry out large-scale on-site monitoring. Therefore, it is necessary to verify the design through numerical simulation and analyze the stresses of the structure under the limit conditions, to provide a basis for a comparative analysis between the HPGEM and dynamite blasting. Considering that the excavation of the left tunnel has been completed, and the two tunnels are not adjacent tunnels, only the right tunnel of the proposed tunnel is considered in the numerical model. Numerical simulations were performed to investigate the vibration velocity and force of the highway roadbed, underground pipeline, and high-speed rail line during dynamite blasting under three working conditions.

According to the relative position relationship of each structure and the geological conditions, the model size is 160 m × 80 m × 100 m (long, high, wide). The element of the model is solid-164. The three main materials used in the model are explosives, rock, and concrete. C30 concrete is considered for the highway roadbed, and the explosives are the No. 2 rock emulsified explosives. The equation of state is defined as follows:

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

(8)

where $P$ is the blasting pressure (MPa); $V$ is the relative volume; $E$ is the internal energy per unit volume (GPa); and $\omega ,A,B,R_1,R_2$ are the material constants.

Actual geotechnical media are discontinuous and inhomogeneous, and it is currently almost impossible to describe these envelopes mathematically directly and objectively. The rock mass is usually regarded as a homogeneous and continuous elastic medium. In this paper, ANSYS 16.0 is used to simplify the model, that is, rock and soil are regarded as elastic–plastic materials. The material of the model is chosen to simulate the geotechnical medium, and the yield condition is shown in Equation (9). The constitutive relationship and numerical model are presented in Figure 8. The concrete of roadbed is simulated by the material of the model. According to the data provided by the geological report and indoor test, the main parameters of the selected material of the model are illustrated in

Table 4. Main parameters of numerically simulated explosives.

Parameters	β (g/cm3)	D (cm/μs)	P (MPa)	A (MPa)	B (MPa)
Value	1.2	0.48	0.097	2.144	1.82 × 10−3
Parameters	R1	R2	ω	E0 (J/cm3)	V0
Value	4.2	0.9	0.15	3.60 × 103	0

and

Table 5. Main parameters of rock and concrete used in numerical simulation.

Parameters	ρ (g/cm3)	E (MPa)	γ	ET (MPa)	σs (MPa)
Rock	2.6	6.00 × 1010	0.27	1.30 × 103	4.00 × 103
Concrete	2.25	3.00 × 1010	0.2	2.50 × 102	2.40 × 103

.

$$\phi ={\displaystyle \frac{1}{2}}{\xi }_{ij}^2-{\displaystyle \frac{{\sigma }_y^2}{3}}=0$$

(9)

$${\xi }_{ij}=s_{ij}-a_{ij},{\sigma }_y=\left[1+{\left({\displaystyle \frac{\dot{\epsilon }}{C}}\right)}^{{\displaystyle \frac{1}{p}}}\right]({\sigma }_0+\beta E_p{\epsilon }_{eff}^p).$$

where $s_{ij}$ is the Cauchy stress tensor; $p$ and $C$ are input constants; ${\sigma }_0$, $\beta$ are the initial yield stress and hardening parameter, respectively; $\dot{\epsilon }$ is the strain rate, $\dot{\epsilon }=\sqrt{{\dot{\epsilon }}_{ij}{\dot{\epsilon }}_{ij}}$; $E_p$ is the plastic hardening modulus, $E_p={\displaystyle \frac{E_{t}E}{E-E_t}}$, with $E$ being the elastic modulus, $E_t$ being the tangential modulus; and ${\epsilon }_{eff}^p$ is the effective plastic strain.

In general, the ramp-up time of the blast load is 8–12 ms, and the unloading time is 80–100 ms. To better analyze the propagation law of the blasting vibration seismic wave in the modeled medium, the computation time of the dynamite explosion simulation in this study is set to 0.3 s and the blast vibration seismic wave propagates in the modeled medium.

(1) Analysis of Blasting Vibration Velocity

The maximum vibration velocity nephograms of the highway roadbed in each direction during blasting under three working conditions are extracted, as presented in Figure 9. Figure 10 presents the maximum vibration velocities of the highway roadbed, underground pipeline, and high-speed rail line under each condition, where they are compared with the fitted values. It can be seen from Figure 9 that the maximum vibration velocities of the highway roadbed under the three conditions are all located at the nearest point on the side of the head-on blast, and their values are within the specified range. It can be seen from Figure 10 that the simulated and the calculated values of vibration velocity under the three conditions are similar, indicating that the numerical simulation results are credible, and confirming the feasibility of applying the parameters in the empirical formula of Sadowski to the proposed tunnel project.

Since structural stress affects structural stability, it is necessary to analyze the first and third principal stresses of the structure under various working conditions. Due to limited space, only the stress state of the highway roadbed is analyzed in this study, where the first principal stress is tensile stress, with positive values; the third principal stress is compressive stress, with negative values, also as shown in Figure 9. The maximum stresses of the highway roadbed in the three conditions are also located at the nearest point on the blasting side, with maximum tensile stresses of 0.87 MPa, 0.793 MPa and 0.989 MPa, respectively, and maximum compressive stresses of 1.83 MPa, 1.081 MPa and 1.39 MPa, respectively. According to the specification, the design tensile strength of C30 concrete is 1.39 MPa, and the design compressive strength is 13.8 MPa. Under the action of blasting dynamic load, its tensile and compressive strengths will be much higher than these two design values. For the highway roadbed under the action of blasting stress, the value is lower than its own ultimate destructive strength, so the highway roadbed is safe and stable.

In summary, the analysis of explosive blasting excavation based on theoretical calculations and numerical simulations confirms that the maximum vibration velocity and the maximum stress subjected to this scheme are within safe limits, and the scheme is feasible.

3.2. HPGEM

3.2.1. Schematic Design

The HPGEM allows rock-breaking tests to be conducted directly on the tunnel face of the project tunnel. Firstly, under the HPGEM rock-breaking scheme, wedge-shaped hollowing rock-breaking testing is carried out to determine the optimal type of hollowing. After the rock-breaking test, the amount of rock breakage was measured on site, and the statistical results are summarized in

Table 6. Comparison of results of rock removal tests.

Hollowing Type	Expansion Pipe Number	Gas Generated Agent Quality (kg)	Rock Breakage Amount (m3)	Unit Consumption (kg/m3)
Wedge-shaped hollowing	6	3	2.40	1.25
Large-diameter hollow Straight-hole hollowing	8	4	2.87	1.39

. It was found that the wedge-shaped hollowing had formed a cavity at the location of the broken rock, and there was no obvious “undercutting” in the cavity (Figure 11). After the large-diameter hollow straight-hole hollowing test, the same cavity was formed at the rock-breaking location, and there was basically no “undercutting” at the bottom of the cavity. Therefore, the hollowing results are as expected, which indicates that both types of hollowing tests are successful. Although the effect of both types of hollowing can meet construction requirements, it can be seen from Table 6 that, in this hollowing test, the unit consumption of wedge-shaped hollowing was 1.25 kg/m³, which is lower than that of the large-diameter hollow hole hollowing of 1.39 kg/m³. Hence, wedge-shaped hollowing is superior to the large-diameter hollow hole hollowing, and wedge-shaped hollowing was adopted in the subsequent test.

Subsequently, different expansion tube burial depths and hole spacings were set to optimize the matching of the expansion pipe hole network parameters with the lithology of the rock mass at the tunnel face. First, three groups of high-pressure gas expansion rock-breaking tests were designed, with three top-down arranged boreholes in each group. The spacing of each group of boreholes was more than 2 m, without interfering with each other. The hole spacings of group 1, group 2 and group 3 were 1.0, 1.2 and 1.4 m, respectively. The depth of the holes was 1.5 m, and the buried depth of the expansion pipe was 1.4 m. Secondly, according to the effect of the first three groups of tests, group 4 and group 5 tests were designed, where the depths of holes in these two groups were 1.4 and 1.6 m, respectively; and the buried depths of the expansion pipe were 1.3 m and 1.5 m, respectively. The rest of the parameters are the same as those of the group 2 tests. The results of the first three groups of tests show that the optimal hole spacing for HPGEM in this tunnel is 1.2 m, and the optimal hole depth is 1.4 m. For monitoring the vibration data during the test, the monitoring program adopted the same monitoring basis and monitoring instrument. The monitoring method and monitoring point arrangement are as described in the previous section. The vibration monitoring points are mainly arranged on the ground in front of the tunnel working face. The monitoring points for rock breakage are arranged at intervals of a few meters.

3.2.2. Monitoring and Fitting

The vibration monitoring data are shown in

Table 7. Measured and calculated PPV of the tunnel with HPGEM.

Number	${\mathit{Q}}_1$ (kg)	R (m)	Monitor PPV (cm/s)	Calculate PPV’ (cm/s)
1	0.5	3	3.389	3.034
2	0.5	4.3	1.713	1.724
3	0.5	43.6	0.057	0.045
4	1	7	1.600	1.305
5	1	5.9	1.810	1.706
6	1	43.6	0.084	0.074
7	1.5	45	0.118	0.095
8	1.5	65	0.039	0.051
9	1.5	6.2	2.237	2.098
10	1.5	11	0.667	0.850
11	1.5	18	0.225	0.391
12	5	18	0.740	0.910
13	7	15	1.659	1.544
14	15	13.6	2.438	3.070
15	20	27.5	1.480	1.245

. It was found that there is an obvious exponential function relationship between the two sets of data. With reference to the process of fitting the Sadowski formula for the vibration velocity of dynamite blasting, the Statistics Analysis System (SAS) software (v.9.4) was used to statistically analyze the above data to fit the formula for calculating the vibration velocity of the rock breakage of the HPGEM of the tunnel in this Equation (10):

$$PPV=e^{3.3205}\cdot {\displaystyle \frac{{Q_1}^{0.7012}}{R^{1.5695}}}$$

(10)

where $Q_1$ is the mass of the explosive (kg), and $R$ is the distance from the vibration monitoring point to the rock-breaking point (m).

The calculated vibration velocity results were compared with the actual measured data to verify the reliability of the fitting formula. It can be seen from Table 7 and Figure 12 that the fitted calculation values match well with the actual measured values, with a correlation coefficient R₂ of 0.946, indicating that the Equation (10) is reasonable. As shown in Figure 12, the fitting formula demonstrates a better fitting degree at lower PPV values. However, as the PPV values increase, the data exhibits greater dispersion. Therefore, the fitting formula may perform better in the context of smaller PPV values.

4. Comparison of the Dynamite Blasting and HPGEM

The vibration velocity under the same geological conditions is mainly affected by the pharmaceutical quality and the R. Therefore, under the same geological conditions, the PPV of the two rock-breaking methods with different R of the same Q or different Q of the same R is compared and analyzed.

Due to the limitations of the site conditions and the differences between the two rock-breaking methods, the field test R and Q cannot be fully consistent. Considering that the reasonableness of the fitting equations for the vibration velocity of the two rock-breaking methods has been verified; therefore, the two fitting equations can be used for the calculation of vibration velocity. To facilitate the comparison, the Q is set to 5, 10, 15, 20 and 25 kg, while the R is set to 5, 10, 15, 20 and 25 m. The specific data are as displayed in

Table 8. Comparison of PPV of dynamite blasting and HPGEM with different Q and R.

Number	Q (kg)	R (m)	${\mathit{P}\mathit{P}\mathit{V}}_1$ (cm/s)	${\mathit{P}\mathit{P}\mathit{V}}_2$ (cm/s)
1	5	5	23.509	6.839
2	5	10	9.051	2.304
3	5	15	5.179	1.219
4	5	20	3.485	0.776
5	5	25	2.563	0.547
6	10	5	32.314	11.120
7	10	10	12.442	3.746
8	10	15	7.119	1.983
9	10	20	4.790	1.262
10	10	25	3.523	0.889
11	15	5	38.923	14.776
12	15	10	14.986	4.979
13	15	15	8.575	2.635
14	15	20	5.770	1.677
15	15	25	4.244	1.182
16	20	5	44.417	18.079
17	20	10	17.102	6.091
18	20	15	9.785	3.224
19	20	20	6.584	2.052
20	20	25	4.843	1.446
21	25	5	49.207	21.141
22	25	10	18.946	7.123
23	25	15	10.840	3.770
24	25	20	7.294	2.400
25	25	25	5.365	1.691

. The vibration velocities of the explosives and aerosols under different Q and R are plotted in Figure 13, in which ${PPV}_1$ and ${PPV}_2$ are the vibration velocities of the explosives and HPGEM, respectively.

As can be seen from Figure 13, the vibration velocity of the dynamite blasting method and HPGEM exhibits a similar pattern of change. In the case of the same agent quality and blasting center distance, the vibration velocity formed by explosives and gas generator explosion is much higher than the HPGEM. In the case of the same R, the greater the Q, the larger the vibration velocity, the larger the difference in vibration velocity between the dynamite blasting and HPGEM. For the same Q, a larger R results in a smaller difference in vibration velocity between the explosive blasting and HPGEM. The smaller the R, the more obvious the difference brought about by the difference in the Q. The opposite is less obvious.

For the same Q and R, the vibration velocity of the explosive blasting method is 2.33–4.7 times that of HPGEM. For the same R, the greater the Q, the smaller this multiplier relationship. But for the same Q, with the increase in the R, the multiplier becomes greater. The smaller the maximum section of the charge (for HPGEM, it is a detonation of the mass of the gas generating agent) and the further away the protected structure is from the point of explosion, the better the vibration rate can be controlled and reduced by the HPGEM. For scenarios where the maximum cross-section of the charge is very large and is close to the protection limits, the use of HPGEM can also significantly reduce the vibration rate, but the effect is relatively weak. The reason for this phenomenon is that the explosives’ blasting vibration mainly generates from explosive shock waves (of course, there are also high-temperature and high-pressure gas effects). Shock waves propagate quickly and cause damage to the nearby zone of the explosion, and then decay into stress and seismic waves, while stress waves propagate relatively slowly in the rock mass. The rock mass was moved by the superposition of explosive gases resulting from the shock waves and explosives’ explosion, while the disturbance of the rock mass by shock waves precedes the uptake of explosive gases in the rock mass. The vibration generated by the HPGEM is basically from the impact of the high-temperature and high-pressure gas on the expansion of the rock wall, but the impact of the shock wave is relatively weak. As the expansion of the fissures in the rock and the extension of the pressure decrease rapidly, the disturbance of the rock mass will decrease. In general, the further the distance, the faster the disturbance decreases.

After understanding the change rule of vibration velocity of the two rock-breaking methods, it is beneficial to compare and analyze the vibration velocities of the two rock-breaking methods when they are employed in difficult engineering sites. Based on the above conclusions and the safety requirements mentioned, the vibration velocities of the HPGEM with the same Q in the limit case were obtained for comparative analysis, as shown in

Table 9. Comparison of ${PPV}_1$ and ${PPV}_2$ in the limit case.

Location	Q (kg)	R (m)	${\mathit{P}\mathit{P}\mathit{V}}_1$ (cm/s)	${\mathit{P}\mathit{P}\mathit{V}}_2$ (cm/s)	V/V1
HR	0.53	5.70	7	1.152	0.165
UP	0.29	4.64	7	1.032	0.147
HSRL	5.15	50.00	1	0.188	0.188

. Similarly, according to the explosive blasting program in the field, the vibration velocity of the HPGEM with the same Q was also acquired, as displayed in

Table 10. Comparison results of ${PPV}_1$ and ${PPV}_2$ in the practical case.

Location		Q (kg)	R (m)	${\mathit{P}\mathit{P}\mathit{V}}_1$ (cm/s)	${\mathit{P}\mathit{P}\mathit{V}}_2$ (cm/s)	${\mathit{P}\mathit{P}\mathit{V}}_2$$/{\mathit{P}\mathit{P}\mathit{V}}_1$
Upper bench	HR	6.80	13.45	6.950	1.795	0.258
	UP	6.80	14.324.00	6.355	1.626	0.256
	HSRL	6.80	56.00	0.972	0.191	0.197
Lower bench	HR	4.00	12.037.00	6.330	1.473	0.233
	UP	4.00	56.00	0.762	0.132	0.173
Pilot	HR	1.00	9.23	4.823	0.845	0.175
	UP	1.00	7.79	6.100	1.103	0.181
	HSRL	1.00	50.00	0.471	0.060	0.127

.

As can be seen from Table 9 and Table 10, in the case of the same Q of explosives and the gas generating agent explosion, the vibration velocity of the HPGEM with various engineering difficulties is much lower than that of the explosives’ blasting method. Moreover, it can be seen from the ratio of vibration velocity that the vibration velocity control efficiency of the HPGEM in the actual operable procedure is basically lower than in the limit case. This is due to the different locations of the three major engineering difficulties. Considering that the excavation design program must be practical to operate, the Q and the R will be adjusted accordingly. However, the smaller vibrations produced by the HPGEM demonstrated its advantage in controlling vibration hazards.

According to the maximum allowable vibration velocity set at each engineering difficulty in the limit case, the maximum section charges of the two rock-breaking methods at each engineering difficulty were back-calculated using the fitting formula obtained from dynamite blasting and HPGEM in the test tunnel (for the HPGEM, it is the quality of single consumption). The results of the comparative analysis are shown in

Table 11. Comparison of maximum Q at one time and rock-breaking volume at the PPV in the limit case.

Location	${\mathit{P}\mathit{P}\mathit{V}}_1$ (cm/s)	R (m)	Dynamite Blasting			HPGEM			m2/m1	A2/A1
			Q (kg)	Unit Consumption (kg/m3)	Rock Breakage Amount A1 (m3)	${\mathit{Q}}_1$ (kg)	Unit Consumption (kg/m3)	Rock Breakage Amount A2 (m3)
HR	7	5.7	0.53	0.6	0.881	6.930	0.87	7.965	13.10	9.04
UP	7	4.64	0.29		0.475	4.372		5.026	15.33	10.57
HSRL	1	50	5.15		8.576	55.776		64.110	10.85	7.48

. The minimum value of 0.6 kg/m³ is taken for the single consumption of dynamite blasting for rocks with hardness coefficients f = 9–15, which is less than the actual single consumption of dynamite blasting. In this case, the maximum segmented Q can produce the maximum amount of rock breakage. Comparison is made with the calculation results of the HPGEM tests to demonstrate the advantages of the HPGEM in terms of the amount of rock breaking and the control of vibration hazards.

As can be seen from Table 11, at the maximum vibration velocity in the limit case, to protect the highway roadbed, underground pipelines and high-speed rail line, the maximum masses of gas agent required for a single initiation of blasting in the high-pressure gas expansion method are 13.103, 15.327 and 10.839 times the maximum sectional charge in dynamite blasting, respectively; while the volumes of the rock breakage in the high-pressure gas expansion method are 9.037, 10.570 and 7.475 times those in dynamite blasting, respectively. In other words, the high-pressure gas expansion method can use more mass of agent than dynamite blasting at one time, without having to be overly limited to segmentation, and can obtain far greater volumes of the rock breakage than dynamite blasting. At the same vibration rate, high pressure gas expansion is also more conducive to increasing the volume of rock breakage.

Considering the feasibility of the actual tunnel excavation program, comparisons of the maximum vibration velocity and the amount of rock breakage under the single maximum charge quantity in the limit case are shown in

Table 12. Comparison of the maximum Q and rock-breaking volume at one time under the PPV under the practical program.

Location		${\mathit{P}\mathit{P}\mathit{V}}_1$ (cm/s)	R (m)	Dynamite Blasting			HPGEM			m2/m1	A2/A1
				Q (kg)	Unit Consumption (kg/m3)	Rock-Breakage Amount A1 (m3)	Q (kg)	Unit Consumption (kg/m3)	Rock-Breakage Amount A2 (m3)
Upper bench	HR	6.950	13.45	6.80	0.91	7.45	46.86	0.87	53.86	6.89	7.23
	UP	6.355	14.32	6.80		7.45	47.49		54.58	6.98	7.33
	HSRL	0.972	56.00	6.80		7.45	69.03		79.34	10.15	10.65
Lower bench	HR	6.330	12.04	4.00	0.73	5.52	31.99		36.77	8.00	6.67
	UP	0.762	56.00	4.00		5.52	48.78		56.07	12.20	10.16
Guide hole	HR	4.823	9.23	1.00	0.9	1.12	11.98		13.77	11.99	12.34
	UP	6.100	7.79	1.00		1.12	11.45		13.17	11.46	11.80
	HSRL	0.471	50.00	1.00		1.12	19.06		21.90	19.06	19.63

, where the unit explosive is the corresponding to actual unit consumption. To protect the highway roadbed, underground pipelines and high-speed rail line, the upper bench, the lower bench, and guide blasting are used for three detonations. In the upper-bench rock breaking, the maximum mass of gas generating agent used in the high-pressure gas expansion method is 6.89, 6.98 and 10.15 times the maximum charge in the dynamite blasting, while the rock-breaking volume is 7.23, 7.33 and 10.65 times, respectively. In the lower-bench rock breaking, the maximum mass of gas generating agent used in the high-pressure gas expansion method is 8.0 and 12.2 times of the maximum charge in the dynamite blasting, while the rock-breaking volume is 6.67 and 10.16 times, respectively. In the guide blasting rock breaking, the maximum mass of gas generating agent used in the high-pressure gas expansion method is 11.99, 11.46, and 19.06 times the maximum charge in the dynamite blasting, while the rock-breaking volume is 12.34, 11.80, and 19.63 times, respectively. In the limit case, the high-pressure gas expansion method can break rock in a single blasting using a much larger charge than dynamite blasting, and can obtain a much larger rock-breakage volume than dynamite blasting. However, the variation in the ratio between high-pressure gas expansion and dynamite blasting in the practical scenario is much greater than that in the limit case, especially in the case of guide rock breaking. The further away from the breaking point, the more advantageous the high-pressure gas expansion method is over dynamite blasting in controlling the vibrations of the fragmented rock and in increasing the volume of fragmented rock. This is mainly due to the rock-breaking mechanism of the high-pressure gas expansion method and the attenuation law of the vibration rate.

During the tunnel blasting excavation, blast vibration monitoring of the adjacent ground or underground buildings (structures), and comparative analysis of the monitoring results with the standard specifications can ensure the safety of adjacent buildings (structures), and can also optimize the blasting parameters. Therefore, the use of the above blasting design for blasting excavation of the test tunnel can meet the requirements of all parties to the project on vibration velocity, and safe construction of the tunnel can also be achieved. Due to the complexity of the site construction environment, the density of the surrounding personnel and vehicles, as well as the difficulty in unifying the minds of all parties, it is difficult to obtain approval for the excavation plan using traditional blasting with explosives. Therefore, combined with the comparative analysis of the above two rock-breaking methods, it is recommended that the high-pressure gas expansion method be used for tunnel excavation. The upper bench, lower bench and guide hole can be blasted according to the above blasting design.

Since the high-pressure gas expansion method can achieve the excavation of larger rock-breakage volume within the maximum allowable vibration velocity, the tunnel can be divided into upper and lower bench blasting areas. Outside the range of section YK9+082–YK9+150, the high-pressure gas expansion method can be adopted for tunnel excavation, and in the range of section YK9+08–YK9+150, guide hole excavation can be expanded, or the bench tunneling method can be used, In this way, the efficiency of rock breaking can be improved, the construction period can be shortened, and the cost saving can be maximized.

5. Conclusions

To investigate the safety performance of the high-pressure gas expansion method in the process of rock breaking, a hard rock tunnel in China was taken as the research object, and a comparative analysis of the vibration caused by this new rock-breaking method and traditional rock breaking using explosives was carried out by means of on-site test, theoretical derivation, and numerical simulation. The main conclusions are as follows:

(1)

Firstly, field tests were conducted on traditional blasting with explosives. The peak vibration velocity prediction formula was fitted based on Sadowski’s formula. Combined with the maximum allowable vibration velocity given by the design, the maximum segmental loading of the project was calculated, and the force and vibration of the buildings near the tunnel during the maximum segmental loading of blasting under three working conditions were obtained through numerical simulation.

(2)

With reference to the dynamite blasting method, field tests of the high-pressure gas expansion method of rock breaking were carried out to determine its optimal hollowing method and rock-breaking effect. Based on the vibration velocities monitored in the field, the vibration attenuation law was explored and the prediction formula for the peak vibration velocity was established.

(3)

A comparative analysis of the dynamite blasting method and the high-pressure gas expansion method was carried out, with emphasis on the effects of different agent qualities, blasting center distances, and the application of engineering difficulties on the PPV. The relationship between the maximum agent quantity and the volume of rock breakage under the limit case, and a practical implementation scheme are discussed.

(4)

The study demonstrates that the high-pressure gas expansion method has low vibration and excellent rock-breaking effect, and is fully capable of replacing explosives in some special areas.