Waveform Characteristics of Tunnel Blast Waves and a Wave-Blocking Method

The impact of blast wave air overpressure (AOp) may cause damage to nearby structures and significant noise pollution. In order to minimize the impact of the blast wave on the buildings around the tunnel, a new wave-blocking trolley (NWBT) was proposed to control the AOp during the construction of the Baitacun tunnel, as the nearby villages were located less than 100m from the tunnel portal. In the study, the characteristics of the blast wave pressure profiles were studied by field measurements and numerical simulations and the Friedlander equation parameters were obtained. Second, the controlling effect and working mechanism of the NWBTwere verified to be effective. The measured peak AOp was weakened from 2.49kPa to 0.55kPa with the operating NWBT, which meets the requirements of Chinese specifications. Furthermore, a numerical simulation for the impact process of the NWBTwas established using the ANSYS/LS-DYNA software. Finally, it was found that a shorter distance from the NWBTto the source of the blast makes a better contribution to its wave-blocking effect. The waveform characteristics obtained in the study contribute to the design of tunnel surrounding structures; the application of the NWBT is a successful wave-blocking method for tunnels adjacent to environmentally sensitive areas.


Introduction
In blast work, a considerable portion of explosive energy is wasted in the form of undesirable environmental side e ects, such as ground vibrations and air blasts [1]. When blasting work is repeatedly performed in neighboring towns, the ground peak particle velocity and air overpressure (AOp) create signi cant annoyance to personnel and residents [2], and it can even cause the breakage of glass, loss of a decorative layer, and displacement of doors and windows [3,4].
Fang [5] and Rodríguez [6,7] have obtained the blast waves propagation characteristics in tunnel generated by rock fragmentation works, but these literatures only focused on the peak of AOp. When the destructive e ects of blast waves need to be studied, the waveforms rst need to be analyzed and mathematically described. In a typical freeeld explosion, the blast waves decay in a spherical wave radially in all directions. e waveform of the blast wave exhibits nonlinear decay behind the shock front, and its simpli ed overpressure-time curve can be described mathematically by the Friedlander equation [8]. e equation cannot be used to describe the near eld, but it is well adapted for the far eld [9]. e most widely used Friedlander equations have been studied experimentally for spherical explosions and incident blast waves. For this case, the explosion was assumed to have occurred mid-air, and the resulting blast wave spherically propagated outward [10]. However, there are few descriptions for blast wave induced by tunnelling rock fragmentation. In contrast to blast waves that radiate in all directions, a wave in a nite space undergoes planar propagation in one direction toward the opening, and the pressure pro les can be very di erent [11].
In addition, when the blasting operation is close to residential buildings, some preconstructed devices to reduce blast AOp are necessary [12]. e air door with a magnetic lock was used to protect against gas explosion in a coal mine [13], but the device is complex and not suitable for large cross-sectional tra c tunnel. A temporary but inconvenient wave-blocking door was commonly placed at the tunnel portal, which was made of bamboo and rubber [14]. And also, the blast wave attenuation can be accelerated by the spoilers in the tunnel [15,16]. e spoilers are a series of at plates installed on the tunnel wall at a certain distance apart, working at an angle with the direction of the blast wavefront. Although these devices are not entirely suitable for tunnel constructions, it can be known from these applications that when the air blast wave propagates in one direction from the blasting face to the tunnel portal, the AOp could be weakened signi cantly if a exible bu er device was established on the propagation path.
Nowadays, ANSYS/LS-DYNA is used widely to simulate dynamic processes and to solve the continuum equations for nonlinear responses of materials and structures. e software was successfully used in the dynamics analysis such as spoiler wave attenuation [15], aircraft bird striking [17], bulletproof materials [18], and rockfall [19]. erefore, numerical simulations can be used to analyze the action process of wave-blocking. e innovations and main contributions of the paper are described as follows: First, the eld experiments were conducted to obtain the shapes and magnitudes of blast waveforms, especially the pressure pro les, during tunnel blasting engineering. en, a new wave-blocking trolley (NWBT) was proposed to control the blast AOp. e device was applied in the Baitacun tunnel in Yunnan, China, and the wave-blocking e ect of the AOp was tested.
Furthermore, a numerical model was established using the ANSYS/LS-DYNA software to analyze the propagation characteristics during the wave-blocking process; and the optimal working area of NWBT in the tunnel was studied.

Theoretical of Friedlander Equation
In a typical Friedlander waveform (Figure 1), the ambient pressure P a is a reference for the positive and negative pressure values. After an explosion, the blast wave reaches a target point in time t 0 , and with time, it reaches the peak AOp P * . e trend continues in the negative direction. After reaching the negative pressure, the pressure then gradually oscillates back to the ambient pressure P a .
e previous research has focused on the positive phase of the blast wave characteristics, which in most cases is more critical to the structural safety.
According to the Friedlander equation, the overpressure P(t) depends on time t, which is measured after the arrival of the shock front to the point of interest, as follows: where P * is the peak overpressure, t 0 is the arrival time of the shock front, t d is the positive phase duration, and b is a decay coe cient of the waveform. e blast wave is also characterized by a positive impulse I * , which is related to the total pressure volume applied on a structure due to an explosion, calculated through the integration of the pressure-time curve as follows: From this equation, the most relevant factors for I * are the peak pressure P * and the positive duration t d , which also have a high correlation with the coe cient b.

Engineering Background.
e Baitacun tunnel is located on the Dali-Nanjian Expressway, Yunnan Province. It is a double-hole tunnel, with a length of 10.79 km. e densely populated residential buildings are within 100 m of the tunnel portal which are susceptible to blasting AOp. Figure 2 shows the site environment near the tunnel portal. e closest distance to the tunnel portal is only 61.2 m.

Blasting Experiment Scheme.
e dimensions of the tunnel cross section were 12.78 m × 10.78 m (width × height), with a horseshoe shape. In order to control the total weight of the explosive, a section was broken at several areas, and millisecond delayed blasting was used. e blasting holes and parameters are shown in Figure 3. e diameter of the blasting hole was 42 mm. e cutting holes and collapsing holes were tilted, and the other holes were perpendicular to the blast face. e depths of the cutting holes were 2.8 m, with a drilling angle of 70°. e depths of the collapsing holes were 2.9 m, and their angles were 80°. e depths of other holes were 2.2 m. e blast is induced by an emulsion explosive, which has high water resistance, and nonelectric millisecond delay detonators. e total weight of explosives Q was approximately 96.0 kg, and the maximum weight q max of all the sequences was 7.6 kg.

Design of NWBT.
As the residential buildings are susceptible to AOp from tunnel blast, a preconstructed trolley for wave-blocking is designed. Figure 4 depicts the details of the NWBT. It consisted of a framework gantry, louvered acoustic panels, wave-blocking curtains, and other ventilation and moving accessories. e outer edge of the NWBT matched the inner pro le of the tunnel lining; and the structural material of NWBT was I-beam. e door curtain was closed during blasting and was usually opened to avoid disrupting tra c. e installation sequence of the NWBT is shown in Figure 5. e NWBT was assembled outside the tunnel. e framework gantry consisted not only of columns and beams but also of the necessary diagonal braces and ribs for stability. It had three oors with stairs and walking panels. en, louvered acoustic panels were installed. Because of the lack of light in the tunnel, re ective signs were put on for safety. Next, the top ventilation fans were installed. Finally, the NWBT was dragged into the tunnel by the loader to a stable position and xed at the bottom. Figure 6 depicts the arrangement of the measuring points. e Point A and Point B were at the front and rear of the NWBT, respectively. e height of the measuring points from the ground was 1. [21], after the blast, wave propagation distance exceeds 5 times the tunnel diameter, the wavefront has been gradually transformed into a plane wave with a certain thickness, and the pressure on the wavefront is basically uniform. e measurement points were set at the area of plane wave propagation, which in the experiments is longer than 55.0 m, and could exclude the interference of blast wave shape. Meanwhile, the working NWBT was placed at 110 m from the tunnel portal in order to facilitate the organization of tunnel construction.

Overview of the Numerical Model.
Since the measured pressure pro les cannot demonstrate the change process of the blast wavefront, a nite element method (LS-DYNA) was used, and the numerical model is shown in Figure 7. To simplify the model, the NWBT consisted of a rigid wall and a curtain, which were simpli ed as a single layer of the shellmesh. e upper edge of the curtain was xed to the rigid wall, and the lower end was free. e tunnel section area was 98 m 2 . Air was the medium for the propagation of the blast waves. e lining wall whose material is shell-mesh con ned the blast wave propagation. Because of the symmetry of the con guration, only one half of the airwave propagation domain was established. e symmetry of the model was established using a displacement constraint boundary, and the exit at both ends was a nonre ection boundary.

Material Models.
e keywords * MAT_HIGH_ EXPLOSIVE_BURN and * MAT_NULL were used to dene the material properties of the explosion and air. e AOp caused by an explosion obeys the Jones-Wilkins-Lee law, which is expressed as follows: where A, B, R 1 , R 2 , and w are constants obtained from the test, E 0 is the initial internal energy ratio, and V is the relative volume, which was taken as 1.0. Table 1 provides these parameters.
e keyword * MAT_PLASTIC_KINEMATIC is suited to model isotropic, so it was used to de ne the lining concrete and rigid wall, which included the density ρ, modulus of elasticity E, Poisson's ratio μ, and yield stress σ, as shown in Table 2.
Meanwhile, the material ( * MAT_PLASTIC_KINE MATIC) is also suited to kinematic hardening plasticity, which is commonly used to simulate the aircraft windshield structure in bird striking analysis [17], bulletproof vest material [18], and protective mesh for rockfall [19]. e same applies to simulating maize plants [22], human ankle structure [23], and other exible materials. So, the No. 3 material model in the Hyper-mesh Material Library ( * MAT_PLASTIC_KINEMATIC) was selected as the simulation material of NWBT curtain by comparing with information of the Hyper-mesh Material Library database as shown in Table 2.
e curtain material parameters were taken with reference to these analyses.

Validation of Model.
Measurements of the blast wave in the unobstructed tunnel were tested several times, and the comparison of the measurements values with the numerical simulations is shown in Figure 8. e horizontal coordinates in the gure are the logarithms of the scaled distances, and the vertical coordinates are the logarithms of the AOp. From the gure, the decay laws of the eld measurements and numerical simulations are similar; and the slope of the curve is relatively close. erefore, it can be considered that the numerical model is appropriate to the on-site practice conditions. Figure 9 shows the measurement of the pressure pro les. e difference between P * at Point A and Point B was very slight because there was no NWBT installed at this time. ere were multiple pulses in the waveform curve, which was due to the multiple blast sources induced by millisecond delayed blasting and was also related to the re ected waves caused by the walls in the tunnel. e Friedlander waveform equation describes a single pulse, so the priority should be to select the Shock and Vibration most representative pulse waveform through a suitable method. Wavelet analysis is considered to be an e ective method for analyzing signals in the time domain [24,25]. e wavelet analysis results of the pressure les are shown in Figure 9. e db8 wavelet function was used, and at the timeenergy distribution of the AOp, four energy peaks were observed at Point A and Point B. e rst and second pulses had larger energies than other pulses and almost the same time di erence (68 ms) in the time domain, and the third and fourth pulses may have been caused by eddy currents or re ected waves. For the sake of comparison, the rst pulse was chosen as the descriptive curve of the Friedlander waveform.

Characteristics of Blast Wave.
e rst pulse in Figure 9 is chosen as the blast waveform for comparison. e Friedlander equation described the pressure pulse of the blast wave very well, as shown in Figure 10. Compared with the peak pressure in explosion work [10], the peak pressure P * of the explosion wave during the tunnel fracturing work was signi cantly smaller and the duration t d was shorter. e positive pressure region had a shorter duration than the negative pressure region. e characteristic parameters of the blast wave from Point A and Point B are shown in Figures 10 and 11, and the tted equations are as follows: e calculated impulse I * fitted was consistent with the actual I * . e Friedlander equation for Point A is shown in (4), with a decay coe cient b of 3.38 and a correlation coe cient R 2 of 0.79. e Friedlander equation for measurement Point B is shown in (5), with a decay coe cient b of 3.39 and a correlation coe cient R 2 of 0.88. e decay coe cient b was close to that obtained for a free-air incident blast wave [10].

Resistance E ect of the NWBT.
e threshold of the AOp is 2.0 kPa in the Chinese code Blasting Safety Regulations (GB6722-2014), which is the safe pressure considering human health. When the NWBT is not operating, the AOp inside the tunnel is beyond the threshold pressure (as shown in Figure 9). e AOp was e ectively attenuated to meet the requirements of the code when the NWBT was operating, as shown in Figure 12. e rst pressure peak in the energy curve of Point B in Figure 13 is decomposed into several peaks in Figure 14(b), with smaller energy values, and the AOp was e ectively weakened. e changes of the blast wave parameters with operating NWBT are shown in Figure 15 and Table 3. First, the   Similarly, the time-energy curve showed that the rst pulse of the blast wave was also the most typical pressure wave when the NWBT was operating. By analyzing the blast parameters of the rst pulse of the blast wave, the NWBT operation caused a signi cant change in the peak pressure P * and time duration td at the front and rear measurement points of the device. However, there was no signi cant change in the impulse I * . e NWBT reduced the blast wave pressure P * , but the impulse I * did not decrease signi cantly due to the extended duration td of the blast wave.

Changes in Blast Wavefront by NWBT.
e ow eld near the NWBT was studied using numerical simulations. Figure 16 shows that the AOp curve in the simulation was consistent with the measured eld. When a blast wave moved in the tunnel, the pressure attenuation was limited due to the partial con nement. When the blast wave bypassed the NWBT, it was absorbed, re ected, or di racted. Figure 17 shows the digital camera images of the swaying process of the curtain when it was impacted by the blast wave, and this process was reproduced by the numerical     simulations. e rigid wall blocked and attenuated most of the pressure waves, while the rotation of the curtain corresponded to energy conversion of the blast wave. e kinetic energy of the blast wave was transformed into the rotational energy of the curtain and the elastic potential energy of the curtain. e con guration of the blast wave was greatly compressed due to the re ection and di raction of the rigid wall and curtain. e blast wave was signi cantly compressed, and the pressure of the blast wave signi cantly increased due to the NWBT block. e di racted blast waves bypassing the rigid wall reached the backside and converged again, thus continuing to propagate in the tunnel. e re ected wave shown by the curve in Figure 15(a) is formed by the reection of the blast wave after impacting the rigid wall. e re ected wave shown by the curve in Figure 15(b) is formed due to the bypassing of the di racted blast waves.

Optimal Working Area of NWBT.
In order to optimize the wave-blocking e ect, the NWBT was placed at di erent locations to compare the degree of pressure attenuation, as shown in Figure 18. Taking the measurement point after NWBT as a comparison, the degree of pressure attenuation is greater as soon as possible at a shorter distance during the blast wave propagation. While the pressure decay at locations 2 and 3 is close, the pressure in the intercepted area is less when the  NWBT is placed closer to the blast source. erefore, although the NWBT needs to be installed after the secondary lining trolley, a shorter distance from the blast source to NWBT available will better perform its wave-blocking effect.

Conclusion and Discussion
Compared with the bamboo shields and bulky wave barriers currently used in the construction, the NWBT achieves great wave-blocking without interrupting traffic in the tunnel. Compared with spoilers, NWBT achieves a larger waveblocking area and can completely block blast waves. e materials used in NWBT are easy to obtain and the assembly process is simple for engineers, making it very easy to use. e conclusions obtained from the field measurements and numerical analysis in this study are as follows: (1) e waveforms of tunnel blasting is significantly different from the blast waveform of a single explosive, the pressure profile has the property of being multipeaked. When the first pressure pulse was selected as the critical pressure waveform, the waveform was well fitted by the Friedlander equation. e peak pressure P * and impulse I * of the blast wave were obtained. e values of the attenuation coefficient b of the Friedlander equation for the blast waves at two measurement points inside the tunnel were 3.38 and 3.39, respectively. In the absence of any control measures and device work, the peak AOp of the blast wave exceeded the threshold pressure of 2.0 kPa of the Chinese regulations. (2) e NWBT played a very effective role in reducing the blast wave pressure. e peak pressure P * was effectively weakened from 2.49 kPa to 0.55 kPa, a decrease of 79.3%, which meets the pressure safety requirement. e duration td of the blast wave increased from 5.6 to 14.9 ms, and the impulse I * did not decrease due to the increase in the duration t d . (3) e interaction process between the blast wave and the NWBT contains a complex flow field. Results from numerical simulations visually indicated that absorption, reflection, or diffraction of the blast wave occurred near the NWBT. e reflected waves in the measured pressure profiles were caused by the diffraction of the blast wave bypassing the block of the NWBT. (4) e degree of attenuation of blast waves is different for varying placements of NWBT in the tunnel. A shorter distance from the NWBT to the source of the explosion, the more it can play its role in blocking the wave.
e NWBT presented in this study has many advantages over other wave-blocking devices such as spoilers and blast doors. e advantages such as high wave elimination efficiency, simple structure, low cost, and convenient installation make it suitable for traffic tunnelling constructions. Of course, the application of the structure needs more practical engineering to verify.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.