# Safety Distance of Shotcrete Subjected to Blasting Vibration in Large-Span High-Speed Railway Tunnels

Authors: Ao Li; Dingli Zhang; Qian Fang; Jiwei Luo; Liqiang Cao; Zhenyu Sun
Journal: Shock and Vibration
 (2019)

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## Abstract

The drill and blast method is widely used in constructing tunnels in rock. Unfortunately, blasting vibration can damage newly performed shotcrete layers which are major support structures to stabilize surrounding structures. Therefore, investigation of the influence of blasting on shotcrete and determining reasonable distance between blasting work face and shotcrete position is of great importance. In this paper, a large-span tunnel excavated by drill and blast method acting as a high-speed railway station has been investigated. Blast vibration in the tunnel was recorded using microseismic monitoring technique. Empirical prediction equations for peak particle velocity (PPV) were obtained through regression analysis based on the obtained monitoring data. The attenuation law of tensile stress imposed on shotcrete layer due to blasting and bond strength of shotcrete-rock interface was also investigated. Minimum safety distance between shotcrete and blasting positions was calculated based on bond failure criterion. Evolution law considering different factors including blasting charge, rock mass class, and setting time of shotcrete was also obtained, which could be applied to determine blast charge shotcrete arrangements for tunnel constructions in future. The obtained results showed that the safety of shotcrete could be ensured and shotcrete falling off the rock could be prevented under current blast constructions.


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## Body

## 1. Introduction

Shotcrete, or sprayed concrete, is a construction technique in which concrete is shot at high velocity onto a suspended surface. Performing shotcrete provides additional benefits such as excellent bonding with most substrates, particularly on those with complex forms or shapes, and rapid and instant capabilities. These advantages allow shotcrete to be widely used as a construction technique in tunnels excavated by the drill and blast method [1–3]. Usually shotcrete and blasting operations are performed alternately, and the main function of shotcrete is to provide a safe working environment for workers and facilitate subsequent operations of support construction such as installing metal meshes and bolts [4, 5]. Therefore, high capability of projecting shotcrete on rock surfaces is vital to the safety of workers and the function of tunnels [6].Using the drill and blast method, tunnels in rock are excavated by blasting large quantities of explosives. These detonations create stress waves that transport energy through rock and surrounding structures. Since shotcrete is applied near the blasting face, it is vulnerable to stress waves created by large-scale blasting in tunnels. Practically, the next blasting cycle should be performed after the final setting strength of shotcrete is reached and a certain distance should be kept between blasting and shotcrete positions. However, if shotcrete is exposed to vibrations at early ages, while it is still in hardening stage, cracks and sheddings may occur in the structure adversely affecting the function of hard concrete, even causing the failure of the whole support structure [7]. To ensure the security of shotcrete, the effect of blast-induced vibrations should be investigated and safety distance threshold from blasting work face, where shotcrete can withstand blast vibration, should be determined [8, 9], as shown in Figure 1.Figure 1
Schematic diagram of safety distance of shotcrete subjected to blast vibration in a tunnel.Blast-induced vibrations are usually characterized by two important parameters, peak particle velocity (PPV) and blast predominate frequency (f) [10, 11]. Researchers have shown that the failure of the inner structures of rock masses is caused by stress waves whose PPV value depends on the dynamic stress and strain of the rock mass [12, 13]. Therefore, once the course of vibration is recorded, its potential consequences can be assessed.Some researchers have investigated the effect of vibration caused by blasting on shotcrete through in situ tests [4–6, 14–16]. Blast vibration responses (especially PPV) of rock and shotcrete are measured with accelerometers and velocimeters placed on rock surfaces and at the floor or arch waist of tunnel. However, because the sensors are in incomplete contact with rocks, vibration signals are easily disturbed and only vibration on the rock surface is measured, but not on the shotcrete because the shotcrete had not been constructed yet when blasting vibration monitoring [6]. Meanwhile, the damage of rock mass at the crown is enormous compared with rock mass at the floor or arch waist because of the double effects of blasting and gravity of rock mass. Therefore, the vibration monitoring inside the rock and at the tunnel crown is vital for the security of shotcrete. In general, the common approach to investigate wave propagation characteristics is by field monitoring data regressed by empirical equations such as Sadovskii equation [17], which is widely used in blasting operations in China [18]. The Sadovsky equation can describe the attenuation of maximum blast vibration velocity (or PPV) which depends on blasting charge (Q), geotechnical parameters (K and α), and the distance between blasting work face and monitoring point (R). In evaluating the safety of the blast vibration of shotcrete, PPV and dominant frequency should be considered simultaneously. Different countries have different criteria for blast vibration to protect fresh concrete [6, 11]. By comparing with allowed values of PPV, security status can be evaluated and the safety distance of shotcrete can be determined.Numerical simulations have also been applied in the prediction of vibration damage to shotcrete due to tunnel explosions based on elastic stress wave theory and structural dynamics [7, 10, 19, 20]. Safety distance thresholds for shotcrete can be evaluated based on different criteria such as maximum tensile stress and Mohr–Coulomb criteria. Among different shotcrete criteria, maximum velocity components or tensile stresses should be compared with allowed values to decide whether shotcrete would fail or not. Therefore, critical distance between blasting work and shotcrete can be determined beyond which shotcrete can withstand blasting vibration. There are only a few theoretical solutions which mainly adopt ray-theoretical method and present mathematical laws to predict PPV based on different blast designs and rock parameters [13]. Based on the allowed value of vibration velocity, safety requirements including blasting parameters and shotcrete distance from blasting point can be determined. On the whole, for the numerical simulations and theoretical solutions, their accuracies depend on related input parameters which are difficult to determine and commonly need to be verified according to the field test results.In general, the safety of shotcrete subjected to blast vibration is affected by blast parameters, geological characteristics, and distance between blast and observation points [21]. It can also be determined by the failure criteria of shotcrete. Research has shown that the failure of shotcrete is mainly due to the yielding of shotcrete-rock interface rather than the destruction of shotcrete itself [22]. This paper aims to determine the safety distance of shotcrete based on the bond failure of shotcrete-rock interface subjected to blasting in tunnel excavations. In this paper, an analysis method based on both in situ tests and theoretical solutions has been used, an approach similar to that in [5–7, 22] but here applied for different geological conditions and tunnel geometries. The monitoring scheme with symmetry testing points inside the rock has been carried out for blast vibration monitoring in the large-span tunnel. Revealing the failure mechanism of shotcrete is of great significance and can ensure the security of the structure. The research methodology is as follows.Firstly, an empirical equation is derived for PPV using regression analysis based on in situ monitoring data. Secondly, the tensile stress imposed on shotcrete-rock interface is calculated through multireflections and transmissions solutions of blast stress wave. Thirdly, adhesive strength of the bond between shotcrete at different ages and rock under various rock conditions is put forth. Then, safety distance is derived based on the bond failure criterion of shotcrete-rock interface. Finally, some detailed guidelines are proposed for young shotcrete considering rock mass class and shotcrete ages.


## 2. Site Description and Field Monitoring

### 2.1. Project Overview

Beijing-Zhangjiakou high-speed railway is about 174 km long with 10 stations and is considered as a crucial link for 2022 Winter Olympics to be held in Beijing and Zhangjiakou in Hebei province (Figure2). Beijing-Zhangjiakou high-speed railway is under construction and is expected to be completed by the end of 2019 and reduces travel time between Beijing and Zhangjiakou from three hours to only one hour.Figure 2
Map of Beijing-Zhangjiakou high-speed railway.Badaling Great Wall Station (from DK67 + 815 to DK68 + 285) is an underground station located below the Guntiangou parking lot in Badaling scenic area. The overburden depth of the station is 102 m and is the deepest high-speed railway station in the world. The station has a 3-level underground structure including platform, hall floor, and equipment floor levels. At platform level (Figure3), the main structure of the station consists of three tunnels which integrate into a triple-arch tunnel. The large-span transition tunnel (from DK68 + 285 to DK68 + 448) with 5 different cross sections is located between the station and standard double-track single-tube tunnel, as shown in Figure 4. The maximum excavation span of the large-span transition tunnel is 32.7 m with an excavation area of 494.4 m2. As the traffic tunnel with the widest excavation span and largest excavation section area in the world, its construction is extremely difficult and has high safety risks [23].Figure 3
Design sketch of Badaling Great Wall Station.Figure 4
Layout and cross section of large-span tunnel (unit: m).Figure5 shows the typical geological profile of the large-span transition section tunnel from DK68 + 285 to DK68 + 448 along the direction of Zhangjiakou. The tunnel passes through a small (F1) and a large (F2) fault and fracture zone. Fault F2 intersects the tunnel at DK68 + 260–300 filled by a compresso-shear fracture with the attitude of 263°∠86°. Rock masses are generally complete with major 3–4 sets of largely developed joints. Groundwater in the area is bedrock fissure water with normal yield of about 2400 m3/d. Table 1 shows rock mass classification obtained according to Chinese classification basic quality (BQ) system and properties of large-span tunnel.Figure 5
Geological profile of large-span tunnel long the direction of Zhangjiakou.Table 1
Rock mass classification and properties of the large-span tunnel.
Mileage
Rock mass classification
Quality
V
p (m/s)
ρ (kg/m3)
Rock types
DK68 + 285–305
V
Very poor
1225
2230
Granite, monzontic granite, diorite-porphyrite
DK68 + 305–360
IV
Poor
3830
2570
Granite, diorite-porphyrite
DK68 + 360–448
III
Fair
4570
2630
Granite


### 2.2. Microseismic Monitoring Layout

Microseismic monitoring technology, an advanced and effective method for monitoring tunnel stability, has been employed in many tunnels [24]. According to this method, the energy released during blasting operations is acquired by geophones spread in certain patterns and analyzed using earthquake seismology and seismic migration techniques. The use of microseismic monitoring allows operators to better understand quantitative data on the location, level, and size of blasting [25]. Symmetric monitoring points inside the large-span tunnel were used for blast vibration monitoring.


#### 2.2.1. Monitoring System

The blasting microseismic monitoring hardware system was composed of vibration sensors, data collector, GPS clock synchronizer, fiber optic converter, and data processing system. Figure6 shows the diagram of microseismic monitoring system network. Single- and three-component vibration geophones with high sensitivity (200 V/m/s) and broad range of target acceptance frequency (4.5–1000 Hz) as well as a 24-channel data collector with high resolution (32 bit A/D, 24 bit A/D), high sampling rate (2000 Hz), high triggering accuracy (+1 μs), and low background noise (<0.15 μV RMS@2 ms, 0.09 μV RMS@2 ms) were adopted. Microseismic collector and monitoring terminal were connected with optical fiber to achieve remote view and control. Time accuracy was guaranteed with the combination of GPS clock synchronizer and optical fiber network.Figure 6
The diagram of microseismic monitoring system network.


#### 2.2.2. Monitoring Points

Two monitoring sections, DK68 + 290 (Section1) and DK68 + 440 (Section 2), were selected for the installation of sensors in the tunnel. Three boreholes were drilled in each section, each about 12 m deep. In each borehole, a three-component sensor (1∗, 2∗, and 3∗) was installed at the depth of 12 m, and a single-component sensor (4∗, 5∗, and 6∗) was placed at about 3 m away from hole entrance coupled using cement grouting (Figure 7). Figure 8 shows monitoring sensors and their installation diagram.Figure 7
Layout of measuring points inside the tunnel at DK68 + 290 (unit: m).Figure 8
Installation of monitoring sensors inside the tunnel: (a) vibration sensor and (b) installing position.
(a)
(b)


## 2.1. Project Overview

Beijing-Zhangjiakou high-speed railway is about 174 km long with 10 stations and is considered as a crucial link for 2022 Winter Olympics to be held in Beijing and Zhangjiakou in Hebei province (Figure2). Beijing-Zhangjiakou high-speed railway is under construction and is expected to be completed by the end of 2019 and reduces travel time between Beijing and Zhangjiakou from three hours to only one hour.Figure 2
Map of Beijing-Zhangjiakou high-speed railway.Badaling Great Wall Station (from DK67 + 815 to DK68 + 285) is an underground station located below the Guntiangou parking lot in Badaling scenic area. The overburden depth of the station is 102 m and is the deepest high-speed railway station in the world. The station has a 3-level underground structure including platform, hall floor, and equipment floor levels. At platform level (Figure3), the main structure of the station consists of three tunnels which integrate into a triple-arch tunnel. The large-span transition tunnel (from DK68 + 285 to DK68 + 448) with 5 different cross sections is located between the station and standard double-track single-tube tunnel, as shown in Figure 4. The maximum excavation span of the large-span transition tunnel is 32.7 m with an excavation area of 494.4 m2. As the traffic tunnel with the widest excavation span and largest excavation section area in the world, its construction is extremely difficult and has high safety risks [23].Figure 3
Design sketch of Badaling Great Wall Station.Figure 4
Layout and cross section of large-span tunnel (unit: m).Figure5 shows the typical geological profile of the large-span transition section tunnel from DK68 + 285 to DK68 + 448 along the direction of Zhangjiakou. The tunnel passes through a small (F1) and a large (F2) fault and fracture zone. Fault F2 intersects the tunnel at DK68 + 260–300 filled by a compresso-shear fracture with the attitude of 263°∠86°. Rock masses are generally complete with major 3–4 sets of largely developed joints. Groundwater in the area is bedrock fissure water with normal yield of about 2400 m3/d. Table 1 shows rock mass classification obtained according to Chinese classification basic quality (BQ) system and properties of large-span tunnel.Figure 5
Geological profile of large-span tunnel long the direction of Zhangjiakou.Table 1
Rock mass classification and properties of the large-span tunnel.
Mileage
Rock mass classification
Quality
V
p (m/s)
ρ (kg/m3)
Rock types
DK68 + 285–305
V
Very poor
1225
2230
Granite, monzontic granite, diorite-porphyrite
DK68 + 305–360
IV
Poor
3830
2570
Granite, diorite-porphyrite
DK68 + 360–448
III
Fair
4570
2630
Granite


## 2.2. Microseismic Monitoring Layout

Microseismic monitoring technology, an advanced and effective method for monitoring tunnel stability, has been employed in many tunnels [24]. According to this method, the energy released during blasting operations is acquired by geophones spread in certain patterns and analyzed using earthquake seismology and seismic migration techniques. The use of microseismic monitoring allows operators to better understand quantitative data on the location, level, and size of blasting [25]. Symmetric monitoring points inside the large-span tunnel were used for blast vibration monitoring.


### 2.2.1. Monitoring System

The blasting microseismic monitoring hardware system was composed of vibration sensors, data collector, GPS clock synchronizer, fiber optic converter, and data processing system. Figure6 shows the diagram of microseismic monitoring system network. Single- and three-component vibration geophones with high sensitivity (200 V/m/s) and broad range of target acceptance frequency (4.5–1000 Hz) as well as a 24-channel data collector with high resolution (32 bit A/D, 24 bit A/D), high sampling rate (2000 Hz), high triggering accuracy (+1 μs), and low background noise (<0.15 μV RMS@2 ms, 0.09 μV RMS@2 ms) were adopted. Microseismic collector and monitoring terminal were connected with optical fiber to achieve remote view and control. Time accuracy was guaranteed with the combination of GPS clock synchronizer and optical fiber network.Figure 6
The diagram of microseismic monitoring system network.


### 2.2.2. Monitoring Points

Two monitoring sections, DK68 + 290 (Section1) and DK68 + 440 (Section 2), were selected for the installation of sensors in the tunnel. Three boreholes were drilled in each section, each about 12 m deep. In each borehole, a three-component sensor (1∗, 2∗, and 3∗) was installed at the depth of 12 m, and a single-component sensor (4∗, 5∗, and 6∗) was placed at about 3 m away from hole entrance coupled using cement grouting (Figure 7). Figure 8 shows monitoring sensors and their installation diagram.Figure 7
Layout of measuring points inside the tunnel at DK68 + 290 (unit: m).Figure 8
Installation of monitoring sensors inside the tunnel: (a) vibration sensor and (b) installing position.
(a)
(b)


## 2.2.1. Monitoring System

The blasting microseismic monitoring hardware system was composed of vibration sensors, data collector, GPS clock synchronizer, fiber optic converter, and data processing system. Figure6 shows the diagram of microseismic monitoring system network. Single- and three-component vibration geophones with high sensitivity (200 V/m/s) and broad range of target acceptance frequency (4.5–1000 Hz) as well as a 24-channel data collector with high resolution (32 bit A/D, 24 bit A/D), high sampling rate (2000 Hz), high triggering accuracy (+1 μs), and low background noise (<0.15 μV RMS@2 ms, 0.09 μV RMS@2 ms) were adopted. Microseismic collector and monitoring terminal were connected with optical fiber to achieve remote view and control. Time accuracy was guaranteed with the combination of GPS clock synchronizer and optical fiber network.Figure 6
The diagram of microseismic monitoring system network.


## 2.2.2. Monitoring Points

Two monitoring sections, DK68 + 290 (Section1) and DK68 + 440 (Section 2), were selected for the installation of sensors in the tunnel. Three boreholes were drilled in each section, each about 12 m deep. In each borehole, a three-component sensor (1∗, 2∗, and 3∗) was installed at the depth of 12 m, and a single-component sensor (4∗, 5∗, and 6∗) was placed at about 3 m away from hole entrance coupled using cement grouting (Figure 7). Figure 8 shows monitoring sensors and their installation diagram.Figure 7
Layout of measuring points inside the tunnel at DK68 + 290 (unit: m).Figure 8
Installation of monitoring sensors inside the tunnel: (a) vibration sensor and (b) installing position.
(a)
(b)


## 3. Analysis of Blast Velocity and Stress Based on Microseismic Monitoring Data

Blasting vibration can be evaluated based on vibration velocity, acceleration, frequency, etc. PPV andf are often applied for this purpose. PPV is defined as the maximum motion velocity of a particle on or in the rock induced by the passage of blast vibration waves [26]. Moment magnitude (Mw) quantitative measure of an earthquake’s magnitude (or relative size) is designed to produce more accuracy accounting for the total energy released by an earthquake or blasting. To fully record the motion, it is necessary to measure three perpendicular longitudinal (x), transverse (y), and vertical (z) components. The peak values of individual components rarely occur at the same instant [27].


### 3.1. Monitoring Results

Microseismic monitoring data of blast vibration including PPV with three perpendicular components, the blasting charge (Q), the distance from the blasting point to the measuring point (R), the predominate frequency (f), and moment magnitude (Mw) were measured.Monitoring results for 23 sets of blasting in the large-span tunnel were collected. One set of monitoring data in the tunnel is shown in Table2, where PPV-X, PPV-Y, and PPV-Z are the maximum values of velocity vectors along longitudinal, transverse, and vertical directions, respectively.Table 2
One set of monitoring data.
Test ID (date)
M
w
Monitoring point
R (m)
f (Hz)
PPV-X (mm/s)
PPV-Y (mm/s)
PPV-Z (mm/s)
Q (kg)
170671 (2017/6/3)
−0.05
1
∗-I
44.2
101
0.24
0.38
0.45
120
4
∗-I
41
—
—
0.82
2
∗-I
51.2
0.24
0.62
0.56
5
∗-I
44.5
—
—
0.68
3
∗-I
37.6
0.53
0.56
0.8
6
∗-I
38.2
—
—
0.91
1
∗-II
73.1
0.10
0.22
0.23
4
∗-II
40
—
—
0.85
2
∗-II
73.3
0.11
0.27
0.26
5
∗-II
68.3
—
—
0.32
3
∗-II
64.8
0.14
0.13
0.28
6
∗-II
64.1
—
—
0.36


### 3.2. Empirical Equation of PPV

Explosion-induced vibration features are mainly influenced by blasting source and geological factors [28]. Several empirical relationships have been suggested by different investigators to describe the attenuation of blast vibration [10–13]. It is hard to determine which empirical formula is the best one, because the fitting errors of different empirical formulas cannot be avoided. The Sadovsky equation covers two site-specific parameters considering the effects of blasting and geology, and they can be determined by regression analysis [17]. Therefore, the Sadovsky equation is most widely used to study the attenuation of blast vibration in China [18], that is,(1)V=KQ3Ra,where V is the particle vibration velocity (mm/s).Equation (1) can be transformed into the following equation:(2)lnV=lnK+a×lnQ3R.SubstitutingY=lnV, b=lnK, and X=lnQ1/3/R into equation (2), the following linear equation can be obtained:(3)Y=b+αX.Based on a large amount of measured data, linear regression analysis is used to obtain a linear relationship betweenY and X data. The parameters K and α can then be obtained. Figure 9 shows empirical fitting curves of PPV attenuation law along longitudinal, transverse, and vertical directions drawn based on the Sadovsky equation (equation (1)) using monitoring data. Attenuation coefficient α was obtained as a fixed value of α=2.3 considering the geological conditions in the large-span tunnel. The fitting parameters of empirical equations along three directions are shown in Table 3.Figure 9
Fitting curves between PPV andR with Q = 120 kg.Table 3
Fitting results of PPV-X, PPV-Y, and PPV-Z (unit: mm/s).
PPV-X
PPV-Y
PPV-Z
Fitting equations
V
=
45
Q
3
/
R
2.3
V
=
65
Q
3
/
R
2.3
V
=
90
Q
3
/
R
2.3The large-span tunnels were excavated below the Badaling Great Wall Scenic, and the overburden depth of the tunnels varied from 52 m to 85 m. To ensure the safety of historic buildings and service infrastructures, the blasting vibration must be strictly controlled. Therefore, the precise blasting technology of electronic detonator was conducted. Compared with conventional blasting technology, the precise blasting technology can reduce the blasting vibration velocity from 5 cm/s to 0.2 cm/s, which makes the fitting parametersK relatively small compared to the published results [4–7]. Analysis of monitoring data (Table 3 and Figure 9) showed that PPV-Z values at blasting vibration monitoring points were about 1.5–2 times higher than PPV-X and PPV-Y. It was concluded that vertical velocity had a major controlling effect on blasting vibration under current geotechnical conditions. Since the monitoring scheme with symmetry testing points inner the tunnel was carried out for blast vibration monitoring under the large-span tunnel construction, distance between the blasting point and monitoring sensors R varied from 38 to 73 m. Because the propagation paths of blasting wave are all in the rock, extrapolations outside this range can also be permitted using the fitted curves.


### 3.3. Distribution of Vibration Predominate Frequency

Previous studies have shown that vibration frequency plays a significant role in vibration-induced rock damages. The natural frequencies of concrete structures are generally below 10 Hz; therefore, high-frequency vibration is beneficial to structural safety because of reduction in the probability of resonance [29]. Blast signal was processed using microseismic analysis software. The diagrams of waveform, time-frequency, and spectrum of a typical blast are shown in Figure 10. As can be seen in Figure 10, the duration time of a typical blasting is 0.7 s. The frequency of a blast was in the range of 20 to 80 Hz, and predominant frequency was about 60 Hz.Figure 10
Blasting signal: (a) waveform and time-frequency analysis and (b) spectrum analysis.
(a)
(b)Distribution of vibration predominate frequency of the 23 blasting signal sets is shown in Figure11. As can be seen, frequency ranged from 55 to 120 Hz, of which 70% of the obtained data were in the range of 90–110 Hz. Hence it was concluded that, under the conditions of this experiment, blasts inside tunnel would not create resonance in concrete structure.Figure 11
Distribution of vibration predominate frequency.


### 3.4. Analysis of Blasting Stress Based on PPV

Strain and dynamic stress can be determined from the value of PPV [30]. Dynamic stress σ corresponding to the PPV of the material due to blasting was [31, 32](4)σ=KnPPV,(5)Kn=ρVp,where Kn is the wave impedance of material (kg/m2·s), ρ is the density of material (kg/m3), and Vp is propagation velocity of P wave (m/s) through the material.


#### 3.4.1. Wave Impedance of Rock Mass and Shotcrete

P waves were focused on due to the first-arrival principle in the paper. The propagation velocity Vp of P waves (m/s) in an elastic material is given by its stiffness, and the density of material is as follows [33, 34]:(6)Vp=Eρ,where E is elastic modulus (GPa).In this work, it was assumed that the development of elastic modulusE for hardening shotcrete followed an empirical function derived from a large number of tests [32, 35]. The elastic modulus Et of C20 shotcrete at different ages t (days) is given as follows:(7)Et=36.721−e−0.4t0.34.By substituting equations (4) and (5) into equation (3), the equation of wave impedance of shotcrete was obtained as follows:(8)ρSVPS=EtρS,where ρS is shotcrete density which was assumed to be 2300 kg·m−3 and VPS is propagation velocity of P wave (m/s) through shotcrete.Based on rock mass properties of large-span tunnel summarized in Table1, the wave impedances of different rock masses could be obtained by equation (3).


#### 3.4.2. Reflection and Transmission of Blasting Wave

Due to different material properties, vibration velocities induced by dynamic loads in shotcrete are different from those in rock masses [32]. Based on the wave theory of reflection and transmission, a wave that is incident (vI) on a boundary generally creates reflected (vR) and transmitted (vT) waves when passing from medium 1 to medium 2. The velocities and stresses of both reflected and transmitted waves could be expressed as [36, 37](9)vR=−FvI,σR=FσI,vT=nTvI,σT=TσI,F=1−n1+n,T=21+n,n=ρVp1ρVp2,where σI is the compressive stress of incident wave vI with σI=ρVp1vI, ρVp1, and ρVp2 are wave impedances in media 1 and 2, respectively, n is wave impedance coefficient ratio of medium 1 to medium 2, F is the reflection coefficient, and T is the transmission coefficient.During tunnel excavation, explosive compressive stress wave (vI) propagating in rock mass was divided into reflected (vR) and transmission (vT) stress waves in shotcrete when encountering rock-shotcrete interface as shown in Figure 12-①. Based on the wave impedances of rock mass (KR) and shotcrete (KS) obtained in Section 3.4.1, the velocities and stresses of vT and vR were given as(10)vR=−F1vI,σR=F1σI,vT=n1T1vI,σT=T1σI,where n1, F1, and T1 are wave impedance coefficient ratio and reflection and transmission coefficients from rock mass to shotcrete, respectively.Figure 12
Three times of reflections and transmissions of blast stress wave.Stress wave theory states that blasting stress wave (vT) only turns into reflection wave (vTR) when passing from the free surface of shotcrete to air because there is no transmission wave with the wave impedance of air (KA) being close to zero as shown in Figure 12-②. The velocities and stresses of vTR and vTT can be calculated as follows:(11)vTR=−F2n1T1vI=n1T1vI,σTR=F2T1σI=−T1σI,vTT=n2T2n1T1vI=0,σTT=T2T1σI=0,where n2, F2, and T2 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to air, respectively, and the values of F2 and T2 are −1 and 0, respectively.Furthermore,vTR was continuously reflected and transmitted when encountering with rock-shotcrete interface as shown in Figure 12-③. The velocities and stresses of vTRR and vTRT were calculated as follows:(12)vTRT=−F3n1T1vI,σTRT=−F3T1σI,vTRT=n3T3n1T1vI,σTRT=−T3T1σI,where n3, F3, and T3 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to rock mass, respectively.Under the existing blast conditions, PPV-Z was much higher than horizontal velocities. Therefore, according to the results obtained from empirical equations for PPV mentioned above, vI as the maximum vibration wave had to be equal to PPV-Z. As shown in Figure 12, after three reflection and transmission cycles of blast stress wave, it was found that only σTR and σTRT were tensile stresses, of which σTRT was imposed on shotcrete-rock interface and σTR was imposed on shotcrete. This could be expressed as(13)σTR=−T1σI=−21+n1σI,σTRT=−n1T12σI=DTRTσI,DTRT=−4n11+n12,where DTRT is the coefficient of tensile stress imposed on the interface.


## 3.1. Monitoring Results

Microseismic monitoring data of blast vibration including PPV with three perpendicular components, the blasting charge (Q), the distance from the blasting point to the measuring point (R), the predominate frequency (f), and moment magnitude (Mw) were measured.Monitoring results for 23 sets of blasting in the large-span tunnel were collected. One set of monitoring data in the tunnel is shown in Table2, where PPV-X, PPV-Y, and PPV-Z are the maximum values of velocity vectors along longitudinal, transverse, and vertical directions, respectively.Table 2
One set of monitoring data.
Test ID (date)
M
w
Monitoring point
R (m)
f (Hz)
PPV-X (mm/s)
PPV-Y (mm/s)
PPV-Z (mm/s)
Q (kg)
170671 (2017/6/3)
−0.05
1
∗-I
44.2
101
0.24
0.38
0.45
120
4
∗-I
41
—
—
0.82
2
∗-I
51.2
0.24
0.62
0.56
5
∗-I
44.5
—
—
0.68
3
∗-I
37.6
0.53
0.56
0.8
6
∗-I
38.2
—
—
0.91
1
∗-II
73.1
0.10
0.22
0.23
4
∗-II
40
—
—
0.85
2
∗-II
73.3
0.11
0.27
0.26
5
∗-II
68.3
—
—
0.32
3
∗-II
64.8
0.14
0.13
0.28
6
∗-II
64.1
—
—
0.36


## 3.2. Empirical Equation of PPV

Explosion-induced vibration features are mainly influenced by blasting source and geological factors [28]. Several empirical relationships have been suggested by different investigators to describe the attenuation of blast vibration [10–13]. It is hard to determine which empirical formula is the best one, because the fitting errors of different empirical formulas cannot be avoided. The Sadovsky equation covers two site-specific parameters considering the effects of blasting and geology, and they can be determined by regression analysis [17]. Therefore, the Sadovsky equation is most widely used to study the attenuation of blast vibration in China [18], that is,(1)V=KQ3Ra,where V is the particle vibration velocity (mm/s).Equation (1) can be transformed into the following equation:(2)lnV=lnK+a×lnQ3R.SubstitutingY=lnV, b=lnK, and X=lnQ1/3/R into equation (2), the following linear equation can be obtained:(3)Y=b+αX.Based on a large amount of measured data, linear regression analysis is used to obtain a linear relationship betweenY and X data. The parameters K and α can then be obtained. Figure 9 shows empirical fitting curves of PPV attenuation law along longitudinal, transverse, and vertical directions drawn based on the Sadovsky equation (equation (1)) using monitoring data. Attenuation coefficient α was obtained as a fixed value of α=2.3 considering the geological conditions in the large-span tunnel. The fitting parameters of empirical equations along three directions are shown in Table 3.Figure 9
Fitting curves between PPV andR with Q = 120 kg.Table 3
Fitting results of PPV-X, PPV-Y, and PPV-Z (unit: mm/s).
PPV-X
PPV-Y
PPV-Z
Fitting equations
V
=
45
Q
3
/
R
2.3
V
=
65
Q
3
/
R
2.3
V
=
90
Q
3
/
R
2.3The large-span tunnels were excavated below the Badaling Great Wall Scenic, and the overburden depth of the tunnels varied from 52 m to 85 m. To ensure the safety of historic buildings and service infrastructures, the blasting vibration must be strictly controlled. Therefore, the precise blasting technology of electronic detonator was conducted. Compared with conventional blasting technology, the precise blasting technology can reduce the blasting vibration velocity from 5 cm/s to 0.2 cm/s, which makes the fitting parametersK relatively small compared to the published results [4–7]. Analysis of monitoring data (Table 3 and Figure 9) showed that PPV-Z values at blasting vibration monitoring points were about 1.5–2 times higher than PPV-X and PPV-Y. It was concluded that vertical velocity had a major controlling effect on blasting vibration under current geotechnical conditions. Since the monitoring scheme with symmetry testing points inner the tunnel was carried out for blast vibration monitoring under the large-span tunnel construction, distance between the blasting point and monitoring sensors R varied from 38 to 73 m. Because the propagation paths of blasting wave are all in the rock, extrapolations outside this range can also be permitted using the fitted curves.


## 3.3. Distribution of Vibration Predominate Frequency

Previous studies have shown that vibration frequency plays a significant role in vibration-induced rock damages. The natural frequencies of concrete structures are generally below 10 Hz; therefore, high-frequency vibration is beneficial to structural safety because of reduction in the probability of resonance [29]. Blast signal was processed using microseismic analysis software. The diagrams of waveform, time-frequency, and spectrum of a typical blast are shown in Figure 10. As can be seen in Figure 10, the duration time of a typical blasting is 0.7 s. The frequency of a blast was in the range of 20 to 80 Hz, and predominant frequency was about 60 Hz.Figure 10
Blasting signal: (a) waveform and time-frequency analysis and (b) spectrum analysis.
(a)
(b)Distribution of vibration predominate frequency of the 23 blasting signal sets is shown in Figure11. As can be seen, frequency ranged from 55 to 120 Hz, of which 70% of the obtained data were in the range of 90–110 Hz. Hence it was concluded that, under the conditions of this experiment, blasts inside tunnel would not create resonance in concrete structure.Figure 11
Distribution of vibration predominate frequency.


## 3.4. Analysis of Blasting Stress Based on PPV

Strain and dynamic stress can be determined from the value of PPV [30]. Dynamic stress σ corresponding to the PPV of the material due to blasting was [31, 32](4)σ=KnPPV,(5)Kn=ρVp,where Kn is the wave impedance of material (kg/m2·s), ρ is the density of material (kg/m3), and Vp is propagation velocity of P wave (m/s) through the material.


### 3.4.1. Wave Impedance of Rock Mass and Shotcrete

P waves were focused on due to the first-arrival principle in the paper. The propagation velocity Vp of P waves (m/s) in an elastic material is given by its stiffness, and the density of material is as follows [33, 34]:(6)Vp=Eρ,where E is elastic modulus (GPa).In this work, it was assumed that the development of elastic modulusE for hardening shotcrete followed an empirical function derived from a large number of tests [32, 35]. The elastic modulus Et of C20 shotcrete at different ages t (days) is given as follows:(7)Et=36.721−e−0.4t0.34.By substituting equations (4) and (5) into equation (3), the equation of wave impedance of shotcrete was obtained as follows:(8)ρSVPS=EtρS,where ρS is shotcrete density which was assumed to be 2300 kg·m−3 and VPS is propagation velocity of P wave (m/s) through shotcrete.Based on rock mass properties of large-span tunnel summarized in Table1, the wave impedances of different rock masses could be obtained by equation (3).


### 3.4.2. Reflection and Transmission of Blasting Wave

Due to different material properties, vibration velocities induced by dynamic loads in shotcrete are different from those in rock masses [32]. Based on the wave theory of reflection and transmission, a wave that is incident (vI) on a boundary generally creates reflected (vR) and transmitted (vT) waves when passing from medium 1 to medium 2. The velocities and stresses of both reflected and transmitted waves could be expressed as [36, 37](9)vR=−FvI,σR=FσI,vT=nTvI,σT=TσI,F=1−n1+n,T=21+n,n=ρVp1ρVp2,where σI is the compressive stress of incident wave vI with σI=ρVp1vI, ρVp1, and ρVp2 are wave impedances in media 1 and 2, respectively, n is wave impedance coefficient ratio of medium 1 to medium 2, F is the reflection coefficient, and T is the transmission coefficient.During tunnel excavation, explosive compressive stress wave (vI) propagating in rock mass was divided into reflected (vR) and transmission (vT) stress waves in shotcrete when encountering rock-shotcrete interface as shown in Figure 12-①. Based on the wave impedances of rock mass (KR) and shotcrete (KS) obtained in Section 3.4.1, the velocities and stresses of vT and vR were given as(10)vR=−F1vI,σR=F1σI,vT=n1T1vI,σT=T1σI,where n1, F1, and T1 are wave impedance coefficient ratio and reflection and transmission coefficients from rock mass to shotcrete, respectively.Figure 12
Three times of reflections and transmissions of blast stress wave.Stress wave theory states that blasting stress wave (vT) only turns into reflection wave (vTR) when passing from the free surface of shotcrete to air because there is no transmission wave with the wave impedance of air (KA) being close to zero as shown in Figure 12-②. The velocities and stresses of vTR and vTT can be calculated as follows:(11)vTR=−F2n1T1vI=n1T1vI,σTR=F2T1σI=−T1σI,vTT=n2T2n1T1vI=0,σTT=T2T1σI=0,where n2, F2, and T2 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to air, respectively, and the values of F2 and T2 are −1 and 0, respectively.Furthermore,vTR was continuously reflected and transmitted when encountering with rock-shotcrete interface as shown in Figure 12-③. The velocities and stresses of vTRR and vTRT were calculated as follows:(12)vTRT=−F3n1T1vI,σTRT=−F3T1σI,vTRT=n3T3n1T1vI,σTRT=−T3T1σI,where n3, F3, and T3 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to rock mass, respectively.Under the existing blast conditions, PPV-Z was much higher than horizontal velocities. Therefore, according to the results obtained from empirical equations for PPV mentioned above, vI as the maximum vibration wave had to be equal to PPV-Z. As shown in Figure 12, after three reflection and transmission cycles of blast stress wave, it was found that only σTR and σTRT were tensile stresses, of which σTRT was imposed on shotcrete-rock interface and σTR was imposed on shotcrete. This could be expressed as(13)σTR=−T1σI=−21+n1σI,σTRT=−n1T12σI=DTRTσI,DTRT=−4n11+n12,where DTRT is the coefficient of tensile stress imposed on the interface.


## 3.4.1. Wave Impedance of Rock Mass and Shotcrete

P waves were focused on due to the first-arrival principle in the paper. The propagation velocity Vp of P waves (m/s) in an elastic material is given by its stiffness, and the density of material is as follows [33, 34]:(6)Vp=Eρ,where E is elastic modulus (GPa).In this work, it was assumed that the development of elastic modulusE for hardening shotcrete followed an empirical function derived from a large number of tests [32, 35]. The elastic modulus Et of C20 shotcrete at different ages t (days) is given as follows:(7)Et=36.721−e−0.4t0.34.By substituting equations (4) and (5) into equation (3), the equation of wave impedance of shotcrete was obtained as follows:(8)ρSVPS=EtρS,where ρS is shotcrete density which was assumed to be 2300 kg·m−3 and VPS is propagation velocity of P wave (m/s) through shotcrete.Based on rock mass properties of large-span tunnel summarized in Table1, the wave impedances of different rock masses could be obtained by equation (3).


## 3.4.2. Reflection and Transmission of Blasting Wave

Due to different material properties, vibration velocities induced by dynamic loads in shotcrete are different from those in rock masses [32]. Based on the wave theory of reflection and transmission, a wave that is incident (vI) on a boundary generally creates reflected (vR) and transmitted (vT) waves when passing from medium 1 to medium 2. The velocities and stresses of both reflected and transmitted waves could be expressed as [36, 37](9)vR=−FvI,σR=FσI,vT=nTvI,σT=TσI,F=1−n1+n,T=21+n,n=ρVp1ρVp2,where σI is the compressive stress of incident wave vI with σI=ρVp1vI, ρVp1, and ρVp2 are wave impedances in media 1 and 2, respectively, n is wave impedance coefficient ratio of medium 1 to medium 2, F is the reflection coefficient, and T is the transmission coefficient.During tunnel excavation, explosive compressive stress wave (vI) propagating in rock mass was divided into reflected (vR) and transmission (vT) stress waves in shotcrete when encountering rock-shotcrete interface as shown in Figure 12-①. Based on the wave impedances of rock mass (KR) and shotcrete (KS) obtained in Section 3.4.1, the velocities and stresses of vT and vR were given as(10)vR=−F1vI,σR=F1σI,vT=n1T1vI,σT=T1σI,where n1, F1, and T1 are wave impedance coefficient ratio and reflection and transmission coefficients from rock mass to shotcrete, respectively.Figure 12
Three times of reflections and transmissions of blast stress wave.Stress wave theory states that blasting stress wave (vT) only turns into reflection wave (vTR) when passing from the free surface of shotcrete to air because there is no transmission wave with the wave impedance of air (KA) being close to zero as shown in Figure 12-②. The velocities and stresses of vTR and vTT can be calculated as follows:(11)vTR=−F2n1T1vI=n1T1vI,σTR=F2T1σI=−T1σI,vTT=n2T2n1T1vI=0,σTT=T2T1σI=0,where n2, F2, and T2 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to air, respectively, and the values of F2 and T2 are −1 and 0, respectively.Furthermore,vTR was continuously reflected and transmitted when encountering with rock-shotcrete interface as shown in Figure 12-③. The velocities and stresses of vTRR and vTRT were calculated as follows:(12)vTRT=−F3n1T1vI,σTRT=−F3T1σI,vTRT=n3T3n1T1vI,σTRT=−T3T1σI,where n3, F3, and T3 are wave impedance coefficient ratio and reflection and transmission coefficients from shotcrete to rock mass, respectively.Under the existing blast conditions, PPV-Z was much higher than horizontal velocities. Therefore, according to the results obtained from empirical equations for PPV mentioned above, vI as the maximum vibration wave had to be equal to PPV-Z. As shown in Figure 12, after three reflection and transmission cycles of blast stress wave, it was found that only σTR and σTRT were tensile stresses, of which σTRT was imposed on shotcrete-rock interface and σTR was imposed on shotcrete. This could be expressed as(13)σTR=−T1σI=−21+n1σI,σTRT=−n1T12σI=DTRTσI,DTRT=−4n11+n12,where DTRT is the coefficient of tensile stress imposed on the interface.


## 4. Determination of Safety Distance of Shotcrete under Bond Failure Criterion

The most fundamental characteristic of shotcrete is its ability to adhere to rock surface which depends on the adhesion strength between shotcrete and rock [32]. It has been found that the failure of shotcrete support is mainly due to the separation of shotcrete and rock at the rock-shotcrete interface [38]. Therefore, to determine the security of shotcrete, the bond strength of shotcrete-rock interface should be compared with the tensile stress of interface caused by blasting.


### 4.1. Bond Strength of Shotcrete-Rock Interface

The bond strength of shotcrete-rock interfaces with C20 shotcrete and rock masses with different classes within 28 days was obtained as follows [32, 36]:(14)σb=2.345σ24hbe−0.858t−0.97,where t is shotcrete age (day) and σ24hb is average evaluation bond strength within 24 hours (MPa), and its value should not be lower than 0.8, 0.5, 0.42, and 0.31 MPa for rock mass classes of II, III, IV, and V, respectively [39].As shown in Figure13, the mechanical parameters of shotcrete were closely related to its age 1–3, 3–7, and 7–28 days are typical curing ages of shotcrete. And the bond strength is in the rapid growth stage within 3 days.Figure 13
Bond strength of interface between shotcrete and different rock mass classes within 28 days.


### 4.2. Calculation of Safety Distance of Shotcrete

Shotcrete-rock interface may suffer from bond failure when maximum tensile stress caused by blasting exceeds the bond strength of the interface which can be expressed as [40](15)σp>σb,where σp is maximum tensile stress with σp=σTRT and σb is the bond strength of shotcrete-rock interface.To ensure the security of shotcrete, the tensile stress of rock-shotcrete interface caused by blasting should be lower than its bond strength. Therefore, the safety distance threshold from blasting work face beyond which the shotcrete is able to withstand blasting vibration has to be derived. Substituting the formulas ofσp and σb obtained in Sections 3.2, 3.4, and 4.1 into equation (15), minimum safety distance equation can be expressed as(16)Rmin=SRexp−0.858t−0.97−1/2.3,SR=Q1/324.8σ24hbKnDTRT−1/2.3,where Rmin is minimum safety distance and SR is a parameter related to blasting charge and geotechnical condition.Figure14 shows that the safety distance of shotcrete is decreased with the increase of age. Also, blasting charge is decreased with the weakening of rock mass to validly reduce the blast vibration. Blasting charge of classes III, IV, and V rock mass conditions were 120, 100, and 80 kg, respectively. Hence, as shown in Figure 14, safety distance is decreased with rock mass condition changing from III to V.Figure 14
Relationship between minimum safety distances and age of concrete for different rock mass class conditions.Because the propagation paths of blasting wave are all in the rock, the PPV can also be predicated using the fitted curves when the distanceR is outside this range, though the distances between the blasting points and monitoring sensors R are within 38–73 m. The sensitivity analysis was conducted to quantify the effects of several inputs parameters which were blasting charge, rock mass class, and age of shotcrete. According to the sensitivity analysis results in Table 4, rock mass class has the greatest influence on safety distance, followed by age of shotcrete and blasting charge.Table 4
Sensitivity of different parameters affecting safety distances.
Parameters
Range of parameters
Sensitivity of parameters
Rock mass class
III, IV, V
0.96
Blasting chargeQ (kg)
140, 120, 100, 80, 60
0.43
Age of shotcretet (h)
0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6
0.50In Chinese Safety Standard for Blasting Vibration (GB6722-2014), some standard values have been provided for safe PPV of mass fresh concrete taking into account vibration frequency, as summarized in Table5 [18]. Based on the empirical equation obtained for PPV-Z and blast predominant frequency in Sections 3.2 and 3.3, minimum safety distance was obtained to satisfy PPV safety standard.Table 5
Safety standard of blasting vibration for mass fresh concrete suggested in Chinese Safety Standard for Blasting Vibration (unit: cm/s).
Fresh concrete of C20
Safety standard of blasting vibration velocity (cm/s)
Predominate frequencyf (Hz)
≤10
10–50
>50
Concrete age
0∼3 d
1.5∼2
2∼2.5
2.5∼3
3∼7 d
3∼4
4∼5
5∼7
7∼28 d
7∼8
8∼10
10∼12Minimum safety distance thresholds for shotcrete were evaluated using bond failure criterion and Chinese Safety Standard for Blasting Vibration, and the obtained results are summarized as shown in Table6. By comparing minimum safety distances determined based on two different criteria, namely, bond failure criterion and Chinese Safety Standard Blasting Vibration, it was observed that both results complied well under classes III and IV rock mass conditions. However, under class V rock mass condition, minimum safety distance using bond failure criterion was much lower. The reason is that rock mass properties under class V condition were significantly different from those under class III and IV conditions, as can be seen in Table 1. The differences in properties were taken into sufficient consideration when using bond failure criterion, but this was not the case for Chinese Safety Standard for Blasting Vibration. Therefore, minimum safety distance using bond failure criterion was found to be more precise and practical under complex conditions.Table 6
Minimum safety distances of shotcretes subjected to blasting vibration using two different criteria (unit: m).
Rock mass class
Q (kg)
Bond failure criterion
Chinese safety standard
0.5–3 d
3–7 d
7–28 d
0–3 d
3–7 d
7–28 d
III
120
5.27–9.24
4.83–5.27
4.83–4.97
7.95–8.61
5.50–6.37
4.35–4.71
IV
100
5.02–8.89
4.56–5.02
4.56–4.71
7.48–8.10
5.18–5.99
4.10–4.43
V
80
2.92–5.52
2.49–2.92
2.49–2.67
6.95–7.52
4.81–5.56
3.80–4.12In this project, the shotcrete of steel fiber concrete with two layers was adopted as the support system. The distance that the excavation of the upper bench lags behind the lower bench was 30 m. The shotcrete thicknesses of primary and secondary layers are 150 mm and 200 mm, respectively. Since primary shotcrete was too close to blasting face, blasting vibration could affect primary shotcrete structure and cause irreversible damage. Therefore, here the safety of secondary shotcrete was considered. Based on excavation and support processes, the distance between secondary shotcrete and blasting point was above 6 m (2 excavation cycles), and the blast was carried out 3 days after shotcrete was performed. Hence, according to minimum safety distances summarized in Table6, the safety of secondary shotcrete was ensured and shotcrete falling off was prevented under the current blast construction.


### 4.3. Recommendations for the Security of Shotcrete

In the construction of large-span tunnels, blasting vibration may cause undesired damages to shotcrete. Based on the above analyses, safety distance can be determined to ensure the security of shotcrete according to the monitoring results of blasting vibration. However, due to the tight time limits of large construction projects, blasting is often performed before bond strength of shotcrete is reached and with the distance between blast work face and shotcrete below safety distance. Despite these problems and difficulties, some effective measurements can be taken to ensure the safety of shotcrete construction, as follows:(1)
Steel fiber shotcretes have high early strength which can improve bond the strength of shotcretes to withstand blast loads in tunnel excavations in short time periods [1, 2, 41–43]. According to equation (16), adopting steel fiber concrete can improve the bond characteristic of the interface (σ24hb) and thus increases the safety distance of shotcrete.(2)
Operation sequences in tunnel excavation can be ordered to reduce blast charge and therefore significantly controls blast vibration [21, 44]. A certain distance should be kept between upper and lower benches to keep the shotcrete from being repeatedly disturbed by blasting in a short time. According to equation (16), when blasting charge was decreased, safety distance of shotcrete was also decreased.(3)
Performing multiple shotcrete layers is an effective method to decrease blasting damage [35, 43]. The initial shotcrete with low layer thickness was performed to seal the rock mass to facilitate the installation of metal meshes and bolts. The subsequent concrete layer with higher thickness was sprayed often with 1–3 days or 1–2 excavation cycle delay to consolidate the compound system of rock mass and support. Because of the increased distance between blast point and shotcrete, the blast vibration imposed on subsequent shotcrete was dramatically decreased.


## 4.1. Bond Strength of Shotcrete-Rock Interface

The bond strength of shotcrete-rock interfaces with C20 shotcrete and rock masses with different classes within 28 days was obtained as follows [32, 36]:(14)σb=2.345σ24hbe−0.858t−0.97,where t is shotcrete age (day) and σ24hb is average evaluation bond strength within 24 hours (MPa), and its value should not be lower than 0.8, 0.5, 0.42, and 0.31 MPa for rock mass classes of II, III, IV, and V, respectively [39].As shown in Figure13, the mechanical parameters of shotcrete were closely related to its age 1–3, 3–7, and 7–28 days are typical curing ages of shotcrete. And the bond strength is in the rapid growth stage within 3 days.Figure 13
Bond strength of interface between shotcrete and different rock mass classes within 28 days.


## 4.2. Calculation of Safety Distance of Shotcrete

Shotcrete-rock interface may suffer from bond failure when maximum tensile stress caused by blasting exceeds the bond strength of the interface which can be expressed as [40](15)σp>σb,where σp is maximum tensile stress with σp=σTRT and σb is the bond strength of shotcrete-rock interface.To ensure the security of shotcrete, the tensile stress of rock-shotcrete interface caused by blasting should be lower than its bond strength. Therefore, the safety distance threshold from blasting work face beyond which the shotcrete is able to withstand blasting vibration has to be derived. Substituting the formulas ofσp and σb obtained in Sections 3.2, 3.4, and 4.1 into equation (15), minimum safety distance equation can be expressed as(16)Rmin=SRexp−0.858t−0.97−1/2.3,SR=Q1/324.8σ24hbKnDTRT−1/2.3,where Rmin is minimum safety distance and SR is a parameter related to blasting charge and geotechnical condition.Figure14 shows that the safety distance of shotcrete is decreased with the increase of age. Also, blasting charge is decreased with the weakening of rock mass to validly reduce the blast vibration. Blasting charge of classes III, IV, and V rock mass conditions were 120, 100, and 80 kg, respectively. Hence, as shown in Figure 14, safety distance is decreased with rock mass condition changing from III to V.Figure 14
Relationship between minimum safety distances and age of concrete for different rock mass class conditions.Because the propagation paths of blasting wave are all in the rock, the PPV can also be predicated using the fitted curves when the distanceR is outside this range, though the distances between the blasting points and monitoring sensors R are within 38–73 m. The sensitivity analysis was conducted to quantify the effects of several inputs parameters which were blasting charge, rock mass class, and age of shotcrete. According to the sensitivity analysis results in Table 4, rock mass class has the greatest influence on safety distance, followed by age of shotcrete and blasting charge.Table 4
Sensitivity of different parameters affecting safety distances.
Parameters
Range of parameters
Sensitivity of parameters
Rock mass class
III, IV, V
0.96
Blasting chargeQ (kg)
140, 120, 100, 80, 60
0.43
Age of shotcretet (h)
0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6
0.50In Chinese Safety Standard for Blasting Vibration (GB6722-2014), some standard values have been provided for safe PPV of mass fresh concrete taking into account vibration frequency, as summarized in Table5 [18]. Based on the empirical equation obtained for PPV-Z and blast predominant frequency in Sections 3.2 and 3.3, minimum safety distance was obtained to satisfy PPV safety standard.Table 5
Safety standard of blasting vibration for mass fresh concrete suggested in Chinese Safety Standard for Blasting Vibration (unit: cm/s).
Fresh concrete of C20
Safety standard of blasting vibration velocity (cm/s)
Predominate frequencyf (Hz)
≤10
10–50
>50
Concrete age
0∼3 d
1.5∼2
2∼2.5
2.5∼3
3∼7 d
3∼4
4∼5
5∼7
7∼28 d
7∼8
8∼10
10∼12Minimum safety distance thresholds for shotcrete were evaluated using bond failure criterion and Chinese Safety Standard for Blasting Vibration, and the obtained results are summarized as shown in Table6. By comparing minimum safety distances determined based on two different criteria, namely, bond failure criterion and Chinese Safety Standard Blasting Vibration, it was observed that both results complied well under classes III and IV rock mass conditions. However, under class V rock mass condition, minimum safety distance using bond failure criterion was much lower. The reason is that rock mass properties under class V condition were significantly different from those under class III and IV conditions, as can be seen in Table 1. The differences in properties were taken into sufficient consideration when using bond failure criterion, but this was not the case for Chinese Safety Standard for Blasting Vibration. Therefore, minimum safety distance using bond failure criterion was found to be more precise and practical under complex conditions.Table 6
Minimum safety distances of shotcretes subjected to blasting vibration using two different criteria (unit: m).
Rock mass class
Q (kg)
Bond failure criterion
Chinese safety standard
0.5–3 d
3–7 d
7–28 d
0–3 d
3–7 d
7–28 d
III
120
5.27–9.24
4.83–5.27
4.83–4.97
7.95–8.61
5.50–6.37
4.35–4.71
IV
100
5.02–8.89
4.56–5.02
4.56–4.71
7.48–8.10
5.18–5.99
4.10–4.43
V
80
2.92–5.52
2.49–2.92
2.49–2.67
6.95–7.52
4.81–5.56
3.80–4.12In this project, the shotcrete of steel fiber concrete with two layers was adopted as the support system. The distance that the excavation of the upper bench lags behind the lower bench was 30 m. The shotcrete thicknesses of primary and secondary layers are 150 mm and 200 mm, respectively. Since primary shotcrete was too close to blasting face, blasting vibration could affect primary shotcrete structure and cause irreversible damage. Therefore, here the safety of secondary shotcrete was considered. Based on excavation and support processes, the distance between secondary shotcrete and blasting point was above 6 m (2 excavation cycles), and the blast was carried out 3 days after shotcrete was performed. Hence, according to minimum safety distances summarized in Table6, the safety of secondary shotcrete was ensured and shotcrete falling off was prevented under the current blast construction.


## 4.3. Recommendations for the Security of Shotcrete

In the construction of large-span tunnels, blasting vibration may cause undesired damages to shotcrete. Based on the above analyses, safety distance can be determined to ensure the security of shotcrete according to the monitoring results of blasting vibration. However, due to the tight time limits of large construction projects, blasting is often performed before bond strength of shotcrete is reached and with the distance between blast work face and shotcrete below safety distance. Despite these problems and difficulties, some effective measurements can be taken to ensure the safety of shotcrete construction, as follows:(1)
Steel fiber shotcretes have high early strength which can improve bond the strength of shotcretes to withstand blast loads in tunnel excavations in short time periods [1, 2, 41–43]. According to equation (16), adopting steel fiber concrete can improve the bond characteristic of the interface (σ24hb) and thus increases the safety distance of shotcrete.(2)
Operation sequences in tunnel excavation can be ordered to reduce blast charge and therefore significantly controls blast vibration [21, 44]. A certain distance should be kept between upper and lower benches to keep the shotcrete from being repeatedly disturbed by blasting in a short time. According to equation (16), when blasting charge was decreased, safety distance of shotcrete was also decreased.(3)
Performing multiple shotcrete layers is an effective method to decrease blasting damage [35, 43]. The initial shotcrete with low layer thickness was performed to seal the rock mass to facilitate the installation of metal meshes and bolts. The subsequent concrete layer with higher thickness was sprayed often with 1–3 days or 1–2 excavation cycle delay to consolidate the compound system of rock mass and support. Because of the increased distance between blast point and shotcrete, the blast vibration imposed on subsequent shotcrete was dramatically decreased.


## 5. Conclusions

In this work, blasting vibration monitoring was carried out using microseismic monitoring technique during the blast excavation of the large-span tunnel of Badaling Great Wall Station. Blasting vibration parameters including peak particle velocity (PPV) and blast predominate frequency (f) were recorded by using the microseismic monitoring system installed inside the tunnel. Empirical equations of PPV were obtained by regression analysis based on monitoring data. The blast vibration tensile stress of shotcrete-rock interface caused by blasting and bond characteristics of interface was also analyzed. The safety distance between blasting and shotcrete was proposed to ensure the security of shotcrete. The main conclusions were drawn as follows:(1)
The equations to predict blast vibration characteristics along longitudinal, transverse, and vertical directions were derived using the Sadovsky empirical equation. Vertical peak particle velocity (PPV-Z) was approximately 1.5–2 times higher than that along radial and tangential directions (PPV-X, PPV-Y).(2)
Due to the different wave impedances of shotcrete and rock masses, the tensile stressσTRT imposed on the shotcrete-rock interface was calculated after reflections and transmissions of blast stress wave caused by blasting.(3)
Based on the bond failure criterion of shotcrete-rock interface, the calculation equation of minimum safety distance of shotcrete subjected to blast vibration was obtained which could be applied to determine blast charge and shotcrete arrangements. It was witnessed that the minimum safety distance of shotcrete was decreased with the increase of age which was more significant in the first three days.(4)
In this project, the distance between secondary shotcrete and blasting point was above 6 m and blasting was carried out 3 days after shotcrete was performed. Therefore, the vibration safety of secondary shotcrete was ensured and shotcrete falling off the rock was prevented.



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*Source: 2429713-2019-10-14.xml*