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It is so important to consider the passive defense problem in any places there have been attacks by varies kinds of military threats and terrorists. It is certain that social security is related to overcoming on these perils and protection from country. Vital facilities are one of examples that should be protected. Vital facilities include roads, bridges, transmission lines, and telecom and media network. With attention to the intense dependent to export and transmit of oil and gas and with consideration of this point that many places are full of gas and oil resource, the protection of these lines is very important. In recent years, occurrence of varies kinds of terrorist accidents in relation to important structures in all the world causes that the explosion loads have special attention. Explosion can generate much damage with vibration in vast soil media. Thus, it is important to predict the dynamic impact load and its treatment response. With attention to regardable development of numerical methods in recent decades, it is possible to investigate the explosion effects on surface and underground structures. In this research, the newest applied method modeling of the explosion phenomenon has been investigated and comprehensive information has been earned. In this investigation, problem of explosion wave’s propagation effects on buried pipes simulated by ABAQUS/CAE 6.10-1 was studied based on the finite element method. Surface explosion effects on gas buried pipe lines and their dynamic response have been investigated depending on properties and their characteristics. The variation of buried pipe depth effects and variation effects in soil properties around pipe in different cases has been considered, and the results are here. The results showed that in buried pipes under surface explosions, displacements, major stresses, and strains decrease in clay, dense, and loose sands with increase of buried depth. These results obtain that because of increase of closuring of pipes in soil when internal friction angle increases for a kind of soil, the stress on pipe rim will decrease also. It was also observed that the pipe performance in clay and loose sands is better than that in compacted sand, respectively.

Vital arteries include roads, stairs, tunnels, transmission lines (water, oil, and gas), and communication and media networks. If one of the vital arteries is damaged, malfunctioning, urban activities, or relief work will be paralyzed during the crisis, thus increasing the loss of life and property. If the threatening factors of vital arteries are divided into two categories, natural and human factors, earthquakes, and explosions can be mentioned as examples of them, respectively. Over recent years, various terrorist incidents on important structures worldwide have caused special attention to be paid to explosive devices, in large cities that use underground spaces for highways, tunnels, and underground pipes. Therefore, it is essential to predict the dynamic impact loads and investigate the behavioral response of the structures. The reliable and economical design of structures requires a better understanding of the sophisticated and practical parameters of these structures. Due to the necessity and importance of these vital arteries, and if there is proper information, we will be able to predict the possible effects of the explosion on them according to the specifications of the existing pipelines; in addition, if necessary, we should take steps to cure them. Also, with such information, the design of pipelines in the future can be more precise and safer, and the considerations related to the passive defense of vital arteries can be considered more effective. In recent years, there have been significant advances in developing numerical and laboratory methods for studying such systems. In the present study, comprehensive information will be obtained by examining the latest methods used to model the explosion phenomenon and the responses obtained from underground structures.

The simulation of the nonlinear part of the soil behavior has been performed using the modified Drucker–Prager plastic processor (cap) model. We also need to specify the level of yield, flow

Mechanical properties of soil.

Mass density | Angle of friction | Flow stress ratio (MPa) | Dilation angle | Damping | Young’s modulus (MPa) | Poisson ratio | |
---|---|---|---|---|---|---|---|

1700 | 35 | 0.8 | 4.81 | 10 | 0 | 107.1e6 | 0.4 |

According to Iran’s 2800 regulations, the selected base soil is type IV, which is considered soft soil. Then, by changing the effective parameters in the interaction and response of the structure, about 50 analyses with different parameters have been performed, which have been then displayed under different diagrams.

In addition, the used mechanical properties for simulation of steel pipeline can be found in Figure

Mechanical properties of used wave-shaped connection in the FE numerical model.

The most common solution to the problem of soil-structure interaction is the analysis based on the substructure method. In this method, the linear problem of soil-structure interaction is separated into a series of simpler subproblems, and then the results are combined using the principle of superposition. In the substructure isolation method [

Drucker–Prager hardening model.

Separation of infrastructures to make calculations more simple: (a) total, (b) substructure I, (c) substructure II, and (d) substructure III.

For solving the problem of the construction response, it is necessary to make and solve the problem of eigenvalue for the model. In calculations related to volumetric waves from the submatrices calculated from the characteristics of each layer, they are used to form eigenvalue equations. In Kiran and Manoj’s study [

Eigenvalue equations:

Eigenvalue equation using numerical techniques:

Matrices

Shi [

The semi-infinite semispace can be modeled by two methods, variable depth and viscous boundary at the base. Substructure methods are valid only for linear analyses. However, soils exhibit nonlinear behavior depends on strain in response to dynamic loading. Nonlinear soil behavior can be considered using the equivalent linear method proposed by Syed and Idris [

In the substructure isolation method, the equations of motion of the SSI system, including the impedance matrix

Furthermore, matrix

In this section, the structural and removed soil characteristics, used in the motion equation coefficient matrix equations (

For a single harmonic input,

Within studying the interaction problem, the dynamic response of the structure is affected by the interactions of the structure, the foundation, and the surrounding soil. There are two general substructural and direct methods available for analyzing interaction issues [

This study operates the conventional model in defining the interaction of contact surfaces, the Columbus friction model. The model has been applied using the contact element, which will be explained below. The Columbus friction model determines the frictional behavior between contact surfaces utilizing a friction coefficient

The frictional behavior of contact surfaces.

Soil and structure interaction is significant, particularly for large and massive structures that have been built in soft soil. When affected by a dynamic load, a dynamic reaction of the soil and structure complex signifies a function of the dynamic characteristics, induced forces, and stimuli, and the dynamic model of the system which involved the dynamic model of the structure linking with the dynamic model of the environment. Interaction is a boundary value problem.

Therefore, it requires an infinite environment model; however, infinite modeling of the environment is not achievable. Hence, some terms must be considered that by a partial model of the infinite environment, the state of radiation (i.e., the waves are not reflected from the infinite environment) is satisfied. If the force, displacement, and dynamic stiffness upon the infinite boundary are displayed with

The purpose of the study soil and structural interaction is to obtain the dynamic stiffness and shape of the wave motion in the meeting points of soil and structure. The direct solution method for studying soil and structure interaction is based on the formulation of finite elements for soil and structure. This feature emphasizes the importance of the method in the topic of the interaction of soil and structure. Another significant point is the ability of the finite element method to consider nonlinear effects, both material and geometric. This makes the method one of the most potent numerical methods in structural analysis.

When an explosion occurs under ideal conditions of the theory, in the vicinity of the solid surface, waved shape will be hemispherical (Figure

The hemispherical wave in superficial explosion.

The parameters of the blast wavefront are significant. The analytical solution of these parameters was first expressed by Huganiot and Rankine to describe shocks in the ideal gas. These equations are expressed for the velocity of the wavefront

An equivalent TNT mass is required before the parameters can be extracted for an explosion. There are several ways to express equivalent TNT, but the simplest is the ratio of the specific mass energy of actual explosives to the specific mass energy of TNT. The specific gravity energy of TNT is equal to 6700 kJ/kg [

There are many relations to maximum overcompression due to conventional (chemical) explosions based on researchers’ explosive applied. Kiran’s relation to the traditional chemical explosion is given [

The ideal blast wave.

When an explosive device explodes on the surface of the earth or at a very short distance from it, the blast wave will ideally have a hemispherical wavefront, which is different from the spherical wavefront obtained in an aerial explosion [_{s} is the overcompression,

Spherical blast wave parameters, at sea level TM5-1300 (1969).

In studies conducted by various researchers such as Bulson, Bashara, and Henrich on the case of blasts, experiments were reported based on the amount of explosive equivalent TNT; therefore, it seems essential to provide a correlation to equate other explosives with TNT. The mass of explosives can be converted to TNT using the combustion temperature [

In these relations,

Conversion coefficient for different explosives.

HBX2 | Minol 2 | Composition B | Amatol | TNT | Explosive material |
---|---|---|---|---|---|

1.30 | 1.34 | 1.04 | 1.04 | 1 | Conversion coefficient |

The compressive waves created due to the explosion propagate in the soil environment, and colliding with the soil causes the soil to crumble and flow [_{i} are the velocity of the wave, density, and the amplitude of the initial stress wave, respectively. Moreover,

The behavior of soil under dynamic loading is one of the most exciting topics for engineers in mines, buildings, and defense structures. Generally, the soil is a three-phase mixture of solid mineral particles, water, and the air. Connected or separated solid particles form the soil skeleton. Water and air are located among the cavities between solid particles of soil. Soil is the three-phase mixture; that is why it is challenging to predict the deformation of soils; not only is the skeletal structure complex, but the properties of each component are fundamentally different. The different deformation characteristics of each phase and soil-structure make the soil deformation mechanism strongly dependent on the ratio of components in the soil and loading conditions. As a result, the mechanism of deformation of saturated and unsaturated soils is different, and such a difference in dynamic loading will be much more noticeable than static loading.

Both the mechanisms of skeletal deformation and the deformation of all soil phases affect simultaneously. However, in different loading stages and depending on the different ratios of components in the soil, one of the mechanisms is dominant so that the other mechanisms can be ignored [

The extraordinary dependence of soil properties on loading conditions makes it tough to develop a unique model for the deformation of soils under dynamic loading, particularly for high explosion rate loading, which varies significantly in different mass charge situations under loading conditions. Within an explosion, the soil close to the mass charge is deeply compacted. Hence, a high-stress wave is generated and propagates outward into the soil. As the distance from the charge increases, the stress wave decreases rapidly, and as a result, the soil compaction decreases. Therefore, in areas close to the charge, the second mechanism is predominant. In contrast, with increasing distance from the mass charge, the first mechanism becomes more and more significant and finally dominates the deformation of the soil. The extent of the nearby area depends on the fundamental characteristics of the soil. Soil deformation mechanisms under static and transient loading have been studied over the years, and many models have been proposed to describe soil behavior under such loads.

However, insufficient research studies have been conducted on soil behavior under transient loads, such as explosion loads, due to these complexities. Modeling the soil response to an extremely variable pressure requires a robust soil model because new behavioral models typically cover a small range of deformations. Besides, in such high-stress conditions, in the vicinity of the charge, it is illogical to consider the rigid materials for the soil particles considered in ordinary soil dynamics. Instead, the solid phase change should be regarded in the soil behavior model. Based on Kandaur’s conceptual analysis of soil deformation, a three-phase behavioral model for shock loading was developed by Wang (2003) to provide all of these requirements. In this model, the soil is considered a three-phase system consisting of solid particles, water, and air, in which the climate fills the solid particles form the soil skeleton, and the space between the particles is filled by water and air. The solid phase is considered plastic. Since the blast load duration is concise and there is not enough time for the water and air to escape from the soil particles, the relative displacement of the air-water and soil skeleton is neglected. Therefore, the model is suitable for describing soil behavior under normal blast loading [

In Figure

Wang three-phase behavior model for blast load: (a) conceptual model; (b) mathematical model.

Mating coefficient.

The value of the reduction coefficient.

Reduction coefficient ( | Soil type |
---|---|

1.5 | Saturated clay |

2.5 | Semisaturated clay and silt |

2.5 | Very dense sand (dry or wet) |

2.75 | Dense sand (dry or wet) |

3 | Loose sand (dry or wet) |

3.25 | Very loose sand (dry or wet) |

Also, the maximum velocity of particles in meters per second at a distance of ^{3}), C is the load wave velocity (m/s), and P_0 is in pascals. The loading wave velocity

Also, the time of continuous explosion compression on underground structures is obtained from equation (

Since the infinite soil environment is modeled in a finite form, the question arises about the dimensions of the soil model. Soil model dimensions should be chosen so that, while small, it has the least impact on the results; to minimize the time of analysis to get accurate results. Because the larger the model, the more accurate the results, but due to the larger dimensions of the model, the time of analysis is extended once the analysis of the model may take days. For this purpose, three models were made according to Table

Models built to analyze the sensitivity of soil model dimensions.

Height (m) | Width (m) | Length (m) | Model no. |
---|---|---|---|

100 | 100 | 100 | 1 |

50 | 100 | 100 | 2 |

25 | 50 | 100 | 3 |

15 | 25 | 50 | 4 |

The above diagrams show the acceleration and wave velocity at the farthest node of the defined models (corner points) for the same loading and boundary conditions. According to this, it can be concluded based on obtained results (i.e., soil with dimensions of 50 100 100 × 25 m). The velocity and acceleration of the blast wave resulting from the explosion reaching the farthest node tend to zero. As the dimensions grow, only the analysis time increases, but there is no change in the results and outputs. Thus, the model that was considered for this project, according to the sensitivity analysis, is model 3, i.e., soil with dimensions of 100 × 50 × 25 meters, Figures

Graph of wave velocity values at the farthest nodes of different models.

Graph of wave acceleration values at the farthest nodes of different models.

The geometry of the model consists of two parts, soil and pipe. The dimensions of each are as follows: soil in the form of a cube with dimensions of 100 × 50 × 25 meters, and a steel pipe with a diameter of 1 meter, a length of 100 meters, and a thickness of 3/14 mm. After determining the geometry of the model, the specifications of the materials used should be defined. Soil and steel specifications are shown in Tables

Characteristics of soil types used in the analyzes.

Soil type | ^{3}) | Ψ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Soft sand | 1600 | 0 | 35 | 7 | 0.4 | 0.27 | 0 | 54.81 | 0.8 | 54.81 |

Hard sand | 2000 | 0 | 25 | 14 | 0.3 | 0.19 | 0 | 44.53 | 0.85 | 44.53 |

Clay | 1800 | 20 | 0 | 4 | 0.3 | 0 | 23.09 | 0 | 1 | 0 |

Steel mechanical properties.

Tank material | ^{3}) | _{y} (MPa) | _{u} (MPa) | ||
---|---|---|---|---|---|

Steel X65 | 7850 | 203 | 0.3 | 448 | 530 |

Two methods can be applied in modeling soil-structure interaction. One is soil replacement modeling with springs in three directions (two directions perpendicular to the pipe and one direction tangent to the pipe). Another way is to build a full model, including soil, pipes, and their interaction in three dimensions. In this study, due to the closest approximation to reality, the second method was utilized. In this modeling, the interaction between soil and pipe elements within the software is modeled on surface-to-surface mode, between the outer surface of the pipe and the inner surface of the soil and by the penalty method. In this method, the normal contact of two levels with the hard contact method is considered to prevent the surfaces from sinking into each other. Also, the tangential interaction of the two surfaces with a friction coefficient of 0.5 that was suggested by Vasouras and Kolbadi [

Since the peripheral soil is semi-infinite, it must be modeled so that all its properties, including its being semi-infinity, are considered. Based on the previously performed sensitivity analysis (Figure

Conditions of symmetry at the lateral boundaries of the soil.

The loads applied to the pipe include the load due to the blast wave, the internal pressure of the pipe, and the overburden soil weight of the pipe. The blast load is applied as a compression-time series for an equivalent TNT mass of 10, 20, and 30 kg at a point on the soil based on the equations presented equation (

Place of blasting and meshing of soil and pipes.

Knowing the nature of each of these methods and gaining experience will be simple to choose the solution. In the explicit method, the results at each moment (_{n} + 1) are obtained directly from the results before (_{n}). In this way, new situations are calculated by considering the velocity and acceleration of the elements at the moment

On the other hand, in the implicit method, the size of Δ

Propagation of the stress wave caused by the explosion in the soil and pipe environment.

To analyze the sensitivity of the parameters affecting the performance of the pipe, the models and the results of their analysis are examined separately. The parameters that underlie the judgment are stress, strain, and displacement. The stress understudy is phonemic stress obtained from the square root of the sum of the principal stresses. Displacement also means the maximum absolute displacement of one of the pipe nodes.

Blast loading was performed on three types of soil (loose sand, hard sand, and clay) and its impact at three different depths. Depth of burial pipe tension, strain, and maximum displacement of the pipe is significantly reduced. The effect of increasing the burial depth of pipes on their behavior against explosion can be mentioned for various reasons, such as increasing the pipe blockage in the soil, increasing the distance of the pipe to the explosion place, and increasing the stiffness of the soil (Table

Specifications of models to investigate the effect of pipe burial depth.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Clay | 100 | 14.3 | 250 (=1.732 MPa) | 2 | 10 | 0 |

2 | Hard sand | 2 | |||||

3 | Soft sand | 2 | |||||

4 | Clay | 3 | |||||

5 | Hard sand | 3 | |||||

6 | Soft sand | 3 | |||||

7 | Clay | 4 | |||||

8 | Hard sand | 4 | |||||

9 | Soft sand | 4 | |||||

10 | Clay | 2 | 20 | ||||

11 | Hard sand | 2 | |||||

12 | Soft sand | 2 | |||||

13 | Clay | 3 | |||||

14 | Hard sand | 3 | |||||

15 | Soft sand | 3 | |||||

16 | Clay | 4 | |||||

17 | Hard sand | 4 | |||||

18 | Soft sand | 4 | |||||

19 | Clay | 2 | 30 | ||||

20 | Hard sand | 2 | |||||

21 | Soft sand | 2 | |||||

22 | Clay | 3 | |||||

23 | Hard sand | 3 | |||||

24 | Soft sand | 3 | |||||

25 | Clay | 4 | |||||

26 | Hard sand | 4 | |||||

27 | Soft sand | 4 |

Analysis results to investigate the effect of pipe burial depth (explosion caused by 10 kg of TNT).

Analysis results to investigate the effect of pipe burial depth (explosion caused by 20 kg of TNT).

Analysis results to investigate the effect of pipe burial depth (explosion caused by 30 kg of TNT).

Based on the relations presented to calculate the mass charge, the weight of the mass charge directly affects the loads caused by the explosion. Therefore, according to the results obtained from the analysis of the models given in Figures

Analysis results to investigate the effect of explosive weight (pipe burial depth 2 meters).

Analysis results to investigate the effect of explosive weight (pipe burial depth 3 m).

Analysis results to investigate the effect of explosive weight (pipe burial depth 4 m).

Specifications of models to investigate the effect of explosive weight.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Clay | 100 | 14.3 | 250 (=1.732 MPa) | 2 | 10 | 0 |

2 | Hard sand | 10 | |||||

3 | Soft sand | 10 | |||||

4 | Clay | 20 | |||||

5 | Hard sand | 20 | |||||

6 | Soft sand | 20 | |||||

7 | Clay | 30 | |||||

8 | Hard sand | 30 | |||||

9 | Soft sand | 30 | |||||

10 | Clay | 3 | 10 | ||||

11 | Hard sand | 10 | |||||

12 | Soft sand | 10 | |||||

13 | Clay | 20 | |||||

14 | Hard sand | 20 | |||||

15 | Soft sand | 20 | |||||

16 | Clay | 30 | |||||

17 | Hard sand | 30 | |||||

18 | Soft sand | 30 | |||||

19 | Clay | 4 | 10 | ||||

20 | Hard sand | 10 | |||||

21 | Soft sand | 10 | |||||

22 | Clay | 20 | |||||

23 | Hard sand | 20 | |||||

24 | Soft sand | 20 | |||||

25 | Clay | 30 | |||||

26 | Hard sand | 30 | |||||

27 | Soft sand | 30 |

Based on the results obtained from the analysis of the models given in Figure

Analysis results to investigate the effect of blast distance from the pipe axis.

Specifications of models to investigate the effect of explosion distance from the pipe axis.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 14.3 | 250 (=1.732 MPa) | 3 | 20 | 0 |

2 | 2 | ||||||

3 | 5 | ||||||

4 | 10 |

According to the results of the analysis of the models, which are given in Table

Specifications of models to investigate the effect of internal pipe pressure.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (MPa) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 14.3 | 0 | 3 | 20 | 0 |

2 | 1.732 _{(=250Psi)} | ||||||

3 | 5 | ||||||

4 | 10 |

Analysis results to investigate the effect of internal pipe pressure.

Pipe pressure | Max displacement (cm) | Stress (MPa) |
---|---|---|

No pressure | 43.7 | 452 |

250 psi (=1.732 MPa) | 43.7 | 452 |

5 MPa | 43.6 | 452 |

10 MPa | 43.6 | 452 |

According to the analysis results, which are given within Tables

Specifications of models to investigate the effect of coefficient of friction between soil and pipe.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Friction coefficient |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 14.3 | 250 (=1.732 MPa) | 3 | 20 | 0.4 |

2 | 0.45 | ||||||

3 | 0.5 | ||||||

4 | 0.55 | ||||||

5 | 0.6 |

Analysis results to investigate the effect of coefficient of friction between soil and pipe.

Friction coefficient | Max displacement (cm) | Logarithmic strain | Stress (MPa) |
---|---|---|---|

0.4 | 22.19 | %1.50 | 386 |

0.45 | 22.20 | %1.50 | 391 |

0.5 | 22.22 | %1.51 | 385 |

0.55 | 22.26 | %1.51 | 386 |

0.6 | 22.30 | %1.50 | 388 |

As expected, the larger the diameter of the pipe, the better the pipe performance as the cross-sectional moment of inertia increases based on Figure

Analysis results to investigate the effect of pipe diameter.

Specifications of models to investigate the effect of pipe diameter.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (MPa) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Soft sand | 50 | 14.3 | 1.732 (=250 Psi) | 3 | 20 | 0 |

2 | 100 | ||||||

3 | 125 | ||||||

4 | 150 |

As expected, the thicker the pipe, the better the performance of the pipe as the moment of inertia increases as can be found in Figure

Analysis results to investigate the effect of pipe thickness.

Specifications of models to investigate the effect of pipe thickness.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Blast distance (m) |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 8 | 250 (=1.732 MPa) | 3 | 20 | 0 |

2 | 10.3 | ||||||

3 | 14.3 | ||||||

4 | 19 | ||||||

5 | 25.4 |

Based on the results obtained from the analysis of the models given in Figure

Analysis results to investigate the effect of internal soil friction coefficient.

Specifications of models to investigate the effect of internal soil friction coefficient.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Friction angle |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 14.3 | 250 (=1.732 MPa) | 3 | 20 | 20 |

2 | 25 | ||||||

3 | 30 | ||||||

4 | 35 | ||||||

5 | 40 |

Based on the results of the analyzes given in Figure

Analysis results to investigate the effect of soil specific gravity.

Specifications of models to investigate the effect of soil specific gravity.

Case | Soil type | Diameter (cm) | Thickness (mm) | Pipe pressure (Psi) | Depth (m) | W_{TNT} (kg) | Soil density (kg/m³) |
---|---|---|---|---|---|---|---|

1 | Soft sand | 100 | 14.3 | 250 (=1.732 MPa) | 3 | 20 | 1600 |

2 | 1700 | ||||||

3 | 1800 | ||||||

4 | 1900 | ||||||

5 | 2000 |

Summary of the achievements of studying the performance of buried pipelines under the effect of explosive loading is presented in this section. Then, based on the author’s experience, to reduce ambiguities, conduct experiments, furthermore analyze some of the obtained results, and also present a series of suggestions and approaches for using the results of this research, some ideas are mentioned in the suggestions section.

As can be seen, from the problem under study, first, a suitable model was constructed in three-dimensional form using the finite element method. Then, in the analysis, by changing the parameters that seemed to be important in the behavior of the pipe under the effect of the surface explosion, we examined the sensitivity of the pipe response to the change of the desired parameter. After analyzing and extracting the results, these results were presented in charts, which were based on judgments and conclusions about pipe behavior. At the end of the analysis used in this study, results were obtained to understand better the behavior and optimal design of buried pipelines under the impact of surface explosions, which are mentioned as follows:

Blast wave arrival velocity depends on the velocity of the soil environment compressive seismic wave. The arrival time of the wave in clay soils is longer than other soils. The blast wave response time to the structure is a significant factor for the response of underground structures such as buried pipes.

Due to the low mass of the pipe and the high dependence of its behavior on the strains that occur in the surrounding soil, it can be stated that the entering velocity spectrum of the pipe is much more critical than the acceleration spectrum.

As the pipe depth increases, the maximum stress, strain, and displacement of the pipe decrease almost linearly. Buried pipes seem to perform better in clay soils and loose sands, respectively, especially while the burial depth of the pipe increases. The reason is that this phenomenon is the higher seismic wave velocity in stiff sandy soils, which is directly related to the modulus of soil elasticity and increases the maximum blast wave compression.

By increasing the blast distance from the tension pipe axis, the maximum strain and displacement of the pipe are significantly reduced. This decreasing trend tends to zero after specific distances (according to environmental conditions, pipes, and explosions); here, it has occurred after 5 meters.

The internal pressure of the pipe and the coefficient of interaction friction between the soil and the pipe have a negligible effect on the response of the pipe.

The larger the diameter and thickness of the pipe, the better the performance of the pipe with increasing the cross-sectional moment of inertia. The relation between the results and the conversions in these parameters is approximately linear.

By increasing the coefficient of internal friction of the soil, the maximum strain and displacement of the pipe decrease. The effectiveness of this parameter is significant compared to other parameters.

While the specific gravity of the soil increases, the maximum pipe stress and strain decrease considerably, but there is no noticeable change in the maximum pipe displacement.

According to the previous results, in the case of buried shell structures, such as pipes, it can be understood that their performance is more affected by the deformation of the structure (such as pipe bending) than the effects of soil-structure interaction.

The data used to support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors of this article are grateful for the valuable guidance of Mr. Abbas Aghasi.