Mechanical Behavior of Buried Pipelines Subjected to Faults

/e length of buried pipelines usually extends thousands of meters or more in engineering, and it is difficult to carry out full-scale tests in the laboratory./erefore, considering the seriousness of pipeline damage and the difficulty of operating tests and other test limitations, it is necessary to develop a reasonable method to simplify the length of the model for a practical lab test. In this research, an equivalent spring model was established to simulate the small deformation section of the pipeline far away from the fault and the effect of fault displacements, pipeline diameters, wall thicknesses, buried depths, soil materials, and spring constraints on the mechanical properties of pipelines was analyzed. Based on the finite element model using ABAQUS software, the results of the shell model with fixed boundary at both ends were compared; in addition, the dynamic effect of pipelines was investigated. /e results show that the two-end spring device can better control the size of the test model and enhance the reliability of the test results. /e vibration response of the pipeline mainly depends on the inconsistent movement of soil at both ends of the fault./e analysis results show that choosing a larger pipeline diameter, smaller buried depth, noncohesive backfill soil, and spring with a smaller elastic coefficient is beneficial to reduce pipeline strain and resist pipeline deformation. A simplified formula of the axial compressive strain of buried pipelines across oblique-slip fault is obtained.


Introduction
e San Fernando earthquake in 1971 gave birth to the lifeline earthquake project [1,2], and then much research has been conducted to understand further the action mechanism of the pipeline under fault movement. Some experimental studies were carried out, mainly including the small-scale test based on shaking tables or the centrifuge device and the full-scale test. Erami et al. [3] carried out a full-scale test to study the pipe-soil interaction equation. e experimental results were compared with the results of the computeraided analysis. e results show that the nature of the soil and the connection nodes have a great influence on the pipesoil interaction. Feng et al. [4] conducted static and dynamic seismic tests on buried pipelines across faults. e results showed that there was no significant difference between the responses of pipelines under the displacement of dynamic test and those under the static test. Demirci et al. [5] conducted a series of experiments to analyze the behavior of continuous buried pipelines subjected to reverse fault motion and developed a novel experimental device for studying pipelines crossing reverse faults. Zhang et al. [6] carried out a full-scale test to study the effect of soil settlement on the pipeline. Zhang et al. [7,8] conducted the shaking table test of buried pipelines under the strike-slip fault and found that the dynamic effect of the pipeline-soil system itself has little effect on the mechanical properties of pipelines. Zhang et al. [9] studied the force process of buried pipelines under the fault through the test and the numerical simulation. Tang et al. [10] carried out the centrifuge test to simulate the reaction characteristics of buried pipelines under the reverse fault. Li et al. [11] used the shaking table device to analyze the field seismic response rules under the consistent and nonconsistent seismic actions. Oskouei et al. [12] conducted multiple sets of tests to evaluate the impact of buried depth on the buried steel pipelines crossing the strike-slip faults and analyzed the effects of different soil deformation forms on the buried pipeline. e full-scale test and the small-scale test based on shaking table device were carried out, respectively, in the Cornell University and the Rensselaer Polytechnic Institute to simulate the fault movement and obtain the mechanical properties of buried pipelines. e above-mentioned studies were from 2005 to 2009 and a series of important results were obtained [13][14][15][16][17]. Kim et al. [18] used the full-scale test device of Cornell University to study the response behaviors of buried concrete pipelines subjected to faults and found that the main failure of pipelines occurs at the joint near the fault. Rojhani et al. [19,20] used the self-made centrifuge test device connected by springs at the end of the pipeline to carry out the simulation tests of stainless steel pipelines under the normal and reverse faults action and found that the test results are in good agreement with the analytical values. Sim et al. [21] carried out the experimental studies of pipelines under the strike-slip and normal faults based on the shaking table device. Rofooei et al. [22,23] carried out a full-size test to study the deformation and buckling behaviors of steel pipelines and HDPE pipelines under the reverse fault simulated by the soil-box and hydraulic driving device.
Relevant research literature [24] has shown that the static test can be used to study the mechanical performance of pipelines subjected to fault at the low frequency of ground motion. Moreover, both ends of the pipeline are usually assumed fixed ends in most experiments and few experiments were conducted to study the pipe-soil constraints far from the fault. In view of this, an equivalent spring model was established to simulate the small deformation section of the pipeline far away from the fault and 27 pipelines crossing different faults were investigated. In addition, the effects of pipeline diameter, buried depth, soil materials, and spring with different elastic coefficients on the mechanical properties of the pipeline were analyzed.

Test Specimens and Soil-Box.
Twenty-seven buried pipelines made of Q235 hot-rolled steel were designed, fabricated, and tested to investigate the effects of different parameters on their mechanical behavior subjected to faults. e geometric parameters of each specimen are given in Table 1. All the specimens had the same length of 3.0 m, and both ends of each pipeline were welded with a nut, which was connected with the spring device and fixed on the soilbox, as shown in Figure 1.
A soil-box, 3.0 m (length) × 1.0 m (width) × 1.1 m (height), was designed to simulate the movement of diverse types of faults, which was removable and mainly contained four parts, that is, fixed and staggered plate, soil-retaining side panel, spring device, and portal steel frame, as shown in Figure 2. e soil-box could be loaded by vertical or horizontal jack. e soil-retaining side panel could rotate around the bottom screw to simulate different angles crossing faults. In practical engineering, the length of buried pipeline between stations usually extends thousands of meters; however, only a small length of the pipeline was taken out as a specimen when the mechanical behavior of the pipeline was tested in the laboratory; the purpose of spring device was to make the pipeline far away from the fault to be stretchable. When selecting the spring coefficient, the stress value of the pipe section at different points from the fault is obtained  Note. e first letters in test coupons "N," "R," "S," and "O" stand for various fault types referring to the normal fault, the reverse fault, the strikeslip fault, and the oblique-slip fault, respectively. e second letters in test coupons "C" and "S" stand for various soil materials referring to the clay, and the medium sand, respectively; "θ," "k," "D," "H," and "t" stand for angles crossing the faults, elasticity coefficients at both ends of the pipelines, diameters of the pipelines, buried depths of the pipelines, and wall thicknesses of the pipelines, respectively.
2 Advances in Civil Engineering through finite element simulation. e axial force at the pipe section is obtained and substituted into the expression of the equivalent spring of the small deformation section of the pipe [24] to determine the spring coefficient of elasticity. e portal steel frame was used to restrict the horizontal displacement in the process of jack-up loading.

Material Properties of Steel Pipelines and Soils.
Tensile coupon tests were conducted to determine the mechanical properties of steel pipelines. e material properties of the steel tubes were determined by tensile tests at ambient temperature. e steel coupons were extracted from the pipelines in the longitudinal direction of the untested specimens.
e material properties of the steel obtained from the tensile coupon tests are listed in Table 2, where E 0 is the elastic modulus, f y is the yield strength, f u is the ultimate strength, and μ is the Poisson ratio. Based on a series of unconsolidated-undrained triaxial tests, the material properties of soils adopted by clay or medium sand were measured, as shown in Table 3, where φ is the internal friction angle, c is the cohesive force, ρ is the density, and μ is the Poisson ratio.

Experiment Procedures.
e soil-box was loaded by horizontal or vertical jack to simulate the fault movement in this experiment; the load based on the displacement control method ranged from 0 mm to 140 mm, which was divided into 14 steps, and each loading displacement was 10 mm. When simulating normal or reverse fault, the fixed plate was fixed on the base, and two vertical jacks at the bottom of the staggered plate were used to produce vertical displacement. When simulating strike-slip fault, a horizontal jack in the middle of the staggered plate (at this point, the fixed plate was regarded as a staggered plate) was used to produce horizontal displacement. When simulating oblique-slip fault, horizontal and vertical jacks were used to load in parallel to simulate the movement along the angle of 45°with fault trend and tendency. Figure 3 presents four types of fault movement.
Since the large deformation section of the pipeline was mainly investigated in this article, strain gauges near the fault area were densely arranged. As shown in Figure 4, 18 strain gauges are symmetrically bonded along the outer surface of the pipeline in the axial direction to measure the strain distribution. Due to the small diameter of the pipe selected in the test, the accurate attach positions were marked and the surfaces of these positions were cleaned with alcohol before the strain gauges were mounted with epoxy resin. Each of the attached gauges was covered with a circle of tape for protection and tested with an ohmmeter every time before the experiment. e strain data of pipelines were collected by DH3816 static strain acquisition system, which can satisfy 60 measuring points at the same time. In addition, the deformation data of pipelines were indirectly measured by the vertical deformation of the rigid rod that was bonded with an adhesive and extended out of the soil surface; the experimental measurement site is presented in Figure 5. Compared with the above strain curve change, there are some differences in points. For example, the measurement point 5-1 in Figure 7 is the pipe section at the fault. When the fault displacement is less than 60 mm, the upper side of the pipeline will generate axial compressive stress under the action of shear force, and within this range, the axial compressive stress will increase with the fault displacement. At the same time, because the pipe section at measuring point 5-1 is restrained by the enhanced dislocation disk and fixed disk, the upper side compressive strain of the pipeline decreases with the further increase of the fault displacement, and the pipeline begins to show axial tensile strain due to the reverse tensile stress. e same principle can explain the  Table 3: Material properties of soils.

Experimental Results and Discussion
Fault plane Fixed area Dislocation area   Advances in Civil Engineering 5 change of axial strain in Figure 7(b). Due to the influence of the internal force change of the pipe section at the measuring point 5-1 on the adjacent pipe section, with the increase of the fault displacement, the axial compressive strain at the measuring points (2-1, 3-1, and 4-1 in Figure 8) showed a trend of first increasing and then decreasing. Moreover, the axial tensile strain of the pipe section at measuring point 6-1 shows a sharp increase trend when the fault displacement is 60 mm, while the axial compressive strain of the pipe section at measuring point 7-1 is relatively less affected; that is, the axial strain of the pipe section at each measuring point is affected by the adjacent pipe section and the distance between the pipe section to the fault at the measuring point. In the same way, the strain changes of the pipe section near the fault can be explained in Figures 9-11.

Effect of the Pipeline Diameters.
ree types of pipelines with diameters of 25 mm, 32 mm, and 40 mm were selected for mechanical properties tests, as shown in Figures 12(a)-12(f ); the effect of different pipeline diameters on the strain of specimens under faults are studied. It can be found that when the fault displacement is 140 mm, the strain response of pipelines with the larger diameter is relatively small, which can be attributed to the fact that increasing the diameter of the pipeline is equivalent to the increase of the moment of inertia of the cross-section, and thus the stiffness of the pipeline becomes larger. erefore, the pipelines with a larger diameter should be chosen in the process of laying buried pipelines in practical projects, which is helpful to bear load and resist deformation.  Advances in Civil Engineering

Effect of the Wall icknesses.
Two types of pipelines with wall thicknesses of 1.0 mm and 2.0 mm were selected for mechanical properties tests, as shown in Figures 13(a)-13(c), which present the effect of the wall thicknesses on the strain of specimens. It can be seen that whether it is on the left-upper side or the right-under side of the pipelines, the strain response of pipelines with larger wall thickness is relatively small, and both the peak compressive strain and the peak tension strain occur near 500 mm from the fault. us, it shows that pipelines with larger wall thickness have better resistance to the fault movement.

Effect of the Buried Depths.
Two types of pipelines with buried depths of 0.3 m and 0.6 m were selected for mechanical properties tests, as shown in Figures 14(a)-14(d), which present the effect of the buried depths on the strain of specimens. It can be seen that the strain responses of NC-1, RC-1, SC-1, and OS-10 are slightly smaller than those of NC-2, RC-2, SC-2, and OS-9, respectively, which indicates that the pipelines crossing faults should be shallowly buried. In addition, this indicates that the greater the buried depth of pipelines, the closer the position of the peak strain of tension and compression to the fault; the main reason is that the soil pressure acting on the pipelines is greater, and a small amount of energy produced by the fault movement is balanced by soil pressure, which results in the deformation area of the pipelines being closer to the fault area.

Effect of the Soil Materials.
Two types of soil materials were selected to study the effect on the strain of pipelines, as shown in Figures 15(a)-15(c). It can be seen that the strain response of pipelines is relatively small when medium sand is used as a backfill. In terms of material properties, the cohesion of clay is much greater than that of medium sand, which results in that the restraint strength of clay to pipelines is significantly greater than that of medium sand to pipelines, and the friction between soil and pipeline is larger; thus, the soil has a greater pulling effect on pipelines. erefore, noncohesive soil materials such as gravel, which usually has a smaller friction coefficient, should be used as a backfill in the process of pipelines laying.

Effect of the Spring Constraints.
In order to study the effect of restraint strength at both ends of a pipeline on its strain response, in this section, two types of springs, which have a relatively small or large elastic coefficient, were selected to study their effect on the strain of pipelines. As shown in Figures 16(a) and 16(b), it can be found that the strain response of pipelines with smaller elastic coefficient is weaker; the reason is that the spring with a larger elastic coefficient has greater restraint strength on both ends of the pipelines, which makes the pipelines far away from the fault unable to expand better along the axis direction, thus resulting in an increase of strain values of the pipelines. erefore, it is unreasonable to set two ends of the pipelines as fixed ends in the model test unless the length of the pipelines is long enough.

Details of the Finite Element
Model. e finite element model was established by ABAQUS software, as shown in Figures 17(a)-17(d). Considering the nonlinearity relationship of pipeline-soil materials and inconsistent displacement in the process of fault movement, the pipeline was modeled using the four-node shell element with reducedintegration (S4R) and the soil was simulated by the eightnode reduced-integration brick solid element (C3D8R). Considering the bond-slip effect of pipeline-soil, the contact pair method was used in the interaction module, mainly including two parts: normal action and tangential action. In this article, the hard contact was adopted in the normal action, and the Coulomb friction model was used to transfer the shear stress of the pipeline-soil surface in the tangential action. In addition, the spring unit was selected to establish the pipeline-end constraint. e spring element is defined by the connectors in the interaction module: first, define the properties of the connection section, select the axis for the translation type, select elastic for the behavior option, and define it as nonlinear. Finally, input the relationship data between force and displacement to complete the definition of spring properties; the second step is to create a connection pair: one end is connected to the node of the pipe end unit and the other end is connected to the reference point. e setting of the spring coefficient "k" is simulated by specifying the spring coefficient in the connecting element. e specific parameters are shown in Table 1. In the mesh generation module, the pipeline mesh within 800 mm from the fault side was compacted and seeded. e sensitivity analysis of the established mesh has been carried out, and the quality of the mesh has been optimized by continuously adjusting the topological relationship and node positions.
Considering the characteristics of the material, the threelinear model and the Mohr-Coulomb model were used to simulate the pipe and the soil [25,26]. e displacement loading method is adopted for simulated loading; that is, displacement is applied to the bottom or side of the mobile terminal.

e Relationship between Strain and Fault Displacement
Time History. In order to investigate the dynamic effect of pipelines, an EI Centro seismic wave with a peak displacement of 140 mm was selected, as shown in Figure 18. e original acceleration of the EI Centro seismic wave was integrated twice, and the baseline was corrected. e obtained displacement curve was applied to the model soil for loading, and the boundary conditions did not change. When inputting seismic waves, taking into account the research of related scholars, the ground motion is scaled at a scale of 1 : 15. e strain of pipeline in the condition of EI Centro seismic wave was compared with the corresponding fault displacement, showing that there is a strong correlation between strain response time history and fault displacement time history. e pipeline strain of measuring point 7-1 of NC-5 changes with the fluctuation of displacement time history, and similar phenomena exist at other measuring points. erefore, it can be considered that the vibration response of pipelines mainly depends on the inconsistent movement of soil at both ends of fault; a static test can be used to study the mechanical properties of pipelines under fault movement.

Equivalent Spring Boundary Verification.
To verify the equivalent spring boundary proposed in this article, the calculation results of the fixed shell model were compared with the equivalent spring boundary model. e fixed shell model was set as follows: the diameter of the pipe was 32 mm, the total length of the pipe was 60 m, the soil is simulated with clay, the fault displacement was set to    Advances in Civil Engineering 140 mm, the angle crossing normal fault was 90°, and the buried depth of the pipe was 0.3 m. e only difference in the equivalent spring boundary model is that the total length of the pipe is 3.0 m, and the other conditions are the same. As shown in Figures 19(a) and 19(b), in which FSM and ESM stand for the fixed shell model and the equivalent spring model, respectively, it can be found that there is little difference between the Mises stress and the vertical deformation under these two cases. It is verified that the equivalent spring boundary model can better simulate the axial tension of the small deformation section of the pipeline and reduce the length of the pipeline required for the model test.
erefore, the effect of different parameters on the resistance to fault movement of pipeline can be studied through the attachment of equivalent spring boundary at both ends of the pipeline.

Comparison of Experimental Results and Finite Element
Results. As shown in Figures 20(a)-20(f ), when the fault displacement was 20 mm, 60 mm, 100 mm, and 140 mm, the axial strain and vertical deformation distribution along the tube axis of different specimens were compared in which FEM and Exp represented the finite element method and the experimental method, respectively. It can be seen that the finite element results are in good agreement with the experimental results, and the strain curve of the pipelines presents a centrosymmetric distribution. With the increase of fault displacement, the strain and deformation values of erefore, choosing pipelines with larger wall thickness is beneficial to prevent local buckling. Figure 22, six different pipeline pressures, 0 MPa, 4 MPa, 6 MPa, 8 MPa, 10 MPa, and 12 MPa, were selected as variables to study their effects on the strain response of pipelines. When the pipeline pressure is small, the effect of pressure on the peak strain of the pipelines is not obvious. Once the pipeline pressure is greater than 4 MPa, the peak tension and compression strain of the pipelines will increase rapidly.

Effect of the Pressure. As shown in
erefore, the application of pressure is not conducive to the resistance of pipelines to fault movement.

Effect of the Soil Materials.
Since the buried pipeline is laid in a wide range, the geological conditions and the stiffness of soil materials are important parameters affecting the mechanical properties of pipelines. ree representative soil materials, silty clay, medium sand, and hard clay, were selected for numerical simulation, as shown in Figure 23. It can be seen that the pipeline crossing in hard clay will enter the plastic strain concentration state more quickly. When Advances in Civil Engineering 13 the fault displacement reaches 1.6 m, the strain of pipeline crossing in silty clay increases slowly, while the strain of pipeline crossing in the sand and hard clay increases rapidly.

Simplified Formula for Strain Calculation of Pipelines.
Relevant scholars have studied the strain calculation methods of pipelines crossing normal, reverse, and strikeslip faults, but few studies have been done on pipelines crossing oblique-slip faults. Compared with the normal, reverse, and strike-slip faults, the effect of oblique-slip fault on the strain response of pipelines is more significant. In this article, the simplified formula of the axial compressive strain of buried pipelines across oblique-slip fault is obtained as follows based on normalizing 13 examples in Section 2.1 (it should be emphasized that this simplified formula is only applicable to the strain calculation and analysis of buried pipelines across oblique-slip fault in this test).  For the buried pipeline model with a fault angle of 90°in this article, the strain of the pipeline is dominated by compressive strain. e pipeline often produces buckling failure under the action of the fault. e buckling can be regarded as a plastic hinge, and the peak compressive strain of the pipeline is also related to the bending angle of the buckling. e bending angle θ can be expressed as follows: where L p is the approximate length of the pipe with large deformation; E is the elastic modulus of the pipe; σ y is the yield stress of the pipe; D is the outer diameter of the pipe; t is the pipe wall thickness; α c is the dimensionless parameter related to the buckling deformation of the pipe.   16 Advances in Civil Engineering Comparing the fitting curve with the example data, the goodness of fit is 0.9612, as shown in Figure 24.

Conclusions
In this article, the mechanical behavior of buried pipelines subjected to faults is studied through experiments and numerical simulations. e following conclusions can be drawn: (1) As the wall thickness and the diameter of the pipeline increase and the buried depth of the pipeline decreases, the peak strain of the buried pipeline decreases under the same working conditions. erefore, increasing the wall thickness and pipe diameter and reducing the buried depth of the pipe are beneficial in reducing the strain response of the buried pipe.
(2) e two-end spring device can better control the size of the test model and enhance the reliability of the test results. (3) e influence of pressure on the peak strain of the pipeline is not obvious when the pipeline pressure is small. However, when the pipeline pressure increases, the peak tensile and compressive strains of the pipeline will increase rapidly. At the same time, the less rigid soil material can delay the growth of pipeline strain. (4) Based on the good agreement between the test results and the finite element analysis, the simplified formula of the axial compressive strain of buried pipelines across oblique-slip fault is obtained, which provides a reference for strain analysis of buried pipelines crossing oblique-slip faults.

Discussion of Future Work
In actual working conditions, pipelines may be damaged by corrosion and cracks [27][28][29][30][31][32]. Damage detection and health monitoring of the pipeline also receive much attention [33][34][35], and a variety of sensors, including fiber optical sensors [36][37][38][39] and piezoceramic transducers [40,41], have been used for pipeline monitoring. In this study, we only consider health specimens, which is inconsistent with actual working conditions. One of the future studies will consider the analysis of damaged specimens and study how this damage occurs and the actual mechanism of action on the pipeline. Detecting the damage of buried pipelines under fault movement in engineering is of great significance. Previous studies have shown that piezoceramic materials have good advantages in pipeline damage detection [42][43][44].
us, piezoceramic materials are commonly used in stress-wave or guided-wave-based damage detection [45][46][47] and health monitoring [48][49][50]. e PZT (Lead Zirconate Titanate), a type of piezoceramic material with a strong piezoelectric effect, is commonly used in damage detection of many different systems [51][52][53], including pipelines [54,55]. However, the real-time damage detection of the buried pipeline during fault movement using PZT transducers has not been adequately addressed in the literature. In another future work, we will explore the real-time damage detection of a buried pipeline during fault movement using distributed PZT transducers and the time reversal method by taking advantage of the developed fault motion simulation experimental setup.

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

Conflicts of Interest
e authors declare no conflicts of interest.