1 Introduction

Underground municipal pipelines are the city's arteries and lifelines. The number of tunneling projects is rapid increasing year by year. The dynamic response, damage mechanism, and safety of an underground pipeline at a close distance to blasting excavation are major theoretical and technical problems in tunnel construction. However, due to unclear damage mechanisms of pipelines subjected to blasting vibration and a lack of effective blasting vibration monitoring methods and safety standards, it is easy to cause major construction accidents. Therefore, it is necessary to thoroughly evaluate the dynamic responses of the pipeline subjected to tunnel blasting vibrations to guarantee the safety of the pipeline during construction.

The blasting vibration on pipelines have been studied by a number of researchers using field and laboratory experiments and numerical simulation methods. De et al. (2016) found that a protective device made of polyurethane material was effective to reduce the damage caused by a blasting load. Linear and nonlinear dynamic responses of underground pipelines under explosions in soil were also studied by Mane and Shete (2017). Formulae for calculating the peak strain of seamless steel pipe based on the distance from the detonation center and the charge were obtained by Zhong et al. (2018). Zhang et al. (2017) found that the axial and circumferential strain of underground pipeline is related to the surface synthetic peak vibration velocity in an exponential function. Liu (2012) analyzed the interaction and failure mechanism between an underground circular cast iron structure and the soil layer under an internal explosion using ABAQUS. Mokhtari and Nia (2015, 2016) analyzed an X65 steel tube using ABAQUS and found that the deformation and maximum equivalent strain decreased as the operating pressure increased and the diameter to thickness ratio decreased. Zhang et al. (2013) simulated and analyzed the deformation and failure modes of an underground pipeline under the impact of an explosion in soil using AUTODYN. Zhang et al. (2016) analyzed the effects of internal pressure, TNT size, wall thickness, and buried depth on the stress and strain of a pipeline using LS-DYNA with the ALE algorithm. Blasting vibration characteristics and safety standard of a circular pipeline passed down by tunnel in a short distance were analyzed (Guan et al. 2019). In order to assess and predict the influence of blasting vibration, a PPV prediction model of gas pipeline under metro tunnel excavation blasting was proposed (Jiang et al. 2018). Besides, the physics and mechanics properties of rock around the pipeline also affect the response of pipe subjected to blasting. Continuum analysis of the structurally controlled displacements for large-scale underground caverns in bedded rock masses was analyzed (Li et al. 2020). Energy evolution characteristics of coal specimens with preformed holes under uniaxial compression was studied (Wu et al. 2020). Multi-scale effect of acoustic emission characteristics of 3D rock damage was investigated (Liu et al. 2019). However, the monitoring method and safety standard of the pipeline under tunnel blasting vibration need to be further studied.

The research on velocity and frequency of blasting vibration and stress response of a tunnel passing close to reinforced concrete pipelines is not systematic. In this paper, based on the blasting construction of a shallow buried big-span tunnel passing underneath water pipelines, the blasting vibration test was carried out, and the blasting vibration velocity and frequency were analyzed. Sodev's empirical formula was used for regression analysis of blasting vibration velocity. Three-dimensional numerical models of a horseshoe-shaped pipelines was established with ALE algorithm using ANSYS/LS-DYNA. The propagation law of a blasting seismic wave was analyzed, and the transverse and longitudinal vibration response characteristics of pipelines under tunnel blasting vibration were studied.

2 The Information of Tunnel and Pipeline and Blasting Vibration Test

2.1 The Tunnel and Pipeline

The total length of a highway tunnel is about 1700 m. Most of the tunnels are shallow buried with a large span. This tunnel passes through more than 13 municipal pipelines at a short distance. Among them, there is a horseshoe-shaped pipeline (Fig. 1). The minimum clear distance is only 13.60 m, which is smaller than the diameter (16.8 m) of the tunnel. The tunnel was constructed using the method of drilling and blasting of up-middle-down short benches. The arrangement of the blast holes and the design of delay detonators of the blast holes of Part I and Part II in the upper bench were given in Fig. 2.

Fig. 1
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Position relationship between tunnel and horseshoe-shaped pipeline

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Fig. 2
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The blasting holes arrangement of top bench

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The horseshoe-shaped water supply pipeline was built in 1990, which is unpressurized water pipeline. The pipe has dimensions of 3.6 m (width) × 4.68 m (height), as shown in Fig. 3. The side and arch wall of pipeline are made of C30 reinforced concrete with a thickness of 40 cm, and above the pipeline is about 1 m thick soil. The rock under the pipeline of the tunnel is pebbly sandy soil.

Fig. 3
figure 3

Structural dimensions of horseshoe-shaped pipeline

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2.2 Blasting Vibration Test and Result Analysis

In this paper, the blasting vibration testing system was composed of a blasting monitor and a 3D velocity sensor, which was used to collect the blasting vibration data when tunnel blasting went through the pipeline. The system was shown in Fig. 4. Since the horseshoe pipeline is about 1.0 m away from the ground, blasting vibration test is conducted on the ground to study the propagation characteristics of blasting seismic wave. The test data of blasting vibration were shown in the Table 1.

Fig. 4
figure 4

The blasting vibration testing system

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Table 1 The test data of blasting vibration
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It can be seen that the vibration velocity of the pipeline increases gradually with the decrease of the distance from the explosion source center under the same charge. The principal frequency of vibration in the Z direction is mainly distributed from 50 to 80 Hz. And the frequency tends to decrease with the decrease of distance from the center of explosion source. At the same time, the natural vibration frequency of most underground pipelines is from 4 to 10 Hz, indicating that the ground vibration caused by tunnel blasting is difficult to generate resonance with the pipelines, which is conducive to the safe operation of underground pipelines (Xu et al. 2003).

In practical engineering, Sodev's empirical formula is often used to determine the vibration velocity of blasting and is mostly used for regression analysis of blasting vibration velocity (Zhang et al. 2008). The Sodev's empirical formula is as follows.

$$V = k\left( {\frac{{Q^{1/3} }}{R}} \right)^{\alpha }$$
(1)

where \(V\) is the particle velocity (cm/s); \(Q\) is the charge (kg); R is the monitoring point from the blasting source (m); \(k\) is the coefficient related to the rock medium and blasting conditions; \(\alpha\) is the attenuation coefficient of vibration.

The peak vibration velocity in the Z direction of the measuring point is the largest, therefore the regression analysis of the peak vibration velocity in the Z direction of the measuring point in Table 1 is carried out. The result was given in Fig. 5. The Sodev's empirical formula of Vz is shown in (2), where, Vz is the velocity of Z direction (cm/s); Q is the charge (kg); and R is the distance from the test points to the explosive source (m). This formula can be used to study the blasting attenuation law of tunnel blasting through water supply pipeline and provide guidance for subsequent tunnel blasting construction.

$$V_{z} = 67.71\left( {\frac{{\sqrt[3]{Q}}}{R}} \right)^{1.42}$$
(2)
Fig. 5
figure 5

Regression analysis curve of blasting vibration velocity

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3 Numerical Model and Simulation Method

3.1 3D Model

A symmetrical model was built by taking the YOZ plane as the symmetric plane. The size of the 3D model is 30 m (length) × 18 m (width) × 30 m (height), the unit size is controlled at about 35 cm, given in Fig. 6. The equivalent diameter method was used to simplify multiple cut holes into one hole, because the distance between the cut holes is much smaller than the distance between the tunnel and the pipeline (Lin et al. 2010). Surface automatic restraint is adopted between the soil layer and the pipeline, and a common joint is adopted between the soil layer and the rock stratum. Symmetric constraints are imposed on the symmetric surface of the model. The top surface is defined as a free surface and the other surfaces are defined as a non-reflective boundary (Jiang et al. 2005). The selection of units, the direction of pipeline length and the steel element have been given in Fig. 7.

Fig. 6
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The finite element model and meshing

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Fig. 7
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Concrete and steel element

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3.2 Material Model and Parameters

3.2.1 Air

The air is described by MAT_NULL material model and EOS_LINEAR_POLYNOMIAL equation of state. The pressure is as follows (Hallquist 2015):

$$P = C_{0} + C_{1} \mu + C_{2} \mu^{2} + C_{3} \mu^{3} + (C_{4} \mu + C_{5} \mu + C_{6} \mu^{2} )E_{0}$$
(3)

where µ = ρ/ρ0 − 1, ρ is the current density, ρ0 is the initial density; E0 is the initial internal energy per volume; C0, C1, C2, C3, C4, C5 and C6 are constants, V0 is the initial volume. The air material parameters are shown in Table 2 (Ma et al. 2011).

Table 2 Parameters of air
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3.2.2 Explosive

The explosive charge weight was modelled using (MAT_HIGH_EXPLOSIVE_BURN). The Jones-Wilkens-Lee (JWL) Equation of State (EOS) is used to calculate the detonation pressure (Hallquist 2015):

$$P = A\left( {1 - \frac{\omega }{{R_{1} V}}} \right)e^{{ - VR_{1} }} + B\left( {1 - \frac{\omega }{{R_{2} V}}} \right)e^{{ - VR_{2} }} + \frac{{\omega E_{0} }}{V}$$
(4)

where E is the internal energy per unit volume, V is the relative volume of the explosive product, and A, B, \(R_{1}\),\({ }R_{2}\), and ω are the equation constants for the explosive, D is the detonation velocity. Table 3 gives the material parameters of No.2 rock emulsion explosive (Liu et al. 2012).

Table 3 Parameters of explosive
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3.2.3 Rock Stratum and Soil

The rock stratum was modeled using MAT_PLASTIC_KINEMATIC material model (Hallquist 2015). The specific parameters are shown in Table 4. E is the elasticity modulus, fy is the yield strength, Etan is the tangent modulus, β is the hardening parameter.

Table 4 Parameters of rock
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The soil layer is modeled using MAT_FHWA_SOIL model, and is suitable for simulating soil materials in explosive problems (Jayasinghe et al. 2013; Qin et al. 2019). Most of the soil layers in the pipeline section below the tunnel are gravel sand, and its material parameters are shown in Table 5 (Lewis 2004). Gs is the specific gravity of soil grain, K is the bulk modulus, G is the shear modulus, c is the cohesion, φ is the internal friction angle, and W is the moisture content.

Table 5 Parameters of soil
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3.2.4 Concrete and Steel

The strength of underground pipeline concrete is C30, which is simulated by the MAT_72R3 model. The parameters of C30 concrete are shown in Table 6 (Malvar and Simoms 1996). The longitudinal reinforcement of underground pipeline is HRB335 with a tensile strength of 335 MPa; the stirrups are HPB235 with a tensile strength of 235 MPa. The reinforcement is modeled using the MAT_PLASTIC_KINEMATIC material model, and the influence of strain rate effect on yield strength is considered according to the COWPER_SYMONDS model. The material parameters are shown in Table 7 (Zhang et al. 2009). ν is the Poisson's ratio, C and P are strain rate coefficients, which are used to define the dynamic increase coefficient of the reinforcement, and Fs is the failure strain.

Table 6 Parameters of concrete
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Table 7 Parameters of steel
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3.3 ALE Algorithm

In order to avoid the mesh serious distortion caused by excessive element deformation in the calculation process, ALE algorithm was selected for tunnel blasting simulation. Compared with Lagrange algorithm, ALE algorithm can effectively deal with large deformation problems, which can also provide a clearer definition of the interface of material flow than Euler algorithm (Li et al. 2008). In this paper, explosive and air are divided into Euler grid, and ALE_MULTI-MATERIAL_GROUP keyword was used to bind them in the same element algorithm. The rock, soil and pipeline were divided into Lagrange grid, and fluid–solid coupling was realized between Lagrange grid and Euler grid by defining CONSTRAINED_LAGRANGE_IN_SOLID (Koneshwaran 2014).

3.4 Model Verification

In order to verify that the numerical simulation results were reasonable, the velocity of the ground vibration during tunnel blasting construction was measured using NUBOX-8016 monitor and compared with the values obtained by numerical simulation. The charge of explosive is 3.2 kg, and the distance from explosive source is 16.80 m. The comparison of particle vibration velocity of monitoring points was given in Table 8. The waveform comparison figure of the measured and simulated vibration on the ground surface was given in Fig. 8. it can be found that the maximum relative error between the simulated vibration velocity and the measured peak velocity of X, Y and Z directions was 8.2%. Therefore, it was reliable to study the dynamic response of underground pipelines under blasting vibration based on the numerical calculation model.

Table 8 Comparison of particle vibration velocity of monitoring points
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Fig. 8
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Time history of velocity at monitoring point

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4 Simulation Result Analysis

4.1 The Blasting Seismic Wave Propagating Rules

The propagation of blasting waves in rocks media at different times was given in Fig. 9. After the detonation of the column charge, the blasting seismic wave propagates in the form of spherical waves through the rock stratum, shown in Fig. 9a. The area of surface wave increases and the peak pressure decreases with the propagation of the blasting wave. The blasting seismic wave propagates to the boundary of rock and soil at t = 10 ms, shown in Fig. 9b. As shown in Fig. 9c, at the time of t = 15 ms, the blasting seismic wave propagates to the lower surface of the pipeline. It can be seen from Fig. 9d that seismic waves are reflected and transmitted at the junction of rock and soil. Some of them are reflected back to the rock stratum and propagate in the rock, while others are transmitted through the interface in the soil layer.

Fig. 9
figure 9

Pressure contours in the rock and soil at different times (unit: 102 GPa)

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The propagation of blasting seismic wave on pipeline at different time was shown in Fig. 10. The blasting seismic wave first reached the bottom of the pipeline right above the explosive, shown in Fig. 10a. Subsequently, seismic waves propagated along the transverse and the longitudinal axes of the pipeline, and the pressure on the pipeline increased gradually, shown in Fig. 10b, c. At about the time of t = 22.5 ms (Fig. 10d), the entire pipeline was subjected to blasting seismic waves. As time passed away, the peak pressure of blasting seismic wave decreased gradually, and when it attenuated completely in the soil, the pipeline stopped its response.

Fig. 10
figure 10

Pressure contours on the horseshoe-shaped pipeline at different times (unit: 102 GPa)

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4.2 Dynamic Response of Pipeline

The vibration response of underground structures is mainly analyzed by the peak vibration velocity and tensile stress of the structure (Guan et al. 2017). The section above the explosion center was first selected to analyze the peak velocity and tensile stress of the element at different parts of the section. Then, taking this cross section as the starting point (0 m), the variation law of the peak vibration velocity and the peak tensile stress of each part of the pipeline along the pipeline longitudinal direction was studied. The selection of each part element and the pipeline longitudinal direction were marked in Fig. 7.

The variation law of peak tensile stress at different sections of different elements of the pipe in case 9 was shown in Fig. 11. It can be seen that there is a big difference between the peak value of tensile stress in each section of the horseshoe pipe just above the explosion center. The peak value of tensile stress of each element of the vault is the largest, followed by that of the bottom plate, and that of the side wall is the smallest. Among them, the peak tensile stress of the element at vault C was the largest, about 0.57 Mpa, followed by was the element at vault A, about 0.45 Mpa. The largest value element of the bottom plate was at I, about 0.31 Mpa. The peak tensile stress of each element of the sidewall were not different from each other, neither of which exceeded 0.2 Mpa.

Fig. 11
figure 11

Comparison of peak tensile stress along the length direction

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The variation law of peak velocity of Z direction at different sections of different elements of the pipe in case 9 was shown in Fig. 12. It can be seen that there is a big difference between the peak value of velocity in each section of the horseshoe pipe just above the explosion center. The bottom plate and the arch roof of the pipeline have the maximum vibration velocity, and the maximum value of the peak vibration velocity occurs at the I of the bottom plate, about 3.17 cm/s, followed by was the C of the arch, about 3.08 cm/s, and the rest of the vibration velocity peaks were all less than 2.0 cm/s.

Fig. 12
figure 12

Comparison of peak tensile stress along the length direction

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The peak value of vibration velocity and the peak value of tensile stress of each part of the horseshoe pipeline change in the longitudinal direction in a relatively consistent way. The peak values occur at 0 to 4 m away from the explosion source, and gradually decrease as the distance from the explosion source increases.

5 Conclusions

  1. 1.

    The velocity of the pipeline increases gradually with the decrease of the distance away from the explosion source center under the same charge. The principal frequency of vibration in the Z direction is mainly distributed from 50 Hz to 80 Hz. And the frequency tends to decrease with the decrease of distance away from the center of explosion source. The ground vibration caused by tunnel blasting is difficult to generate resonance with the pipelines, because the natural frequency of most underground pipelines is from 4 Hz to10 Hz.

  2. 2.

    The maximum relative error between the simulated vibration velocity and the measured peak velocity of X, Y and Z directions was 8.2%. It was reliable to study the dynamic response of underground pipelines under blasting vibration based on the numerical model.

  3. 3.

    The blasting seismic wave first reached the bottom of the pipeline right above the explosive. Subsequently, seismic waves propagated along the transverse and the longitudinal axes of the pipeline, and the pressure on the pipeline increased gradually. And when it attenuated completely in the soil, the pipeline stopped its response.

  4. 4.

    The peak value of tensile stress of each element of the vault is the largest, followed by that of the bottom plate, and that of the side wall is the smallest. However, the velocity of the bottom plate and the arch roof of pipeline are the largest. The peak values of velocity and tensile stress exist in 0 to 4 m away from the explosion source, and gradually decrease as the distance away from the explosion source increases.

The damage of pipeline under tunnel blasting vibration is mainly governed by the principal tensile stress. However, the velocity is generally monitored to protect the pipeline from the blasting. Therefore, the coupling relationship between the velocity and the principal stress of pipeline to blasting vibration is supposed to be investigated in the future research.