# Field Investigation of Blasting-Induced Vibration in Concrete Linings during Expansion of Old Highway Tunnel

Authors: Ya-Qiong Wang; Lin-Jin Gong; Nan-Nan An; Xing-Bin Peng; Wei Wang; Zhi-Feng Wang
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

Numerous mountain highway tunnels in China do not satisfy the current traffic design standards and therefore need to be rebuilt or expanded. The drilling-blasting method is the primary method employed in China for expanding mountain highway tunnels, and it is crucial to monitor the vibrations caused by blasting. This study conducted a field investigation of the vibrations caused by blasting during the expansion of Yujiaya tunnel, which was built in 1999. The blasting-induced vibrations in the new and old concrete linings were monitored and analyzed during the expansion. The measured values of the peak particle velocity (PPV) varied within the range of 0.097–8.246 cm/s. The attenuation law of the PPV was determined via a regression analysis using Sadovsky’s empirical formula. The relationship between the main vibration frequency and the distance from the blasting source was expressed as a power function. Finally, the safety distances of the concrete linings subject to blasting vibrations were analyzed and discussed.


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## Body

## 1. Introduction

In China, numerous old mountain highway tunnels have undergone local collapse, water leakage, and lining cracking, among other issues [1–5]. These highway tunnels are in a subhealth state, have entered the “high maintenance” management period, and do not satisfy current traffic design standards; thus, they must be rebuilt or expanded [6]. The drilling-blasting method is the primary method employed in China for the construction of mountain tunnels [7–9], where blasting control is the key issue faced during the process of expanding old tunnels [10–13]. During tunnel expansion and the construction processes involved, blasting vibrations of different strengths inevitably cause macroscopic damage or microscopic cumulative damage to underground structures or adjacent buildings [14–18]. If the blasting control is not reasonable, it may cause a continuous collapse of the old concrete lining, introducing considerable difficulty to the expansion of tunnels [19–22]. Therefore, it is important to monitor blasting-induced vibration during the process of expanding old tunnels for ensuring safety [23–26]. Several studies have investigated the effects of underground engineering blasting on adjacent structures (in terms of the critical limit, dynamic response caused by blasting, etc.) via field tests, numerical simulations, and model tests [27–31]; however, most of them focused on the linings of existing tunnels, adjacent buildings, airport runways, and hydropower stations [32–36]. In the case of a wireless sensor network, Lai et al. [37] investigated the effects of blast-induced vibrations on the structure of the existing tunnel. Feldgun et al. [14] proposed a comprehensive approach to simulate an explosion occurring inside a buried axisymmetric lined cavity. However, there have been few studies on the effects of blasting vibrations caused by in situ expansion of highway tunnels, which require close attention.This study aimed to perform a field test to investigate the vibrations caused by blasting during thein situ expansion of the Yujiaya tunnel, which was built in 1999; it is the first in situ expansion project conducted in the Shaanxi Province. In this study, the vibration velocity and the main vibration frequency in the new and old concrete linings were measured. The attenuation law of the peak particle velocity (PPV) for the new and old concrete linings was analyzed. The relationship between the main vibration frequency and the distance to the blasting source was examined. Additionally, the safety distances of concrete linings subject to blasting vibrations were investigated.


## 2. Project Background

Yujiaya tunnel is a single-hole tunnel located on the S309 line of the highway from Lueyang County to Kang County, Shaanxi province, as shown in Figure1. After complete construction, it was opened to traffic on June 15, 1999. On July 14, 2015, because the top lining concrete of the tunnel partially collapsed, the tunnel was analyzed and tested in detail to verify its quality status. As shown in Figure 2, the test results indicated that Yujiaya tunnel had the following damage: a partial collapse of the lining, cracks in the lining and water leakage, an insufficient lining thickness and defects, an insufficient lining strength, drainage system failure, no lighting, no fire protection, safety facilities, and so forth. Figure 3 presents cross-sectional views of the Yujiaya tunnel before and after expansion. As shown, the height and width of the old Yujiaya tunnel were 7.8 and 8.5 m, respectively. To improve the traffic conditions, they were increased to 8.75 and 10.0 m, respectively, in the new Yujiaya tunnel. Figure 4 presents a longitudinal view of the Yujiaya tunnel and the geological conditions. As shown, the Yujiaya tunnel was approximately 518 m long (medium-long tunnel) with mileage piles of K101 + 850 – K102 + 368. The geological conditions for the Yujiaya tunnel are also presented in Figure 4. As shown, the strata in the tunnel area were mainly composed of phyllite rock, and the Yujiaya tunnel crossed three fault fracture zones and limestone strata. The unconfined compressive strength of the phyllite rock ranged from 12.8 to 39.6 MPa.Figure 1
Plan view of the location of Yujiaya tunnel.Figure 2
Damage to Yujiaya tunnel: (a) partial collapse of the lining; (b) cracks in the lining; (c) leakage; (d) poor traffic conditions.
(a)(b)(c)(d)Figure 3
Cross-sectional views of Yujiaya tunnel before and after expansion.Figure 4
Longitudinal view of Yujiaya tunnel and the geological conditions.Thein situ expansion process of the tunnel is mainly divided into two phases: demolition of the old lining structure and excavation of local surrounding rock. The old lining is demolished mainly via the cutting method along with low-magnitude vibration and loose, weak blasting. Moreover, the excavation of the surrounding rock is mainly conducted via weak blasting, and mechanical machines can be used for this process. In the in situ expansion, two and three rows of boreholes are arranged around the rock in the upper and lower steps, respectively, which are perimeter holes and auxiliary holes from the outside to the inside, as shown in Figure 5. The perimeter holes are spaced and uncoupled charge structures, whereas the auxiliary holes are continuous uncoupled charge structures. A slight delay in blasting is applied between each row of holes (different-colored holes use different detonator segments). The detonator segments correspond to1¯,2¯,and5¯, and the delay between adjacent detonator segments is 100 ms (determined according to the blasting engineer’s experience). Thus, layer-by-layer detonation is performed from the adjacent free face to the outside, eliminating the stress wave superposition effect caused by the explosion.Figure 5
Layout of blasting holes during the construction for expanding Yujiaya tunnel.


## 3. Field Monitoring Program

### 3.1. Monitoring Principle Using TC-4850

The blasting vibration testing system was primarily composed of a signal sensor (picker) and a data recorder. A three-vector vibration sensor and a TC-4850 self-recording instrument (Chengdu Zhongke Instrument Co., Ltd.) were used during the monitoring process. The sensor converted the blasting vibration signals to electrical signals, which were then converted to digital signals through analog-to-digital conversion via the self-recording instrument. Finally, the data recorder was connected to the computer through a special data line after the test, and the vibration signals were extracted, stored, processed, and analyzed using the Blasting Vibration Analysis software [38]. The test process is depicted in Figure 6. In the field test, the PPV and main vibration frequency were monitored. The PPV and the main vibration frequency were in the ranges of 0–35 cm/s and 0–10 kHz, respectively, and their test accuracies were 0.0001 cm/s and 0.1 Hz, respectively.Figure 6
Principle for testing the blasting-induced vibrations.


### 3.2. Monitoring Scheme and Layout of Test Points

The layout of the monitoring points adhered to the following principles: (1) the location and direction monitoring of the maximum PPV; (2) real-time monitoring of the blasting vibrations; and (3) observation of the attenuation law of the blasting vibrations. According to the foregoing monitoring principles and the propagation law of blast stress waves, the monitoring sections were arranged on both sidewalls of the new and old sections of the Yujiaya tunnel. Two monitoring points were set in each section. The monitoring points were determined to be at the same height as that of the side walls: approximately 1.5 m above road level, at which it was convenient to perform measurements. As shown in Figure7, four monitoring points were arranged for each blasting process denoted as C1, C2, C3, and C4.Figure 7
Layout of the monitoring points in the tunnel lining.The distances between the monitoring points on each side and the blasting source wereR1, R2, R3, and R4. A three-vector sensor was installed at each monitoring point to measure three vibration velocities: the horizontal radial velocity VX, horizontal tangential velocity VY, and vertical velocity VZ. Because the terrain at each monitoring point was relatively flat and the height difference between adjacent monitoring points was small, the influence of the height difference on the propagation of the blasting stress wave could be neglected in the field test.


## 3.1. Monitoring Principle Using TC-4850

The blasting vibration testing system was primarily composed of a signal sensor (picker) and a data recorder. A three-vector vibration sensor and a TC-4850 self-recording instrument (Chengdu Zhongke Instrument Co., Ltd.) were used during the monitoring process. The sensor converted the blasting vibration signals to electrical signals, which were then converted to digital signals through analog-to-digital conversion via the self-recording instrument. Finally, the data recorder was connected to the computer through a special data line after the test, and the vibration signals were extracted, stored, processed, and analyzed using the Blasting Vibration Analysis software [38]. The test process is depicted in Figure 6. In the field test, the PPV and main vibration frequency were monitored. The PPV and the main vibration frequency were in the ranges of 0–35 cm/s and 0–10 kHz, respectively, and their test accuracies were 0.0001 cm/s and 0.1 Hz, respectively.Figure 6
Principle for testing the blasting-induced vibrations.


## 3.2. Monitoring Scheme and Layout of Test Points

The layout of the monitoring points adhered to the following principles: (1) the location and direction monitoring of the maximum PPV; (2) real-time monitoring of the blasting vibrations; and (3) observation of the attenuation law of the blasting vibrations. According to the foregoing monitoring principles and the propagation law of blast stress waves, the monitoring sections were arranged on both sidewalls of the new and old sections of the Yujiaya tunnel. Two monitoring points were set in each section. The monitoring points were determined to be at the same height as that of the side walls: approximately 1.5 m above road level, at which it was convenient to perform measurements. As shown in Figure7, four monitoring points were arranged for each blasting process denoted as C1, C2, C3, and C4.Figure 7
Layout of the monitoring points in the tunnel lining.The distances between the monitoring points on each side and the blasting source wereR1, R2, R3, and R4. A three-vector sensor was installed at each monitoring point to measure three vibration velocities: the horizontal radial velocity VX, horizontal tangential velocity VY, and vertical velocity VZ. Because the terrain at each monitoring point was relatively flat and the height difference between adjacent monitoring points was small, the influence of the height difference on the propagation of the blasting stress wave could be neglected in the field test.


## 4. Results and Discussion

### 4.1. PPV

In the field test, the vibration velocities in different directions were measured. Figure8 presents typical curves of the measured vibration velocities (VX, VY, and VZ) in the new concrete lining for one test. As shown, the peak vibration velocities (PPVs) in the three directions were 0.197, 0.280, and 0.384 cm/s, respectively. To further study the attenuation law of the peak vibration velocities caused by blasting in the expansion of the Yujiaya tunnel, 10 field tests were conducted during the construction process, and a large amount of PPV data was collected, as shown in Table 1. Many researchers have proposed prediction formulas for blasting vibration, which are generally based on Sadovsky’s empirical formula, and the parameters are revised and perfected in actual blasting engineering. Additionally, formulas for predicting the relationship among the PPV, trinitrotoluene (TNT) weight, and safe distance were also proposed in China and were incorporated into the Safety regulations for blasting in China [39]. The PPV can be predicted as follows:(1)PPV=KQ1/3Rα=KPD−α,(2)PD=RQ1/3,where PPV represents the PPV (in cm/s); Q represents the TNT weight (kg); R represents the linear distance from the blasting source to monitoring points (m); K and α are parameters related to the blasting vibrations, which are influenced by the rock characteristics, site conditions, blasting methods, and so forth; and [PD] represents the proportional distance (m/kg1/3).Figure 8
Typical curve of measured vibration velocities (VX, VY, and VZ) for the new concrete lining (in test 1, R4 = 110.8).Table 1
Measured PPVs in this case history.
Test numberTNT weight per delay (kg)Distance to blasting source (m)PPV of new concrete lining (cm/s)Distance to blasting source (m)PPV of the old concrete lining (cm/s)VXVYVZVXVYVZ150.4R2 = 20.37.2586.5016.647R3 = 29.64.5726.8755.006R1 = 42.72.9042.2061.324R4 = 110.80.1970.2800.384227.3R2 = 19.76.4655.5354.943R3 = 20.05.7018.2465.476R1 = 52.61.3460.6401.674R4 = 74.20.3751.1651.211331.2R2 = 22.74.1213.1943.030R3 = 40.43.3073.6412.741R1 = 44.01.1221.0671.846R4 = 95.70.4451.2650.915427.3R2 = 31.62.1002.9112.120R3 = 50.81.8652.2731.978R1 = 98.00.5050.1940.178R4 = 70.91.9961.9971.044531.2R2 = 48.91.4741.8260.807R3 = 37.23.6534.9192.007R1 = 109.50.1700.1700.242R4 = 70.80.4031.8241.189627.3R2 = 29.93.6172.6541.637R3 = 42.41.2792.2891.686R1 = 117.20.1800.1370.378R4 = 101.50.3590.8040.840731.2R2 = 26.54.1812.2093.261R3 = 55.31.6662.8511.798R1 = 71.30.7900.2890.256R4 = 135.20.4060.4880.703827.3R2 = 36.21.2722.1672.122R3 = 44.80.9102.5411.345R1 = 79.20.6490.2920.323R4 = 156.60.4220.6580.256931.2R2 = 28.41.8402.4921.715R3 = 87.00.8400.9881.697R1 = 78.60.2940.6930.867R4 = 114.20.2060.7400.1931027.3R2 = 42.91.6732.1950.730R3 = 98.10.6860.2160.363R1 = 140.40.1590.0970.409R4 = 120.40.5450.4520.938According to the field test data for the blasting vibrations in Table1, the variations of the PPV with respect to the proportional distance ([PD]) for the new and old concrete linings were analyzed via regression analysis. Figures 9 and 10 present the variation of the PPV with respect to [PD] for the new concrete lining and the old concrete lining, respectively. As shown, the measured PPVs in the new and old concrete linings of the Yujiaya tunnel decreased with an increase in the proportional distance, indicating that the PPV was higher for a larger TNT weight and lower for a longer distance to the blasting source. Because the surrounding rock structure of the new tunnel differed from that of the old tunnel lining, the incident and reflection modes of the stress wave were different, resulting in significant differences in the PPV between the new and old concrete linings. According to the regression analysis using equations (1) and (2), the corresponding attenuation parameters K and α of stress wave propagation were determined, and then the empirical formula for the attenuation of the PPV in each direction was obtained, as follows (as shown in Figures 9 and 10):New concrete lining:(3)VX=170.15PD−1.810,R2=0.82,VY=206.92PD−1.965,R2=0.79,VZ=68.69PD−1.523,R2=0.73.Old concrete lining:(4)VX=124.41PD−1.599,R2=0.78,VY=216.59PD−1.632,R2=0.84,VZ=74.32PD−1.359,R2=0.70.Figure 9
Variation of the PPV with respect to [PD] for the new concrete lining.Figure 10
Variation of the PPV with respect to [PD] for the old concrete lining.Comparing the fitted curves in Figures9 and 10 reveals that the K value of the new concrete linings varied between 68 and 206 and that α varied greatly, ranging from 1.523 to 1.965. However, the K value of the old concrete linings varied widely (between 74 and 216), and α varied from 1.359 to 1.623. Therefore, the PPV caused by blasting was attenuated faster in the new concrete lining than in the old concrete lining. In the case of the new concrete lining, when the stress wave encounters a free surface, joint fissure, or fault during the propagation process, it may be reflected and refracted, which can result in energy loss of the stress wave and rapid attenuation of the PPV. Additionally, because the new tunnel excavation forms a circular cutting groove, similar to the artificial damping belt, the blasting stress wave cannot directly act on the primary support structure; rather, it affects the primary support structure through the tunnel floor and the vault diffraction at the monitoring points of the new concrete linings. It was mainly affected by the stress in the X and Y directions; thus, the PPV in the Z direction was lower than that in the other directions for the new concrete linings. Additionally, the correlation coefficients of the fitting curves (R2) were relatively small, ranging from 0.70 to 0.84. This is explained as follows: the geological surrounding rock conditions in the tunnel were complex, the blasting conditions and environmental factors changed significantly, and the difference between the installation position and the height of the instrument may have led to an error in the measurement of the PPV. However, overall, the attenuation law of the PPV was consistent with Sadovsky’s empirical formula.


### 4.2. Main Vibration Frequency

In many countries, the influence of the main vibration frequency of the blasting stress wave is considered during the formulation of the Blasting Safety Regulations. Previous studies indicated that the main vibration frequency of blasting vibrations affects the damage to buildings and structures [40–42]. The main vibration frequency closer to the natural frequency of the buildings results in greater damage to the buildings. A large amount of data for the main vibration frequency induced by blasting in this case history was collected, as shown in Table 2. Additionally, the distribution of the measured main vibration frequency was analyzed for the new and old concrete linings. As shown in Figures 11 and 12, the measured main vibration frequency was divided into five intervals: 0–30, 30–60, 60–90, 90–120, and >120 Hz. The main vibration frequency in this case history was mainly distributed in the range of 0–90 Hz (approximately 85% of the data). Figure 13 presents the variation of the main vibration frequency with respect to the distance to the blasting source. As shown, the main vibration frequency measured in the blasting was higher (between 11.72 and 147.45 Hz), but with the increasing distance to the blasting source, the main vibration frequency decreased, similar to the investigation results for the frequency variation reported by Singh et al. [36, 43]. This confirms the accuracy of the test results. Additionally, because the natural frequencies of most ground structures are relatively low, it is more difficult for high-frequency vibration to resonate with adjacent structures, and the vibration does not damage buildings or structures. To quantitatively evaluate the relationship between the main vibration frequency and the distance to the blasting source, a regression analysis of the observed data was performed, which indicated that a power function (y = 2018x−0.93, R2 = 0.77) may be reasonable, as shown in Figure 13.Table 2
Observed main vibration frequency for the examined case history.
Test numberTNT weight per delay (kg)Distance to blasting source (m)Main vibration frequency of new concrete lining (Hz)Distance to blasting source (m)Main vibration frequency of old concrete lining (Hz)FXFYFZFXFYFZ150.4R2 = 20.345.62117.1489.65R3 = 29.6123.2593.95113.28R1 = 42.740.2523.5318.90R4 = 110.811.7223.4323.45227.3R2 = 19.7119.61127.9764.52R3 = 20.0118.6083.32108.76R1 = 52.627.3535.8754.60R4 = 74.237.4527.6218.55331.2R2 = 22.762.55112.36108.42R3 = 40.428.98127.65105.26R1 = 44.044.6850.2972.68R4 = 95.722.9269.3020.15427.3R2 = 31.675.6967.4525.68R3 = 50.887.8265.0549.60R1 = 98.035.8920.5826.50R4 = 70.917.8735.6528.37531.2R2 = 48.956.6769.8529.62R3 = 37.2122.0578.6260.25R1 = 109.529.6825.4619.60R4 = 70.835.8042.6839.07627.3R2 = 29.939.8367.79130.34R3 = 42.455.5465.0646.58R1 = 117.219.6215.6722.18R4 = 101.522.1532.5828.40731.2R2 = 26.5127.6586.20147.45R3 = 55.378.5265.4345.09R1 = 71.338.6642.1819.57R4 = 135.212.5624.1119.50827.3R2 = 36.283.3469.2274.05R3 = 44.885.6276.5355.45R1 = 79.223.8056.4979.52R4 = 156.613.6817.9826.80931.2R2 = 28.4112.3656.2678.32R3 = 87.025.68102.6039.86R1 = 78.642.3265.2425.60R4 = 114.225.6422.3032.051027.3R2 = 42.957.2961.0787.00R3 = 98.172.5845.6219.82R1 = 140.417.8524.6820.55R4 = 120.442.2622.8021.09Figure 11
Distribution of the measured main vibration frequency for the old concrete lining.Figure 12
Distribution of the measured main vibration frequency for the new concrete lining.Figure 13
Variation of the main vibration frequency with respect to the distance to the blasting source.


### 4.3. Discussion on Safety Distance of Concrete Linings

In this study, the PPVs at different distances from the blasting source were determined via the field test. However, the PPVs close to the blasting source could not be monitored, owing to safety considerations. Therefore, the PPVs at different distances from the blasting source were calculated using equation (4). Figure 14 presents the variation of the PPV in different directions with respect to the distance from the blasting source for the concrete lining. The PPV curve is based on equation (4). As shown, for the TNT weight of Qmax = 50.4 kg, if the PPV is > 20 cm/s, damage may be induced to the concrete lining, and the safety distance for the case of 10 ≤ VX ≤ 20 cm/s is 16–24 m. The safety distances for the cases of 10 ≤ VY ≤ 20 cm/s and 10 ≤ VZ ≤ 20 cm/s are 12–18 and 10–17 m, respectively. The obtained safety distances are valuable references for similar tunnel construction projects.Figure 14
Variation of the PPV with respect to the distance from the blasting source for the concrete lining.


## 4.1. PPV

In the field test, the vibration velocities in different directions were measured. Figure8 presents typical curves of the measured vibration velocities (VX, VY, and VZ) in the new concrete lining for one test. As shown, the peak vibration velocities (PPVs) in the three directions were 0.197, 0.280, and 0.384 cm/s, respectively. To further study the attenuation law of the peak vibration velocities caused by blasting in the expansion of the Yujiaya tunnel, 10 field tests were conducted during the construction process, and a large amount of PPV data was collected, as shown in Table 1. Many researchers have proposed prediction formulas for blasting vibration, which are generally based on Sadovsky’s empirical formula, and the parameters are revised and perfected in actual blasting engineering. Additionally, formulas for predicting the relationship among the PPV, trinitrotoluene (TNT) weight, and safe distance were also proposed in China and were incorporated into the Safety regulations for blasting in China [39]. The PPV can be predicted as follows:(1)PPV=KQ1/3Rα=KPD−α,(2)PD=RQ1/3,where PPV represents the PPV (in cm/s); Q represents the TNT weight (kg); R represents the linear distance from the blasting source to monitoring points (m); K and α are parameters related to the blasting vibrations, which are influenced by the rock characteristics, site conditions, blasting methods, and so forth; and [PD] represents the proportional distance (m/kg1/3).Figure 8
Typical curve of measured vibration velocities (VX, VY, and VZ) for the new concrete lining (in test 1, R4 = 110.8).Table 1
Measured PPVs in this case history.
Test numberTNT weight per delay (kg)Distance to blasting source (m)PPV of new concrete lining (cm/s)Distance to blasting source (m)PPV of the old concrete lining (cm/s)VXVYVZVXVYVZ150.4R2 = 20.37.2586.5016.647R3 = 29.64.5726.8755.006R1 = 42.72.9042.2061.324R4 = 110.80.1970.2800.384227.3R2 = 19.76.4655.5354.943R3 = 20.05.7018.2465.476R1 = 52.61.3460.6401.674R4 = 74.20.3751.1651.211331.2R2 = 22.74.1213.1943.030R3 = 40.43.3073.6412.741R1 = 44.01.1221.0671.846R4 = 95.70.4451.2650.915427.3R2 = 31.62.1002.9112.120R3 = 50.81.8652.2731.978R1 = 98.00.5050.1940.178R4 = 70.91.9961.9971.044531.2R2 = 48.91.4741.8260.807R3 = 37.23.6534.9192.007R1 = 109.50.1700.1700.242R4 = 70.80.4031.8241.189627.3R2 = 29.93.6172.6541.637R3 = 42.41.2792.2891.686R1 = 117.20.1800.1370.378R4 = 101.50.3590.8040.840731.2R2 = 26.54.1812.2093.261R3 = 55.31.6662.8511.798R1 = 71.30.7900.2890.256R4 = 135.20.4060.4880.703827.3R2 = 36.21.2722.1672.122R3 = 44.80.9102.5411.345R1 = 79.20.6490.2920.323R4 = 156.60.4220.6580.256931.2R2 = 28.41.8402.4921.715R3 = 87.00.8400.9881.697R1 = 78.60.2940.6930.867R4 = 114.20.2060.7400.1931027.3R2 = 42.91.6732.1950.730R3 = 98.10.6860.2160.363R1 = 140.40.1590.0970.409R4 = 120.40.5450.4520.938According to the field test data for the blasting vibrations in Table1, the variations of the PPV with respect to the proportional distance ([PD]) for the new and old concrete linings were analyzed via regression analysis. Figures 9 and 10 present the variation of the PPV with respect to [PD] for the new concrete lining and the old concrete lining, respectively. As shown, the measured PPVs in the new and old concrete linings of the Yujiaya tunnel decreased with an increase in the proportional distance, indicating that the PPV was higher for a larger TNT weight and lower for a longer distance to the blasting source. Because the surrounding rock structure of the new tunnel differed from that of the old tunnel lining, the incident and reflection modes of the stress wave were different, resulting in significant differences in the PPV between the new and old concrete linings. According to the regression analysis using equations (1) and (2), the corresponding attenuation parameters K and α of stress wave propagation were determined, and then the empirical formula for the attenuation of the PPV in each direction was obtained, as follows (as shown in Figures 9 and 10):New concrete lining:(3)VX=170.15PD−1.810,R2=0.82,VY=206.92PD−1.965,R2=0.79,VZ=68.69PD−1.523,R2=0.73.Old concrete lining:(4)VX=124.41PD−1.599,R2=0.78,VY=216.59PD−1.632,R2=0.84,VZ=74.32PD−1.359,R2=0.70.Figure 9
Variation of the PPV with respect to [PD] for the new concrete lining.Figure 10
Variation of the PPV with respect to [PD] for the old concrete lining.Comparing the fitted curves in Figures9 and 10 reveals that the K value of the new concrete linings varied between 68 and 206 and that α varied greatly, ranging from 1.523 to 1.965. However, the K value of the old concrete linings varied widely (between 74 and 216), and α varied from 1.359 to 1.623. Therefore, the PPV caused by blasting was attenuated faster in the new concrete lining than in the old concrete lining. In the case of the new concrete lining, when the stress wave encounters a free surface, joint fissure, or fault during the propagation process, it may be reflected and refracted, which can result in energy loss of the stress wave and rapid attenuation of the PPV. Additionally, because the new tunnel excavation forms a circular cutting groove, similar to the artificial damping belt, the blasting stress wave cannot directly act on the primary support structure; rather, it affects the primary support structure through the tunnel floor and the vault diffraction at the monitoring points of the new concrete linings. It was mainly affected by the stress in the X and Y directions; thus, the PPV in the Z direction was lower than that in the other directions for the new concrete linings. Additionally, the correlation coefficients of the fitting curves (R2) were relatively small, ranging from 0.70 to 0.84. This is explained as follows: the geological surrounding rock conditions in the tunnel were complex, the blasting conditions and environmental factors changed significantly, and the difference between the installation position and the height of the instrument may have led to an error in the measurement of the PPV. However, overall, the attenuation law of the PPV was consistent with Sadovsky’s empirical formula.


## 4.2. Main Vibration Frequency

In many countries, the influence of the main vibration frequency of the blasting stress wave is considered during the formulation of the Blasting Safety Regulations. Previous studies indicated that the main vibration frequency of blasting vibrations affects the damage to buildings and structures [40–42]. The main vibration frequency closer to the natural frequency of the buildings results in greater damage to the buildings. A large amount of data for the main vibration frequency induced by blasting in this case history was collected, as shown in Table 2. Additionally, the distribution of the measured main vibration frequency was analyzed for the new and old concrete linings. As shown in Figures 11 and 12, the measured main vibration frequency was divided into five intervals: 0–30, 30–60, 60–90, 90–120, and >120 Hz. The main vibration frequency in this case history was mainly distributed in the range of 0–90 Hz (approximately 85% of the data). Figure 13 presents the variation of the main vibration frequency with respect to the distance to the blasting source. As shown, the main vibration frequency measured in the blasting was higher (between 11.72 and 147.45 Hz), but with the increasing distance to the blasting source, the main vibration frequency decreased, similar to the investigation results for the frequency variation reported by Singh et al. [36, 43]. This confirms the accuracy of the test results. Additionally, because the natural frequencies of most ground structures are relatively low, it is more difficult for high-frequency vibration to resonate with adjacent structures, and the vibration does not damage buildings or structures. To quantitatively evaluate the relationship between the main vibration frequency and the distance to the blasting source, a regression analysis of the observed data was performed, which indicated that a power function (y = 2018x−0.93, R2 = 0.77) may be reasonable, as shown in Figure 13.Table 2
Observed main vibration frequency for the examined case history.
Test numberTNT weight per delay (kg)Distance to blasting source (m)Main vibration frequency of new concrete lining (Hz)Distance to blasting source (m)Main vibration frequency of old concrete lining (Hz)FXFYFZFXFYFZ150.4R2 = 20.345.62117.1489.65R3 = 29.6123.2593.95113.28R1 = 42.740.2523.5318.90R4 = 110.811.7223.4323.45227.3R2 = 19.7119.61127.9764.52R3 = 20.0118.6083.32108.76R1 = 52.627.3535.8754.60R4 = 74.237.4527.6218.55331.2R2 = 22.762.55112.36108.42R3 = 40.428.98127.65105.26R1 = 44.044.6850.2972.68R4 = 95.722.9269.3020.15427.3R2 = 31.675.6967.4525.68R3 = 50.887.8265.0549.60R1 = 98.035.8920.5826.50R4 = 70.917.8735.6528.37531.2R2 = 48.956.6769.8529.62R3 = 37.2122.0578.6260.25R1 = 109.529.6825.4619.60R4 = 70.835.8042.6839.07627.3R2 = 29.939.8367.79130.34R3 = 42.455.5465.0646.58R1 = 117.219.6215.6722.18R4 = 101.522.1532.5828.40731.2R2 = 26.5127.6586.20147.45R3 = 55.378.5265.4345.09R1 = 71.338.6642.1819.57R4 = 135.212.5624.1119.50827.3R2 = 36.283.3469.2274.05R3 = 44.885.6276.5355.45R1 = 79.223.8056.4979.52R4 = 156.613.6817.9826.80931.2R2 = 28.4112.3656.2678.32R3 = 87.025.68102.6039.86R1 = 78.642.3265.2425.60R4 = 114.225.6422.3032.051027.3R2 = 42.957.2961.0787.00R3 = 98.172.5845.6219.82R1 = 140.417.8524.6820.55R4 = 120.442.2622.8021.09Figure 11
Distribution of the measured main vibration frequency for the old concrete lining.Figure 12
Distribution of the measured main vibration frequency for the new concrete lining.Figure 13
Variation of the main vibration frequency with respect to the distance to the blasting source.


## 4.3. Discussion on Safety Distance of Concrete Linings

In this study, the PPVs at different distances from the blasting source were determined via the field test. However, the PPVs close to the blasting source could not be monitored, owing to safety considerations. Therefore, the PPVs at different distances from the blasting source were calculated using equation (4). Figure 14 presents the variation of the PPV in different directions with respect to the distance from the blasting source for the concrete lining. The PPV curve is based on equation (4). As shown, for the TNT weight of Qmax = 50.4 kg, if the PPV is > 20 cm/s, damage may be induced to the concrete lining, and the safety distance for the case of 10 ≤ VX ≤ 20 cm/s is 16–24 m. The safety distances for the cases of 10 ≤ VY ≤ 20 cm/s and 10 ≤ VZ ≤ 20 cm/s are 12–18 and 10–17 m, respectively. The obtained safety distances are valuable references for similar tunnel construction projects.Figure 14
Variation of the PPV with respect to the distance from the blasting source for the concrete lining.


## 5. Conclusions

At present, several old mountain highway tunnels in China need to be rebuilt or expanded because of the declining health of concrete linings and the growing traffic demands. It is important to monitor the vibrations caused by blasting to avoid the continuous collapse of the old concrete lining during the expansion of old mountain highway tunnels. In this study, a case history of the expansion of the Yujiaya tunnel, located in Shaanxi Province and constructed in 1999, was analyzed. During the expansion process, the blasting-induced vibrations in the new and old concrete linings were monitored. The results indicated that the measured values of the PPV varied within the range of 0.097–8.246 cm/s. By performing a regression analysis with Sadovsky’s empirical formula, the attenuation law of the PPV was determined. A power function was established to quantitatively evaluate the relationship between the main vibration frequency and the distance to the blasting source. The results indicated that the safety distance of concrete linings for the case of 10 ≤VX ≤ 20 cm/s is 16–24 m, and the safety distances for the two cases of 10 ≤ VY ≤ 20 cm/s and 10 ≤ VZ ≤ 20 cm/s are 12–18 and 10–17 m, respectively.



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