Safety assessment of upper water pipeline under the blasting vibration induced by Subway tunnel excavation

Engineering Failure Analysis 104 (2019) 626–642

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Safety assessment of upper water pipeline under the blasting vibration induced by Subway tunnel excavation

T

⁎

Xia Yuqing, Jiang Nan , Zhou Chuanbo, Luo Xuedong Faculty of Engineering, China University of Geosciences, Wuhan, China

A R T IC LE I N F O

ABS TRA CT

Keywords: Water pipeline Dynamic response Blasting vibration Safety assessment Subway

In order to assess the safety of a buried DN1200 water supply pipeline under blasting vibration induced by subway tunnel excavation, we established a 3D numerical model of the real field engineering based on the Ling-Qing section of Tsingtao Metro Line 3. According to the field blasting monitoring test of ground surface, the reliability of the numerical model and the parameters is proved. Then, the dynamic response of the pipeline in empty state under the blasting vibration is discussed. Meanwhile, the crack strength of reinforced concrete pipe is determined based on the fracture mechanics theory. Based on the analysis, the safety of the empty pipeline under the blasting vibration is assessed. Next, we further assessed the safety of pipeline in the state of full-filled water without pressure and full-filled water with 0.2 MPa pressure (the normal working state). The results indicate that the upper water pipeline in the three states is safe under the blasting vibration induced by subway tunnel excavation with adopted parallel cut blasting method.

1. Introduction Since the beginning of subway construction in China in the 1950s, China's urban rail transit construction has entered a golden period of development. In the next ten years, China's rail transit market will build 7395 km of subway lines. By 2020, there will be 33 cities in China with 177 subway lines [1]. However, many cities have poor early urban planning, and pipeline distribution is intricate. It is inevitable to cross complex pipeline areas during subway construction and blasting excavation. The vibration induced by blasting may cause damage to adjacent buried pipelines and affect normal supply of residents. So, it is necessary to assess and ensure the safety of adjacent buried pipelines during blasting excavation of tunnels passing through the pipelines. Up to the present, there is not much research on the safety assessment and protection of pipeline subjected to blasting of tunnel excavation [2,3]. Limao Zhang assessed the risk of existing pipeline in tunneling environments without considering the blasting vibration effect [4]. Dowding, Charles H et al. presented methodology and guidelines for the evaluation and protection of buried pipelines subjected to the effects of blasting [5]. However, much more research has studied by scholars and most of them focused on the influence of surface mine blasting, underwater explosion and other surface explosion of terrorism and military on pipeline [6–9]. Siskind, D.E et al. studied surface coal mine overburden blasting near four steel and one PVC pipeline of 15 to 51 cm-diam with vibration, strain and pressure monitored. No failures occurred from blasting [10]. GP Kouretzis et al. introduced a robust methodology for the analytical calculation of strains in flexible buried pipelines due to surface point-source blasts [11]. Ojdrovic et al. analyzed the effects of blasting on pre-stressed concrete cylinder pipe (PCCP) lines and proposed guidelines for arriving at safe peak particle velocity (PPV) of blasts [12]. Yan et al. analyzed the dynamic responses of pipelines in soft soil to ground explosion [13]. ⁎

Corresponding author at: Faculty of Engineering, China University of Geosciences, Wuhan, No.388, Lumo Road, Hubei, Wuhan 430074, China. E-mail address: [email protected] (N. Jiang).

https://doi.org/10.1016/j.engfailanal.2019.06.047 Received 19 September 2018; Received in revised form 2 June 2019 Available online 22 June 2019 1350-6307/ © 2019 Published by Elsevier Ltd.

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Abedi et al. presented a mathematical method to calculate the displacements of pipelines under an equivalent blast dynamic load, resulting in a fourth-order inhomogeneous partial differential equation which has to be solved so that the pipe displacement and PPV could be found. Furtherly, the maximum particle velocity is calculated by Fourier transform [2]. WANG et al. carried out a laboratory similar model test which variables such as charge and distance are considered, and a formula between the maximum velocity transfer coefficient and the stiffness coefficient of pipe-soil were defined. Finally, a safety vibration criterion based on the design value of fatigue strength is proposed. Rigas established a cube scaling model of the ground in contact with the pipeline and the stress on the pipeline were directly related to the PPV of the ground in contact with the pipeline based on the Huber-Hencky-Mises stresses approach [14].As a new research method, numerical simulation is increasingly used in related blasting research [15]. Zhang et al. studied the effect of blasting vibration on underground pipeline by field monitoring and numerical simulation, and the relationship between PPV and tensile stress of the pipeline is established. Based on the ultimate tensile strength criterion, the blasting vibration safety criterion of pipeline under empty state is calculated and proposed [3]. Parviz, Mohsen et al. used LS-DYNA to simulate the dynamic response of water in buried pipeline subjected to blast [16]. However, none of them studied the different dynamic response of water supply pipelines under different working conditions. In this paper, we focused on the Ling-Qing section where the tunnel and the water supply pipeline are parallel in Tsingtao metro line 3. First, based on the field blasting vibration monitoring under three different condition of pipeline, a 3D numerical model is established to analyze the dynamic response of buried pipeline subjected to blasting vibration by using FNM software ANSYS/LSDYNA and verified its reliability with monitoring data under condition of empty of pipeline (Section 3). Then, the different PPV and peak effective stress (PES) subjected to metro tunnel blasting vibration on water supply pipeline in state of empty (Section 4), fullfilled water without pressure (Section 5), normal working condition with 0.2 MPa water pressure are discussed (Section 6), also, the criterion of crack (tensile) strength of concrete pipes is calculated. Finally, the safety of pipeline under blasting vibration is assessed based on the ultimate tensile strength criterion. 2. General information of metro tunnel project 2.1. Tunnel and geological conditions The project is located in the Ling-Qing section of Tsingtao Metro Line 3 subway tunnel. Tsingtao metro line 3 has a total length of 25.2 km, crossing three municipal districts, Shinan District, Shibei District and Licang District, with 22 stations. As shown in Fig. 1, the geological conditions of the construction stratum are mainly Quaternary, surrounding rock grades IV to V. the tunnel section is relatively flat with the Quaternary sedimentary soil distributed on the ground surface. The surrounding rocks under the soil layer are mainly strong weathered granite and light weathered granite. Fig. 2 shows that the DN1200 water supply pipeline with diameter of 120 cm and wall thickness of 15 cm is directly above the tunnel. The minimum distance between 2.8 m buried depth pipeline and the tunnel are only 8. 9 m and they are parallel. Repeatedly blasting vibration may damage the pipeline during tunnel excavation. On the one hand, blasting vibration may influence the stabilization of surrounding rock and lead to the settlement of pipeline, which may occur damage to pipeline; on the other hand, due to high pressure water flowing in pipe and its wide diameter, there will be a huge influence to citizens and tunnel construction after damage. So, in this project, large diameter hollow parallel cutting hole with 0. 9 m depth, 40 cm of its diameter and 0. 75 m cyclical footage is implemented to control blasting vibration reasonably. 2.2. Blasting design parameters Fig. 3 demonstrates the arrangement of cutting holes based on blasting design. The tunnel is excavated by drilling and blasting method, large diameter hollow parallel cut with depth of 0. 9 m, 40 cm of its diameter and 0.75 m cyclical footage is applied, the cutting holes are centered on the hollow hole with diameter of 150 cm, four cutting holes and four expansion cutting holes are annularly distributed. Each hole is charged with 0.2 kg explosive. The holes of different colors represent different initiation sequences, and the holes initiates from inside to outside. Schematic diagram of arrangement of blast holes in the upper bench is shown in Fig. 4. 3. Numerical simulation and verification 3.1. Dimensions of numerical simulation and boundary conditions Blasting vibration may cause damage to the water supply pipeline under normal working conditions which may lead to serious consequence to residents even tunnel construction. Therefore, pipeline was suspended by water affairs bureau temporarily and in state of empty. Large diameter hollow parallel cut was implemented to lower the blasting vibration and vibration velocity on surface above pipeline was monitored by TC-4850, the device has a three-dimensional vibration detector with sampling frequency of 0~1000 HZ, which is high-precision and high reliability. To analyze and evaluate the dynamic response of water pipeline subjected to blasting excavation, ANSYS/LS-DYNA is used to establish the numerical calculation model when the vertical distance from the tunnel excavation face to the pipeline with 2.8 m buried depth is 8.9 m according to the practical blasting excavation construction of the metro tunnel. In order to avoid the boundary effect of the model, the distance from the tunnel to the bottom of the model is > 3 times of the height of the tunnel, and the distance 627

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Fig. 1. Tsingtao Metro Line 3 layout.

between the tunnel and the edge of the model is > 3 times of the tunnel width. The model materials include soil, rock, explosives, plugging mud, water and prestressed concrete pipe, the overall size of the model is 48 m ×39 m ×20 m. The 8-node SOLID164 solid element is used to establish the model. ALE grids are used for explosive, light weathered granite, water and plugging mud [17], Lagrange grids are used for soil, water pipeline and strong weathered granite. CONSTRAINED_LAGRANGE_IN_SOLID keyword is used to simulation Fluid-structure interaction (FSI) between water and the pipeline [18]. To truly reflect the characteristics of the contact between the pipe and the soil, the command CONTACT_AUTOMATIC_SURFACE_TO_SURFACE is used to model the contact condition of the pipeline and the soil. The model adopts cm-g-s unit system. The top surface of the model and hollow hole is considered as a free constrained boundary and all other surfaces are set to be non-reflecting boundaries [19]. The charge weight of cutting holes is great than that of other blasting holes, and its induced vibration is also great than that of the other blasting holes, so only cutting holes are selected for numerical analysis [20]. The cutting holes layout, hole depth and charge weight in numerical simulation are consistent with Section 2.1. For simplification, the explosive is concentrated charged at the bottom of the holes and inverse initiation is adopted for cutting holes, and the rest of the cutting holes is filled with plugging mud. The finite element mesh size for the pipeline part is approximately equal to 20 cm and 60 cm for rock and soil. Numerical model size and boundary conditions are shown in Fig. 5. 3.2. Constitutive model and calculation parameters The parameters in the model include explosive, soil, pipeline, light weathered granite, strong weathered granite, plugging mud and water. Emulsion explosives and water gel explosives are often used in blasting construction in Tsingtao metro, and No. 2 rock emulsion explosive is used in this tunnel section and numerical model. Relevant parameters shown in following tables (Tables 1 through 6). The Jones-Wilkins-Lee (JWL) EOS is a high energy combustion model used to describe the chemical reaction process and predict a large range of pressure caused by explosion using experimentally-obtained parameters [21]. In this study, JWL EOS is chosen to 628

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Ground surface Soil

Monitoring points

900

280

890

Pipeline

3000

620

Strong weathered granite Light weathered granite

y z

x Fig. 2. Schematic diagram of spatial location of tunnel and the pipeline.

Fig. 3. Schematic diagram of arrangement of cutting holes.

describe the explosion and expressed as follows:

ω ⎞ −R1 V ω ⎞ −R2 V ωE0 P = A ⎛1 − e + B ⎛1 − e + R1 V ⎠ R2 V ⎠ V ⎝ ⎝ ⎜

⎟

⎜

⎟

(1)

where, P and V are the pressure of the detonation and the relative specific volume respectively, E is the internal energy per unit volume, A, B, R1, R2 and ω are material constants. The numerical calculation parameters are selected based on the indoor mechanical test results. Rock and soil in simulation is simplified to be homogenous without considering the influence of internal cracks and weak planes in rock mass. MAT_PLASTIC_KINEMATIC material model is used for Strong weathered granite, light weathered granite and plugging mud [22]. The stress-strain formula of MAT_PLASTIC_KINEMATIC is as follow.

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Fig. 4. Schematic diagram of arrangement of blast holes in the upper bench

Fig. 5. Numerical model and boundary conditions. Table 1 Explosive parameters. Density (g/cm3)

Detonation velocity (m/s)

Detonation pressure (GPa)

A (GPa)

B (GPa)

R1

R2

E0 (GPa)

ω

1. 09

3600

3. 24

214.4

18.2

4. 15

0. 95

4. 26

0.15

Table 2 Physical and mechanical parameters of soil. Density(g/cm3) 1.8

Shear modulus (MPa) 4.0

Plastic hardening modulus 0

Pressure cutoff 7.03 × 10

630

−6

Effective plastic strain

Spall type

1.2

3

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Table 3 Physical and mechanical parameters of pipeline. Density (g/cm3)

2.4

Pressure hardening exponent N

0.61

Shear modulus (GPa) Strain rate coefficient C Normalized cohesive strength A Normalized pressure hardening B Normalized maximum strength smax Crushing pressure pc (MPa) Crushing volumetric strain μc Locking pressure pt (GPa) Locking volumetric strain μl

12.3 0.007 0.79 1.6 7 8 5.6 × 10−4 1.05 0.1

Quasi-static uniaxial compressive strength fc (MPa) Maximum tensile hydrostatic pressure T (MPa) Quasi-static uniaxial compressive strength ε0(s−1) Amount of plastic strain before fracture εmin Damage constant D1 Damage constant D2 Damage constant K1 (GPa) Damage constant K2 (GPa) Damage constant K3 (GPa)

24 2.7 1 × 10−6 0.01 0.04 1.0 17.4 38.8 29.8

Table 4 Physical and mechanical parameters of lightly weathered granite. Density (g/cm3)

Passion ratio

Elastic modulus (GPa)

Yield strength (MPa)

Tangent modulus (MPa)

2.6

0.25

52

60

20

Table 5 Physical and mechanical parameters of plugging mud. Density (g/cm3)

Passion ratio

Elastic modulus (GPa)

Yield strength (MPa)

Tangent modulus (MPa)

1.9

0.35

11

6

0.2

Table 6 Physical and mechanical parameters of strongly weathered granite. Density (g/cm3)

Passion ratio

Elastic modulus (GPa)

Yield strength (MPa)

Tangent modulus (MPa)

2.0

0.0.22

0.3

42

3.0

1

ε P⎤ ⎡ σY = ⎢1 + ⎛ ⎞ ⎥ (σ0 + βEP εPeff ) C⎠ ⎝ ⎣ ⎦

(2)

where, σY is yield stress, σ0 is initial yield stress, ε is strain rate, C and P are strain rate parameters, εPeff is effective plastic strain, EP is plastic hardening modulus, β is hardening coefficient. MAT_ELASTIC_PLASTIC_HYDRO_SPALL material model is used for soil. Constitutive equation can be expressed as

σy = σ0 + Eh ε p + (a1 + pa2 ) max[p, 0]

(3) EE

where, σ0 is initial yield stress of materials. σy is yield stress of material. Both are expressed as effective stress. Eh = E −t E is plastic t hardening modulus defined in terms of Young's modulus, ε p is equivalent plastic strain. MAT_JOHNSON_HOLMQUIST_CONCRETE material model is used for concrete pipeline [23]. This model can be used for concrete subjected to large strains, high strain rates and high pressure. The equivalent strength is expresses as a function of the pressure, strain rate, and damage. The pressure is expressed as a function of the volumetric strain and includes the effect of permanent crushing. Therefore, the HJC model is more accurate than the elastic model to describe the dynamic response of concrete of practical engineering in simulation. The expression is defined as

σ ∗ = [A (1 − D) + Bp∗n ](1 + c ln ε∗)

(4) ·∗

where D is the damage parameter, p∗ = p/f′ is the normalized pressure and ε = equivalent plastic strain and plastic volumetric strain, and is expressed as

D=

∑

ΔεP + ΔμP D1 (P ∗ + T ∗) D2

· · ε / ε0

is the dimensionless strain rate, D, both from

(5)

where Δεp and Δμp are the equivalent plastic strain and plastic volumetric strain, D1 and D2 are material constants and T ∗ = T / fc′ is the normalized maximum tensile hydrostatic pressure. All physical and mechanical parameters are shown in the following tables. 631

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Fig. 6. Location of the monitoring points.

3.3. Field vibration monitoring and reliability analysis of numerical simulation Since the pipeline is buried in the soil, and the pipeline company does not allow excavation to reveal the pipeline for monitoring. In order to complete the comparison and verification of the actual blasting vibration monitoring results. 3 TC-4850 self-recording devices were set up on the ground surface directly above the pipeline to extract the peak particle velocity. The TC-4850 self-recording devices developed and manufactured by Zhongke (Chengdu) Instruments Company Limited is used to monitor the vibration. The devices contain a trisector sensor with measuring vibration ranging from 0.001 cm/s to 35.4 cm/s and measuring frequency ranging from 0 to 1000 Hz. Monitoring points layout is shown in Fig. 6. Three TC-4850 self-recording devices are placed on point 1, 2, 3 on the surface directly above the pipeline. Distance between each two monitoring points is 4 m. A total of three blasting monitoring is performed. Three blasting vibration monitoring was not carried out continuously, some blasting process was not monitored in the whole monitoring work. The water pipe is suspended for each blasting. Horizontal axial (Z axis), horizontal tangential (X axis), and vertical (Y axis) velocities are collected. Vibration monitoring data is shown in Table 7. The simulation results with empty pipeline model show that the maximum vibration velocity at the surface is No. 2 point, reaching 0.849 cm/s. Fig. 7 shows the resultant velocity of simulation and field monitoring points along Z axis on surface directly above the pipeline and the minus sign represents the excavated area. The resultant velocities between numerical simulation and field measured data at point 2 are relatively close, while the resultant velocities in simulation and field data are slightly different at point 1 and 3, which could be explained that the location of tunnel face and the condition of soil is different in three field vibration monitoring. Furthermore, Because of the material fracture, rock mass joints and weak structural planes in the rock formations, the stress wave and vibration in field attenuate faster than that in the numerical simulation. The pipeline is the main object in this study, the propagation and attenuation of the vibration between tunnel direction and the pipeline direction are different. So, it is unnecessary to validating the model with other monitoring points in the tunnel. Figs. 8 and 9 show the velocity-time histories of ground Table 7 Surface monitoring data under empty states of pipeline. cycle

a

b

c

Monitoring points

1 2 3 1 2 3 1 2 3

Vibration velocity

Vector composition velocity

Maximum vertical component

Maximum tangent component

Maximum axial component

V1(cm/s)

V2(cm/s)

V3(cm/s)

V(cm/s)

0.351 0.450 0.351 0.432 0.633 0.751 0.458 0.471 0.191

0.180 0.430 0.180 0.210 0.274 0.100 0.269 0.590 0.140

0.190 0.610 0.190 0.220 0.634 0.180 0.157 0.440 0.160

0.430 0.871 0.438 0.528 0.935 0.779 0.554 0.874 0.286

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Fig. 7. Velocity of simulation and monitoring points along Z axis on surface directly above the pipeline.

Fig. 8. Field measured vibration velocity in Y direction.

surface between field measured curves and numerical simulation. As is shown in Fig. 7, the surface velocity decreases gradually with the distance from the explosive increasing. The maximum velocity occurs on NO. 2 point on ground surface directly above the pipeline which is in the same cross section where the explosive is located. No cavity effect occurs in the tunnel [24]. So, the damage and dynamic response of pipeline and ground at the cross section where No. 2 point is located is the greatest under blasting vibration. In the field monitoring, the monitoring points on the ground is located directly above the explosive, and the vibration velocity in vertical direction is the largest in the three vector directions. In Fig. 8, the vibration velocity curves of segment 1 of detonators is similar to the vibration velocity curve caused by cut blasting in numerical simulation. Comparison of the numerical simulation data and the field measurement data shows that the numerical calculation model and the parameter selection are reasonable. It is feasible to study the dynamic response of pipeline subjected to the blasting vibration by numerical simulation.

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Fig. 9. Simulation vibration velocity in Y direction.

4. Safety assessment of pipeline in empty state 4.1. Dynamic response of pipeline in empty state The cross section of the pipeline which is directly above the explosive source is vital for vibration analysis. In order to assess the safety of buried water supply pipeline subjected to excavation. As is shown in Fig. 10 16 points on the cross section of the pipeline are selected to analyze the dynamic response, As we know, the blasting seismic wave may cause the vibration and change the stress and strain of pipeline. In the numerical simulation, the effective stress is used to assess the safety of the pipeline, the effective stress is obtained based on the von Mises yield criterion, which is part of plasticity theory that applies best to ductile materials. Based on the criterion, prior to yield, material response can be assumed to be a nonlinear elastic, viscoelastic or linear elastic behavior. Because the von Mises yield criterion is independent of the first stress invariant, it is applicable for the analysis of plastic deformation for ductile materials such as concrete,

Fig. 10. The cross section of pipeline directly above the explosive source. 634

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Fig. 11. Resultant PPV.

as onset of yield for these materials does not depend on the hydrostatic component of the stress tensor. The peak particle velocity (PPV) and peak effective stress (PES) are suitable to describe the response of concrete JHC model under blasting load. According to the simulation calculation, resultant PPV and PES of each point on the pipeline are analyzed and shown in Figs. 11 and 12. Distribution of resultant velocity along the Z axis on bottom of the pipeline is shown in Fig. 13. From Figs. 11 and 12, it is clear that the greatest PPV is at the bottom of the pipeline followed by middle part and the top part. The greatest PPV at bottom is 2.52 cm/s which is 1.35 times than the top. The welcome blast side points with 0.315 MPa is greater than those in the other side. Along the Z axis of the pipeline, the greatest PPV occurs in the cross section where the explosive is located and

Fig. 12. Peak effective stress. 635

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Fig. 13. Distribution of velocity along the Z axis on the bottom of the pipeline.

decreases to both ends of the pipeline. 4.2. Criterion of crack (tensile) strength of concrete pipes Crack strength calculation of reinforced concrete pipe is based on the existence of macroscopic surface cracks before cracking. Fracture mechanics theory is used to analyze the crack strength of reinforced concrete pipe [25]. Criterion for unstable propagation of crack: (6)

K1 ≤ K1C where, K1 is the stress intensity factors of crack; K1C is fracture toughness of material. Based on fracture mechanics literature:

(7)

K1 = Yσ πα L

R pL

πα

Y = πα tan L is geometrical factor of crack; α is fracture length; σ = A , A0 is equivalent concrete area, R is inner radius of pipe. 0 L is length of pipeline (1000 mm). There is size effect in K1C, based on Weibull statistical theory of brittle rupture, size effect conversion is conducted in the following formula: 1/2

W K1LC = K1SC ⎛ L ⎞ ⎝ WS ⎠ ⎜

⎟

1/ α

⎛ VS ⎞ ⎝ VL ⎠

⎜

⎟

(8)

where, K1C , WL, WS, VS, VL are fracture toughness, interface height and volume in size of large or small respectively. α is the shape parameter of Weibull distribution. Which can be roughly considered as 10. K1CL,

S

K1SC = 0.8fc = 9ft

(9)

fc is compressive strength of concrete cube with size 20 × 20 × 20 cm, ft is cleavage strength. The calculation formula for rupture strength of reinforced concrete pressure pipes is:

p=

A0 K1C RL L tan

πα L

(10)

where t is ply of pipeline. According to pipeline on site, inner radius R = 600 mm, t = 75 mm, so the rupture strength of pipe is 1.62 MPa based on the formula above. According to Nan Jiang [26] The following relationship exists between ultimate tensile strength of the material and dynamic ultimate tensile strength

σt = σt 0 [1 + 0.121 lg(vH )] = KD σt 0

(11)

where, [σt] is dynamic tensile strength, σt0 is static tensile strength, vH is the rate of loading, vH = σH/σ1; σH is arbitrary acceleration (σH > 1), σ1 is loading speed, σ1 = 0.1 MPa/s; KD is dynamic strength improvement coefficient. 636

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Fig. 14. Empty.

The loading speeding of rock can be 106 MPa/s under blasting seismic wave. In general, the loading speed of tunnel is between 10~103 MPa.so:

KD ∈ (1.24, 1.48)

(12)

Dynamic ultimate tensile strength of the pipeline is 1.24–1.48 time than static ultimate tensile strength. So, the ultimate tensile strength of the pipeline under dynamic load is 2.01 MPa. The maximum effective stress of pipeline subjected to blasting vibration under empty state is 0.315 MPa, which is much lower than the dynamic ultimate tensile strength 2.01 MPa. It is safe for the empty pipeline under the first three blasting. 5. Safety assessment of pipeline in state of full-filled water without pressure Pipeline is suspended for the first three blasting to ensure its safety. Monitoring data and numerical simulation results show that the surface vibration velocity directly above the pipe in the state of empty is small. Since then, water supply pipeline was no longer disabled and water pressure of pipe is lowered to nearly zero which can be considered to be full-filled with water without pressure in further tunnel excavation. Same field monitoring layout is set during blasting excavation. The monitoring data shows that the greatest resultant velocity occurs on the site of No. 2. Point, reaching 0.825 cm/s. According to blasting design, the model size, boundary conditions, and material constitutive of model in numerical simulation are the same as the one which is in state of empty. Same numerical simulation model is created and pipeline is full-filled with water without pressure, which is shown in Figs. 14 and 15. Vibration velocity and effective stress of pipeline in state of full-filled water without pressure are analyzed in numerical simulation. *MAT_NULL material model is used for water, the equation of state uses keywords *EOS_GRUNEISEN, which is expressed as follows:

P=

(

ρ0 C 2μ ⎡1 + 1 − ⎣

γ0 2 μ2

)μ −

a 2 μ⎤ 2 ⎦ μ3

2

+ (γ0 + aμ) E

u>0

⎡1 − (S1 − 1) μ − S2 μ + 1 − S3 ⎤ (μ + 1)2 ⎦ ⎣

(13)

Fig. 15. Full-filled water without pressure. 637

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Table 8 Physical and mechanical parameters of water. Density (g/cm3)

C (m/s)

S1

S2

S3

γ0

1.0

1480

2.56

1.986

1.2268

0.5

P = ρ0 C 2u + (γ0 + au) E

u>0

(14)

where C is sound speed in water, u = ρ/ρ0 − 1, ρ is the water density after disturbance, ρ0 is initial water density, E is specific internal energy, γ0 is coefficient of GRUNEISEN, S1, S2, S3 is VS − VP slope coefficient, α is volume correction coefficient. Detailed parameters are shown in Table 8. According to numerical calculation, the peak particle velocity and peak effective stress on cross section of pipeline where explosive is located are shown in Figs. 16 and 17. The velocity of No.2 point in numerical simulation is 0.836 cm/s which is close to 0.825 cm/s of field monitoring. The greatest PPV at bottom is 2.35 cm/s, and the welcome blast side points with the greatest effective stress 0.234 MPa are greater than those in the back side. Compared to empty state, velocity and effective stress of pipeline slightly decline. It is clear that the water in the pipe lower the dynamic response of pipe, which is beneficial to pipeline protection，Field observations and numerical simulations show that the pipeline is not damaged and no leakage occurs. Fluid-solid interaction (FSI) is the interaction between two-phase media. Deformed solids deform or move under fluid loading. Inversely, deformation and motion of the solids affects the fluid, thus changing the distribution and size of the fluid load. DAA and NDAA method [27–29] were often applied to analyze the interaction between the water and structure based on the plane wave hypothesis. At present, the researches on the dynamic response of pipelines or liquid storage tanks under liquid-filled or empty states subjected to external loads are based on experiments [30–32]. Yang Chen [33] used ANSYS/LS-DYNA combined with fluid-structure interaction algorithm to analyze the different responses of oil storage tanks under different liquid heights, the relationship between the vibration velocity of the tank wall and the liquid heights was established. Meanwhile the different responses of the oil storage tank under different dominant vibration frequencies were also calculated. Under the circumstances that the first 20th order natural vibration frequencies of the empty or the FSI model tank is low, the PPV on the wall surface is decreasing with the decrease of the blasting vibration frequency. Since the dominant frequency of blasting vibration is much larger than the natural vibration frequency of the oil storage tank, the relationship between the response of the oil storage tank and the dominant frequency of the blasting vibration cannot be analyzed by the conclusion: the closer the dominant frequency of blasting vibration is to the natural vibration frequency of the oil storage tank, the more intense response of the structure. Model analysis is also conducted by ANSYS to calculate the natural vibration frequency of the pipeline in empty state and full water without pressure in this paper. As shown in Figs. 18 and 19 below, it is found that the natural vibration frequency of the liquidfilled pipeline (length: 5 m) is slightly lower than that of the empty pipeline (first order natural vibration frequency: empty state 84 HZ, full water without pressure 78 HZ), which is consistent with some researches. The natural vibration frequencies of buried pipelines of different sizes mentioned in many literatures are close to 100 HZ [34]. However, the dominant frequency of blasting

Fig. 16. Resultant PPV. 638

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Fig. 17. Peak effective stress.

Fig. 18. Empty.

vibration is mostly concentrated in 10~30 HZ, and some are as high as 50 HZ [35], which is still far below the natural vibration frequency of the buried pipeline. Therefore, the conclusion that the closer the dominant frequency of blasting vibration is to the natural vibration frequency of the pipeline, the more intense response of the structure cannot explain the phenomenon in which the natural vibration frequency of the pipe decreases and then the vibration response of the pipe also decreases after the pipe is full-filled with water. It could be explained that the presence of water in the pipeline may induce the effect of added mass. The pipe vibrates in the water, the impact load not only does work for the pipeline, but also for the water in the pipeline. The static pressure and vibration of the water in the pipeline can absorb and dissipate the explosive impact energy. The conclusion that the liquid in the container could improve the anti-explosion capacity of structure against deformation and damage has been drawn in many literatures [31,33], but these findings are directly measured by experiments and theoretically explanations are lacking. The theoretical analysis on the FSI of liquid-filled pipeline under external impact load is rather complex, which is not discussed in this paper. Correlational analysis will be 639

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Fig. 19. Full water without pressure.

carried out in further research. 6. Safety assessment of pipeline in working state Monitoring data, field observations and numerical simulation indicate that the pipeline is safe under the condition of empty and full-filled water without pressure. To minimize the inconvenience caused to residents due to the abnormal working state of pipeline, the pipeline is set to be normal working state with 0.2 MPa water pressure when blasting excavation. Arrangement of blasting holes, the model size, boundary conditions, material constitutive of model in numerical simulation is also the same as the one which is in state of empty. Same numerical simulation model is created and pipeline is in normal working state with 0.2 MPa water pressure, which is shown Fig. 20. Same field monitoring layout is set during blasting excavation. And field measured result shows that the greatest resultant velocity occurs on the site of No. 2. Point, reaching 0.956 cm/s. The PPV and PES on cross section of the pipeline where explosive is located are analyzed, as is shown in Figs. 21 and 22. Compared with the empty state and full-filled water without pressure, the PPV and PES are significantly increased, the pipeline under normal working state is the most disadvantage condition subjected to blasting vibration. The PPV on the cross section of the pipeline is 7.55 cm/s and the PES is 1.47 cm/s. The vibration response on the welcome blast side is stronger than that of back side, the dynamic response characteristics of the pipeline under normal working state are the same as those of the pipeline under empty state. It can be seen in the Figs. 21 and 22, The numerical simulation results show that PPV at the ground surface directly above the explosive is the greatest, reaching 0.8501 cm/s, which is consistent with the practical monitoring results. The PPV of ground surface in normal working state is close to that in state of full-filled water without pressure and empty state. Therefore, the different dynamic responses due to the changes of different working conditions of the pipeline cannot be reflected by monitoring the ground surface

Fig. 20. Normal working state. 640

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Fig. 21. Resultant PPV.

Fig. 22. Peak effective stress.

velocity. The maximum effective stress of pipeline subjected to blasting vibration under normal working state is 1.47 MPa, which is lower than the dynamic ultimate tensile strength 2.01 MPa. It is safe for the pipeline under the normal working state subjected to blasting. Field observations and numerical simulations show that the pipeline is not damaged and no leakage occurs. The adopted parallel cut blasting method is proved to be applicable for pipeline protection. Previous literatures have also shown that the PPV and PES of the pipeline increase with the increase of the internal pressure of the pipeline [36,37]. The correlational theoretical that the increase of pipeline internal pressure will lead to the decrease of pipeline antiexplosion capacity is complex and scarce, which will be discussed in further studies. 7. Conclusion (a) Based on the numerical simulations and monitoring data, it can be considered that the cross section of the pipeline where the explosive is located is the most unfavorable part of the pipeline. The greatest PPV is at the bottom of the cross section followed by middle part and top part. No cavity effect occurs in the tunnel, the cross section of the pipeline directly above the explosion is the 641

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most dangerous section. (b) It can be seen from the numerical analysis that the pipeline is safe under these three different conditions subjected to blasting vibration. PPV and PES of the pipe are smallest when it is full-filled with water without pressure compared to empty and normal waking states. The presence of the water in the pipeline can absorb and dissipate the explosive impact energy. (c) In the practical project, minimizing the water pressure is conductive to pipeline protection and the damage of the buried pipeline subjected to the blasting vibration can be reduced. Safety of pipeline can be ensured without affecting the water supply to residents under blasting vibration. Acknowledgments The study was sponsored by the National Natural Science Foundation of China (Grant No. 41807265 and 41572281), and the Natural Science Foundation of Hubei Province of China (Grant No. 2017CFB310). 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