Numerical studies were carried out to investigate the vibration of buried pipeline subjected to blast seismic waves. The numerical model contains a 5 tons of explosive, an X70 buried pipeline and different kinds of soils. The stress and the vibration velocity of the pipeline were acquired during the simulation. The influence of buried depth on vibration velocity was also revealed in the paper

Chong Ji

Kejian Song

Quanjun Xu

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 411 
Numerical simulation of buried pipeline subjected to 
blast seismic waves 
Chong Ji1, Kejian Song2, Quanjun Xu3 
College of Field Engineering, PLA University of Science and Technology, Nanjing, China 
2Corresponding author 
E-mail: 1blastingcaptain@163.com, 2song_kejian@163.com, 3xquanjun@hotmail.com 
(Accepted 31 August 2015) 
Abstract. Numerical studies were carried out to investigate the vibration of buried pipeline 
subjected to blast seismic waves. The numerical model contains a 5 tons of explosive, an X70 
buried pipeline and different kinds of soils. The stress and the vibration velocity of the pipeline 
were acquired during the simulation. The influence of buried depth on vibration velocity was also 
revealed in the paper. 
Keywords: numerical simulation, buried pipeline, vibration velocity, blast wave. 
1. Introduction 
Buried pipelines are mainly used for distribution of water, gas, oil, etc., and are considered as 
the most important elements of lifelines. When subjected to blast seismic wave, the structure may 
cause serve disasters [1, 2]. Accordingly, analysis of buried pipeline subjected to dynamic loads 
is popular in recent years. 
Newmark [3] and Kuesel [4] first attempt to seismic design of buried pipelines likely be 
damaged by earthquakes or far explosions. Malachowski et al. [5] applied the blast load to the 
pipes with and without protective cover using ALE method. Mokhtari [6] used a combined 
Eulerian-Lagrangian method to study the response of buried steel pipelines to explosion, and 
generally concerns finding safe distance of explosion where pipeline does not undergo plastic 
deformation. There are many others use the finite element method, the finite-difference method 
or their combination to solve the problem [7, 8]. 
The present paper investigated the dynamic response of buried pipeline subjected to blast wave 
numerically. An Arbitrary Lagrangian-Eulerian method was adopted to develop a full-coupled 3D 
finite element model. By choosing proper material models, the dynamic process was studied with 
accuracy. The velocity and the stress of the pipeline was obtained, and the influence of buried 
depth was studied in the analysis. The results obtained from the present study can be used for 
improvement in protective design of steel pipelines. 
2. Numerical simulation 
2.1. Finite element model 
In the present paper, the mechanical performance of buried pipelines subjected to blast wave 
is studied numerically using nonlinear finite element code LS-DYNA. Considering the 
symmetries of the geometrical model, to save computation time, a half of the system was modeled 
as shown in Fig. 1. The ALE model involves six different material types. Eulerian meshes were 
generated for the explosive and the air. On the other hand, the Lagrangian meshes were used to 
model the field medium, the back-filling layer, the fine sand soil and buried pipelines. The model 
was constructed with Solid 164 solid element and g-cm-us unit. The material of the pipeline is 
X70, with a diameter 1219 mm and wall thickness 26.4 mm. The explosive used in the analysis 
was emulsion explosive. The distance between the pipeline and the explosion center was around 
50 m. The finite element model is shown in Fig. 1. 
NUMERICAL SIMULATION OF BURIED PIPELINE SUBJECTED TO BLAST SEISMIC WAVES.  
CHONG JI, KEJIAN SONG, QUANJUN XU 
412 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
Pipeline
Explosive
Air
Field medium
Back-filling layer
Fine sand soil  
Fig. 1. Finite element model 
2.2. Material behavior 
The explosive charge was modeled using the high explosive burn material model and the 
Jones-Wilkin-Lee (JWL) equation of state (EOS). The JWL equation of state defines the pressure 
as a function of the relative volume, ܸ and initial energy per volume, ܧ, such that: 
ܲ = ܣଵ ൬1 −
߱
ܴଵܸ൰ ݁
ିோభ௏ + ܤଵ ൬1 −
߱
ܴଶܸ൰ ݁
ିோమ௏ + ߱ ܧܸ, (1)
where ܣଵ, ܴଵ, ܤଵ, ܴଶ and ߱ are material constants, ܲ is the pressure, ܸ is the relative volume of 
detonation product and ܧ is the specific energy with an initial value of ܧ଴. The emulsion explosive 
C-J parameters and the JWL equation of state parameters: ߩ௘ = 0.6 g/cm3, ܦ = 6.93 km/s,  
݌஼௃ = 1.5 GPa, ܣଵ = 132.8 GPa, ܤଵ = 0.439 GPa, ܴଵ = 5.3, ܴଶ = 1.2, ߱ = 0.21,  
ܧ଴ = 3.2×109 J/m3, respectively. 
Material Type 9 of LS-DYNA (*MAT_NULL) is used to model the behavior of the air. Air 
mass density ߩ଴ and initial internal energy ݁଴ are 1.29 kg/m3 and 0.25 J/cm3, respectively. 
There are three different kinds of soils used in the analysis. In order to simulate the behavior 
of soil in this research, a plastic hardening model was used based on the soil properties. The yield 
stress and the strain rate has the following relationship: 
ߪ௬ = ቎1 + ൬
ߝሶ
ܥ൰
ଵ
௉ ൫ߪ଴ + ߚܧ௉ߝ௉௘௙௙൯቏ , (2)
ܧ௉ =
ܧ௬ܧ௧௔௡
ܧ௬ − ܧ௧௔௡,  (3)
where ܥ, ܲ are the Cowper-Symonds strain rate parameters, respectively; ܧ௬ is Young modulus; 
ߪ଴ is the initial yield stress; ߝሶ is applied strain rates; ܧ௣ is the plastic hardening modulus. The 
parameters of the model can be seen in [8]. 
The X70 pipeline material has been modeled using the Johnson-Cook (JC) constitutive relation 
and the Gruneisen equation of state. The JC model accounts for isotropic hardening, strain rate 
sensitivity and thermal softening. The model defines the yield stress ߪ௬ as: 
ߪ௬ = ሾܣ + ܤሺߝ௣̅ሻ௡ሿሾ1 + ܥlnߝሶ∗ሿሾ1 − ሺܶ∗ሻ௠ሿ, (4)
where ܣ , ܤ , ܥ , ݊  and ݉  are the material parameters determined by experiments. ߝሶ∗  is the 
dimensionless effective strain rate for and ܶ∗ is the homologous temperature. The parameters of 
the X70 pipeline can be seen in [9]. 
NUMERICAL SIMULATION OF BURIED PIPELINE SUBJECTED TO BLAST SEISMIC WAVES.  
CHONG JI, KEJIAN SONG, QUANJUN XU 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 413 
2.3. Finite element formation 
The damage of the buried pipeline depends mostly upon the stress state. So the analysis of 
stress distribution can be helpful to the vibration analysis. The wave propagation progress and 
vibration of the pipeline are studied through numerical simulation. 
Fig. 4 shows the stress distribution of buried pipeline at different times after explosion. From 
the figure we can see, the blast waves arrive to buried pipeline at ݐ = 3.3 ms. Then shock waves 
propagate to the end side of the pipeline. At the time ݐ = 11.9 ms, the stress waves travel through 
the entire pipeline. At this time, the bottom earth generates a resistance to prevent the vibration of 
the pipeline and produce the stress concentration at the bottom face of the pipeline. With the 
vibration of the pipeline, the stress concentration area keeps decreasing. At ݐ = 70 ms, there is 
little stress left on the surface of the pipeline. 
 
a) ݐ = 3.3 ms 
 
b) ݐ = 8.4 ms  c) ݐ = 9.4 ms  d) ݐ = 11.9 ms 
 
e) ݐ = 12.3 ms  f) ݐ = 14.8 ms  g) ݐ = 30 ms  h) ݐ = 70 ms 
Fig. 2. Stress distribution of buried pipeline at different times 
3. Results and discussion 
3.1. Velocity analysis 
After explosion, the middle points of the pipeline are closest to the explosion center. The 
vibration of the middle points of the pipeline need to be observed intensively. So we choose four 
points on fracture surface, namely A, B, C and D to analysis the vibration. The positions of the 
points are shown in Fig. 3. The velocity of the four points are analyzed. 
 
Fig. 3. The cross section of the pipeline 
NUMERICAL SIMULATION OF BURIED PIPELINE SUBJECTED TO BLAST SEISMIC WAVES.  
CHONG JI, KEJIAN SONG, QUANJUN XU 
414 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
Fig. 4 shows the velocity-time curves of the four points at the cross section. The distance from 
the explosion center is 50 m, and the buried depth 1.2 m. From the figures we can see, when the 
stress wave propagates to point A, the body wave contribution most to the vibration velocity in 
the ݔ direction and ݕ direction. The amplitude and scope are almost the same in the two directions. 
The peak velocities of point A and B are 1.17 cm/s and 1.98 cm/s in the reverse ݔ direction. The 
vibration velocity in the ݖ direction is small and can be ignored. On the other hand, the peak 
velocities of point C and D are 0.69 cm/s and 2.13 cm/s in the reverse y direction. The velocity in 
the ݖ direction can also be ignored. 
a) Point A 
x direction
y direction
z direction
 
b) Point B 
c) Point C 
y direction
x direction
z direction
 
d) Point D 
Fig. 4. Velocity-time curves of the points at the cross section 
 
Fig. 5. Peak velocity curves in radial direction 
 
 
Fig. 6. Peak velocity curves in  
circumferential direction 
Fig. 5 shows the radial peak velocity curves of four points. The figure shows that with the 
NUMERICAL SIMULATION OF BURIED PIPELINE SUBJECTED TO BLAST SEISMIC WAVES.  
CHONG JI, KEJIAN SONG, QUANJUN XU 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 415 
increase of the distance to the end of the pipeline, the peak velocity keeps decreasing. At the 
distance of 4.7 m from the central point, point C has the smallest velocity 0.26 cm/s of the four 
points, while point B and D have almost the same velocity values. Fig. 6 shows the distribution of 
peak velocity in circumferential direction at the cross section. From the figure we can see, with 
the increase of the distance from the explosion center, the peak velocity shows downtrend. The 
largest velocity appears at the left side of the pipeline and the smallest velocity appears at the  
right side. 
3.2. Influence of buried depth 
Figs. 7-9 show the peak velocity curves at the middle point of the pipelines with the distance 
from the explosion center 45 m, 50 m and 60 m, respectively. From the figures we can see that 
circumferential vibration velocity increase with the increase of buried depth. The differences of 
the peak velocities among different depth decrease with the increase of the explosion distance. At 
the distance of 60 m, the peak velocities among different depth become almost the same. 
Fig. 10 shows the relationship between circumferential vibration velocity and the buried depth. 
From the figure we can see that the vibration velocity decrease with the increase of the distance 
from the explosion center. At the buried depth of 0.6 m, the peak velocity change little with the 
increase of the depth.  
 
Fig. 7. Peak velocity curves at the distance of 45 m 
 
Fig. 8. Peak velocity curves at the distance of 50 m 
 
 
Fig. 9. Peak velocity curves at the distance of 60 m
 
 
Fig. 10. Relationship between peak velocity  
curves and buried depth 
4. Conclusions 
The vibration of the buried pipeline was studied numerically in the paper. The stress and the 
vibration velocity were studied through numerical simulation. The influence of buried depth was 
NUMERICAL SIMULATION OF BURIED PIPELINE SUBJECTED TO BLAST SEISMIC WAVES.  
CHONG JI, KEJIAN SONG, QUANJUN XU 
416 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
also acquired. The results show that, with the decrease of the distance to the end of the pipeline, 
the radial peak velocity becomes smaller, and with the increase of the distance from the explosion 
center, the peak velocity shows downtrend. The circumferential vibration velocity increases with 
the increase of buried depth, and at the buried depth of 0.6 m, the peak velocity change little with 
the increase of the depth. 
Acknowledgement 
This research was financially supported by the National Nature Science Foundation of China, 
No. 11102233. The authors would like to gratefully acknowledge this support. 
References 
[1] Isoyama R., Katayama T. Practical performance evaluation of water supply networks during seismic 
disaster, lifeline earthquake engineering. The Current State of Knowledge, ASCE, 1981, p. 111-122. 
[2] Toki K., Sato T. Estimation of damage of water distribution systems by earthquakes. Recent Advance 
in Lifeline Earthquake Engineering in Japan, ASME, 1985, p. 89-96. 
[3] Newmark N. M. Problems in wave propagation in soil and rock. Proceedings of International 
Symposium on Wave Propagation and Dynamic Properties of Earth Materials, University of New 
Mexico Press, Albuquerque, 1968, p. 7-26. 
[4] Kuesel T. R. Earthquake design criteria for subways. Journal of the Structural Division, 1969, 
p. 1213-1231. 
[5] Malachowski J., Mazurkiewicz L., Gieleta R. Analysis of structural element with and without 
protective cover under impulse load. Proceedings of 12th Pan-American Congress of Applied 
Mechanics, Port of Spain, Trinidad, 2012. 
[6] Mokhtari M., Alavi Nia A. A parametric study on the mechanical performance of buried X65 steel 
pipelines under subsurface detonation. Archives of Civil and Mechanical Engineering, Vol. 15, 2015, 
p. 668-679. 
[7] O’Daniel J. L., Krauthammer T. Assessment of numerical simulation capabilities for 
medium-structure interaction systems under explosive loads. Computers and Structures, Vol. 63, 1997, 
p. 875-887. 
[8] Lu Yong, Wang Zhongqi, Chong Karen A comparative study of buried structure in soil subjected to 
blast load using 2D and 3D numerical simulations. Soil Dynamics and Earthquake Engineering, 
Vol. 25, 2005, p. 275-288. 
[9] Ji Chong, Long Yuan Local damage effects of X70 steel pipe subjected to contact explosion loading. 
Chinese Journal of High Pressure Physics, Vol. 27, 2013, p. 567-574 


Numerical simulation of buried pipeline subjected to blast seismic waves

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Numerical simulation of buried pipeline subjected to blast seismic waves

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