# Seismic Sequence Effects on Buried Pipelines Crossing Nonuniform Sites with Ground Settlement by Dynamic Centrifuge Test

Authors: Hongtao Zhang; Yufei Zhao; Mingxu Gao
Journal: Advances in Civil Engineering
 (2022)

---

## Abstract

The deformation and residual strength of the buried pipeline caused by the earthquake in nonuniform sites has an important influence on the safety of the pipeline. Most of the previous research focuses on the permanent ground deformation (PGD) caused by fault or transient ground deformation (TGD) due to seismic wave propagation independently. The mechanical character of buried pipelines crossing nonuniform sites during seismic sequence after ground settlement has not been studied. This article carried out a dynamic centrifuge experiment to simulate the seismic response of buried pipelines of polyvinyl chloride (PVC) and aluminum alloy (AL) horizontally crossing the loose and dense site and study the residual strength of pipelines after an earthquake. Two simulated seismic waves with 0.6 g and 0.3 g of input peak ground accelerations (PGAs) were inputted in sequence to simulate the strong and weak earthquakes. The deformations of ground and pipelines were obtained during and after seismic. The numerical model consistent with the experiment was established and compared with test, and it was found that the strain of pipeline caused by TGD was different between numerical and experimental results, especially in the loose site. The mechanical model of the pipeline by earthquake indicated that the total strain of the pipeline was composed of bending deformation by PGD and axial deformation by TGD. PGD caused by a strong earthquake had great effects on the deformation and residual strength of the pipeline. The strain of pipeline by TGD was compressive-extensional alternating mode between the loose and dense site and the strain amplitude reached peaks near the block interface in the loose site. The residual strain of pipeline in the dense site was a compressive strain, while in the loose site, it was compressive-extensional alternating mode and varied with the stiffness of the pipeline.


---

## Body

## 1. Introduction

Evidence from past earthquakes indicates that buried pipelines can cause unpredictable damage in unprepared sites. These seismic effects can be divided into two main groups of hazards: (a) transient ground deformation (TGD) due to seismic wave propagation and (b) permanent ground deformation (PGD), with failure caused by active fault movements, landslides, liquefaction-induced settlement, or lateral spreading.Most of the previous research on the deformation of buried pipeline was related to PGD effects. Kennedy et al. [1] proposed a simplified procedure accounting for inelastic strains for conservatively evaluating pipeline behavior during fault movement. This method was used late in the ASCE standard [2]. The simple numerical method for the response of buried pipes under PGD was mainly using springs to approximate the action between soil and pipes. Vazouras et al. [3, 4] proposed verification of a buried steel pipeline crossing the strike-slip and normal fault, and an analytical method for the calculation of the axial and bending pipeline strains was presented and compared with centrifuge results by Ha et al. [5]. It was found that tension and bending were the prevailing modes of deformation in the buried pipelines with fault movement, and the pipeline section would undergo yield with relatively large fault displacements.Ni and Mangalathu [6] proposed a dissipated energy method to calculate the maximum and minimum pipe strains crossing a normal fault perpendicularly and compared with [3] and the centrifuge results [7], and a parametric study was conducted to investigate the sensitivity of parameters, including backfill material, dip angle, burial depth, and pipe strength.Recently some detailed finite element models were established to give a more comprehensive and rigorous analysis for this problem. Zhang et al. [8] proposed a new finite element model of buried steel pipelines crossing strike-slip faults considering equivalent boundary springs, and an analytical method was developed to determine the stiffness coefficient of equivalent boundary springs. It was found that the maximum axial displacement and strain under the fixed constraint are less than the results from the proposed model.Far et al. [9] built the expressions to describe both the tensile and compressive deformation for the estimation of the maximum induced strain through parametric studies involving finite element analyses of 18 different load cases of buried pipelines crossing strike-slip faults. Jalali et al. [10] described the results of full-scale experiments and finite element modeling of buried steel pipelines under reverse faulting. It was demonstrated that finite element analysis with standard constitutive models could provide reliable calculations as long as adequately refined meshes are employed that reproduce the shear localization observed in the soil medium.Ni et al. [11] developed three-dimensional finite element models for buried pipelines subjected to differential ground movements associated with normal faulting, where material nonlinearity, geometric nonlinearity, and the contact, detachment, and slippage behavior on the soil-pipe interface were explicitly modeled, and satisfactory reproductions of the centrifuge experiments [12] were compared, where four centrifuge tests were conducted on model pipelines to quantify the flexural response of pipelines of differing flexural stiffness to normal flexible pipelines, and illustrate how “stiff pipeline” soil reaction models significantly overestimate peak strains for flexible pipelines, and whether the situation was the same during seismic has not studied yet.Numerical modeling of the interaction of pressurized large diameter gas buried pipelines with normal fault ruptures [13] was carried out and compared with centrifuge tests [14], considering different fault angles and operating conditions. Banushi et al. [15] studied the buried operating pipeline subjected to strike-slip fault movement, considering operating pressure and temperature, compared with other numerical methods. Results indicated that the operating pressure had a beneficial effect to the ovalization limit state of the pipeline.Most of the pipeline damage reported is attributed to PGD, but there is also strong evidence that wave propagation has contributed to pipe damage, especially TGD in nonuniform sites and undesirable deformations in the pipe, which is overlooked in the present standards of practice [16]. The effect of inhomogeneous soil on pipeline seismic demand was first studied by Hindy and Novak [17] using the dynamic equilibrium of an elastic lumped-mass beam model of the pipeline and appropriate soil springs and dashpots. A major conclusion was that body waves traveling along a pipeline laid through two different soils caused peak axial and bending stresses near the boundary of the two media and were larger than the ones in the homogeneous. Predictions also revealed that bending stresses due to S-waves were much smaller than the axial stresses due to P-waves.Lee et al. [18] proposed the line elements incorporating inelastic cubic formulation to represent the buried pipeline. Various parameters such as the type of buried gas pipeline, end-restraint conditions, soil characteristics, single and multiple earthquake input ground motions, and burial depths were studied to obtain the response characteristics of strains in a buried pipeline section.Psyrras et al. [19] numerically investigated the elastic-plastic buckling response of buried steel pipelines subjected to transient differential ground motions arising from strong lateral site inhomogeneities and indicted axial stress concentration in the critically affected pipeline segment near the material discontinuity. The strong excitation will cause much response, but how the different stiffness of the soil-pipe interface (SPI) and PGD caused by seismic will affect the buried pipeline during seismic is not clear.Experimental modeling is more effective for seismic investigation of the interaction of soil and pipes. Shaking table tests modeling small diameter pipes crossing a vertical fault were performed under 1 g conditions on instrumented 20 mm diameter acrylic prototype pipes buried in dry Toyoura sand [20]. Four different pipe fault crossing angles were examined with the lifting of the hanging wall occurring both during and after the application of dynamic shaking. 1 g shaking table tests were performed to study pipe deformations in sandy slopes under dynamic landsliding of burial depth [21]. It was found that the horizontal strains had a major impact on total strains of a pipe embedded at shallow depths in a slope and increasing burial depth had a negative correlation with the impact of this strain type.Yan et al. [22] carried out a shaking table model test to explore the seismic responses of a deeply buried pipeline under uniform and nonuniform excitations in the three directions and found that nonuniform seismic excitation had a great influence on the acceleration amplification in soil and the strain and displacement of the pipeline, due to strong pipe and soil interaction under nonuniform excitation. It also predicted that the permanent displacement of the pipeline produced by uniform excitation could be negligible, but it could not be neglected for nonuniform excitation and need to be further studied.Psyrras et al. [23] found that the pipe response was predominantly axial while bending became significant at stronger excitations using the shaking table model test. Strain distributions displayed clear peaks at or near the block interfaces, with magnitudes increasing at resonant frequencies and with excitation levels.The conventional shaking table test has some limitations because of the lack of a real stress state simulation. Thus, there was an attempt to install the shaking table on a centrifuge to simulate the stress state of the soils during an earthquake. Seismic centrifugal experiments were originally used to study the seismic behavior of pipes in liquefiable soil and three model pipes made of aluminum alloy were used where the normal and tangential earth pressures were measured in the loose and dense silica sand [24]. Later dynamic centrifuge model tests were conducted to study the uplifting behaviors of shallow-buried pipelines subjected to seismic vibration in liquefied sites [25]. Excess pore pressure and earth pressure around the pipelines and the forces on the pipelines before and during soil liquefaction were estimated. Recently, the availability of dynamic centrifuge tests has been confirmed by a variety of research, like tunneling deformation [26–28] investigated by a dynamic centrifugal model by loading a series of earthquake waves and seismic response of group-pile foundation in a slope [29].Laterally varying soil conditions can profoundly affect stress distribution and magnitude of the buried pipeline during seismic [30]. Further research is necessary on the development of the dynamic SPI under seismic shaking, including the PGD and TGD coupled effect caused by seismic simultaneously. In this study, dynamic centrifuge model was constructed to investigate the seismic performance and dynamic deformation of buried pipelines in nonuniform sites during an earthquake, with different levels of input peak ground acceleration (PGA). The seismic behavior study of the pipe under earthquake conditions mainly focused on deformation analyses that were monitored by strain gauges and laser displacement meters, which were caused by PGD before and during seismic and TGD by seismic waves parallel to the pipe length. Responses of pipes of different materials (polyvinyl chloride (PVC) and aluminum alloy (AL)) under seismic were compared. The purpose of the paper was to illustrate the mechanical behavior of buried pipelines crossing dense and loose sites with strong and weak seismic sequences after uneven ground settlement. The deformation and residual strain of pipelines in the dense and loose sites were obtained.


## 2. Experimental Apparatus and Method

### 2.1. Centrifuge Experiment

The centrifuge used in this experiment was built in 1991 by the China Institute of Water Resources and Hydropower Research (IWHR), as shown in Figure1. The shaking table equipped with this centrifuge was the first centrifuge vibration equipment capable of conducting independent horizontal and vertical two-way vibration in China. The centrifuge can generate up to 30 g horizontal and 20 g vertical excitation under a maximum centrifugal g-level of 80 g. Table 1 summarizes the specifications of the centrifuge.Figure 1
Photo of dynamical centrifuge in IWHR.Table 1
Technical specifications of the centrifuge.
Key termSpecificationMax.centrifuge acceleration80 gMax.shaking acceleration30 g (horizontal)/20 g(vertical)Payload capacity400 kgMax.shaking displacement5 mmShaking frequency range400 HzPayload mounting area900 mm × 700 mm × 800 mmThe dynamic response of the buried pipeline under the action of earthquake load was simulated to the maximum extent, and the gravity acceleration of the centrifuge was determined to be 40 g. The dynamic centrifuge test was scaled by the Buckinghamπ theorem based on dimensional analysis. In this model test, the practical project and the modeling equipment were combined, the gravitational acceleration g, normal stress σ, and length L were selected as the controlling parameters, and their scale ratios were 40, 1, and 1/40. The scale ratios of the rest of the primary parameters determining the model design could be deduced from the three controlling parameters and were displayed in Table 2.Table 2
Scale ration related to pipe modeling.
QuantityScale ration (model/prototype)g: gravitation40L: length1/40ρ: density1c: cohesion1ϕ: angel of internal friction1t: time1/40σ: normal stress1F: force1/402


### 2.2. Model

In this paper, the pipes were scaled by the reduced-scale ratio of 40 directly. No anchors were used at the ends of the pipe on the conservative side and left the pipeline ends free to move horizontally. This decision was driven by the belief that, away from any lateral ground heterogeneities, a pipeline was expected to move with the soil under vertically incident in-plane shear waves [12, 19]. Considering the box length of 750 mm, a pipe length of 640 mm was chosen so that 55 mm spaces were left between the pipe ends and the side walls to minimize boundary effects. Model pipe length 640 mm, pipe outer diameter 16 mm, thickness 0.5 mm were representative of a scenario in which prototype pipe length 25.6 m, outer diameter 0.64 m, thickness 0.02 m, and the geometry of the model was displayed in Figure 2.Figure 2
Dimension of the model box and buried pipeline with sensors (mm). (a) Front view. (b) Plan view. (c) Model in the test.
(a)(b)(c)Because uneven ground settlement was usually induced by fault movement and the sharp change of mechanical properties near the fault was often found, Kaolin clay and Fujian sand were used to represent the nonuniform sites, and the obvious difference between the mechanical properties of the two soils may reveal the effect more clearly. “Soil-1” and “Soil-2” were represented as Kaolin clay (loose site) and Fujian sand (dense site), respectively, and the disparity of soil parameters was designed to amplify the character of the nonuniform site. The indoor experiment was carried out to obtain the elastic modulus of Kaolin and Fujian sand. The related mechanical parameters of soils are listed in Table3.Table 3
Soil parameters in model.
Density (kg/m3)Cohesion (kPa)Angel of friction (°)Shear modulus (MPa)Soil-1120002017Soil-22100030300PVC pipe and AL pipe were buried in the soils together. The stress-strain relationship curves of PVC and AL were simplified, as shown in Figure3. The material parameters are listed in Table 4. The scaling law for bending stiffness (unit: N·m2) in the centrifuge is 1/404 (Model/Prototype). Because the shaking direction was parallel to the pipe and the ratio of the distance of PVC and AL pipe to pipe diameter was nearly 10, and the deformation of the pipe was just in the vertical plane. The interaction between the PVC and AL pipe was small and neglected.Figure 3
Stress-strain curve of AL and PVC pipe.Table 4
Pipe parameters in model.
PipeElastic modulus (GPa)Poisson’s ratioNominal yield strain (%)Limit strain (%)Bending stiffness in prototype (N·m2)PVC2.70.41.8305.06 × 106AL710.30.2101.33 × 108Kaolin was directly placed into the box to represent the loose site, while Fujian sand was made by air pluviation technique shown in Figure4. In this test, the density of Fujian sand was set as 2100 kg/m3. The sand was air-dried and added into the funnel, and the height of falling sand was determined to be 0.46 m, which could reach the required density. The Kaolin clay was first weighted and then directly placed into the model box. After finishing, the density of Kaolin was calculated. A piece of cardboard was vertically placed in the center of the box, and different soils were placed on both sides, respectively. When the soil height reached 0.216 m, the cardboard was pulled out, and two pipes (PVC and AL) were put in. The cardboard was placed vertically in the same position and on different soils on both sides. Stop packing the soils until the height was 0.448 m, and finally draw out the cardboard.Figure 4
Fujian sand made by air pluviation technique.After the model was completed, the model box was hoisted into the centrifuge and fixed with bolts. There were two laser displacement meters (LDMs) for vertical displacement and 15 couples of axial strain gauges (Str-1, …, Str-30) with 40 mm intervals evenly installed for collection of the seismic responses of the pipes, as shown in Figures2(b) and 2(c). The seismic responses of the two pipelines were mainly represented by the tensile and compressive strain on the crown of the pipe, which were monitored by axial strain gauges parallel to the shaking direction.


### 2.3. Input Seismic Acceleration

To analyze the seismic responses during the strong and weak earthquake and postearthquake residual strength of buried pipelines, different PGAs of recorded strong ground motions with a time period 24 s of Parkfield 1966 were inputted into the base of the experimental model to simulate the real seismic condition. The input seismic records were processed by converting the horizontal PGAs to 0.3 g and 0.6 g. The time histories of normalized acceleration amplitude are shown in Figure5. According to the similarity law, the duration of each input wave was 0.6 s in the model but 24 s in situ because of the time scale ratio of 40. Two simulated seismic waves with 0.6 g and 0.3 g PGAs were inputted to the bottom of the container in sequence after the displacement monitored by the LDMs system became stable at the centrifugal g-level of 40.Figure 5
Time histories of normalized acceleration amplitude in a prototype.


## 2.1. Centrifuge Experiment

The centrifuge used in this experiment was built in 1991 by the China Institute of Water Resources and Hydropower Research (IWHR), as shown in Figure1. The shaking table equipped with this centrifuge was the first centrifuge vibration equipment capable of conducting independent horizontal and vertical two-way vibration in China. The centrifuge can generate up to 30 g horizontal and 20 g vertical excitation under a maximum centrifugal g-level of 80 g. Table 1 summarizes the specifications of the centrifuge.Figure 1
Photo of dynamical centrifuge in IWHR.Table 1
Technical specifications of the centrifuge.
Key termSpecificationMax.centrifuge acceleration80 gMax.shaking acceleration30 g (horizontal)/20 g(vertical)Payload capacity400 kgMax.shaking displacement5 mmShaking frequency range400 HzPayload mounting area900 mm × 700 mm × 800 mmThe dynamic response of the buried pipeline under the action of earthquake load was simulated to the maximum extent, and the gravity acceleration of the centrifuge was determined to be 40 g. The dynamic centrifuge test was scaled by the Buckinghamπ theorem based on dimensional analysis. In this model test, the practical project and the modeling equipment were combined, the gravitational acceleration g, normal stress σ, and length L were selected as the controlling parameters, and their scale ratios were 40, 1, and 1/40. The scale ratios of the rest of the primary parameters determining the model design could be deduced from the three controlling parameters and were displayed in Table 2.Table 2
Scale ration related to pipe modeling.
QuantityScale ration (model/prototype)g: gravitation40L: length1/40ρ: density1c: cohesion1ϕ: angel of internal friction1t: time1/40σ: normal stress1F: force1/402


## 2.2. Model

In this paper, the pipes were scaled by the reduced-scale ratio of 40 directly. No anchors were used at the ends of the pipe on the conservative side and left the pipeline ends free to move horizontally. This decision was driven by the belief that, away from any lateral ground heterogeneities, a pipeline was expected to move with the soil under vertically incident in-plane shear waves [12, 19]. Considering the box length of 750 mm, a pipe length of 640 mm was chosen so that 55 mm spaces were left between the pipe ends and the side walls to minimize boundary effects. Model pipe length 640 mm, pipe outer diameter 16 mm, thickness 0.5 mm were representative of a scenario in which prototype pipe length 25.6 m, outer diameter 0.64 m, thickness 0.02 m, and the geometry of the model was displayed in Figure 2.Figure 2
Dimension of the model box and buried pipeline with sensors (mm). (a) Front view. (b) Plan view. (c) Model in the test.
(a)(b)(c)Because uneven ground settlement was usually induced by fault movement and the sharp change of mechanical properties near the fault was often found, Kaolin clay and Fujian sand were used to represent the nonuniform sites, and the obvious difference between the mechanical properties of the two soils may reveal the effect more clearly. “Soil-1” and “Soil-2” were represented as Kaolin clay (loose site) and Fujian sand (dense site), respectively, and the disparity of soil parameters was designed to amplify the character of the nonuniform site. The indoor experiment was carried out to obtain the elastic modulus of Kaolin and Fujian sand. The related mechanical parameters of soils are listed in Table3.Table 3
Soil parameters in model.
Density (kg/m3)Cohesion (kPa)Angel of friction (°)Shear modulus (MPa)Soil-1120002017Soil-22100030300PVC pipe and AL pipe were buried in the soils together. The stress-strain relationship curves of PVC and AL were simplified, as shown in Figure3. The material parameters are listed in Table 4. The scaling law for bending stiffness (unit: N·m2) in the centrifuge is 1/404 (Model/Prototype). Because the shaking direction was parallel to the pipe and the ratio of the distance of PVC and AL pipe to pipe diameter was nearly 10, and the deformation of the pipe was just in the vertical plane. The interaction between the PVC and AL pipe was small and neglected.Figure 3
Stress-strain curve of AL and PVC pipe.Table 4
Pipe parameters in model.
PipeElastic modulus (GPa)Poisson’s ratioNominal yield strain (%)Limit strain (%)Bending stiffness in prototype (N·m2)PVC2.70.41.8305.06 × 106AL710.30.2101.33 × 108Kaolin was directly placed into the box to represent the loose site, while Fujian sand was made by air pluviation technique shown in Figure4. In this test, the density of Fujian sand was set as 2100 kg/m3. The sand was air-dried and added into the funnel, and the height of falling sand was determined to be 0.46 m, which could reach the required density. The Kaolin clay was first weighted and then directly placed into the model box. After finishing, the density of Kaolin was calculated. A piece of cardboard was vertically placed in the center of the box, and different soils were placed on both sides, respectively. When the soil height reached 0.216 m, the cardboard was pulled out, and two pipes (PVC and AL) were put in. The cardboard was placed vertically in the same position and on different soils on both sides. Stop packing the soils until the height was 0.448 m, and finally draw out the cardboard.Figure 4
Fujian sand made by air pluviation technique.After the model was completed, the model box was hoisted into the centrifuge and fixed with bolts. There were two laser displacement meters (LDMs) for vertical displacement and 15 couples of axial strain gauges (Str-1, …, Str-30) with 40 mm intervals evenly installed for collection of the seismic responses of the pipes, as shown in Figures2(b) and 2(c). The seismic responses of the two pipelines were mainly represented by the tensile and compressive strain on the crown of the pipe, which were monitored by axial strain gauges parallel to the shaking direction.


## 2.3. Input Seismic Acceleration

To analyze the seismic responses during the strong and weak earthquake and postearthquake residual strength of buried pipelines, different PGAs of recorded strong ground motions with a time period 24 s of Parkfield 1966 were inputted into the base of the experimental model to simulate the real seismic condition. The input seismic records were processed by converting the horizontal PGAs to 0.3 g and 0.6 g. The time histories of normalized acceleration amplitude are shown in Figure5. According to the similarity law, the duration of each input wave was 0.6 s in the model but 24 s in situ because of the time scale ratio of 40. Two simulated seismic waves with 0.6 g and 0.3 g PGAs were inputted to the bottom of the container in sequence after the displacement monitored by the LDMs system became stable at the centrifugal g-level of 40.Figure 5
Time histories of normalized acceleration amplitude in a prototype.


## 3. Results and Discussions

For this experimental model, the main analysis was focused on the dynamic axial strain of the two pipes. Additionally, the dynamic vertical displacements of the soils were measured by the LDMs system. The following description was based on the prototype dimension.


### 3.1. PGD of Soils Caused by Seismic

The centrifugal g-level was raised from 1 g to 40 g to represent the real soil stress state before the seismic experiment, so the soil settlement would unavoidably happen during the centrifugal acceleration elevated. The surface of the Soil-1 after seismic was shown in Figure6(a) and could not be recorded because of the excessively large displacement. The lateral spreading of Soil-2 after 0.3 g seismic was found, as shown in Figure 6(b).Figure 6
Surface of soils after 0.3 g seismic in the model. (a) Vertical displacement of soil-1. (b) Lateral spreading caused by seismic.
(a)(b)The time histories of vertical displacement of the Soil-2 in the prototype were marked as “before seismic,” “after 0.6 g seismic,” and “after 0.3 g seismic,” respectively, in Figure7 after the centrifugal g-level was 40 g. The displacement value measured by LDM has fluctuated between the true value such as the vertical displacement of Soil-2 before seismic is 5 cm in amplitudes in prototype (0.125 cm in model scale). Here the relative displacement value of PGD caused by 0.6 g seismic and 0.3 g seismic was calculated for comparison. Ground uneven settlement measured was not used in this paper.Figure 7
Time histories of vertical displacement of soil-2 in the prototype.The vertical PGD of the Soil-2 caused by a 0.6 g earthquake was about 16 cm in prototype (4 mm in the model) calculated by the displacement of “after 0.6 g seismic” minus the displacement of “before seismic” and by 0.3 g earthquake was about 5 cm calculated by the displacement of “after 0.3 g seismic” minus the displacement of “after 0.6 g seismic.” The vertical TGD amplitude of the Soil-2 caused by a 0.6 g earthquake was about 5 cm, and by a 0.3 g earthquake was about 4 cm. Compared with a 0.3 g earthquake, the PGD was mainly caused by a 0.6 g earthquake, and the vertical TGD caused by different seismic waves was similar and neglected for simplicity in the following analysis.


### 3.2. Initial Strain of Pipeline before Seismic

The time histories of strains of AL and PVC pipe under seismic waves were shown in Figures8(a)–8(f) and 9(a)–9(f) for some locations, especially near the soil interface. Because of the strain gauges failure, Str-4 and Str-20 were not recorded. The corresponding results were interpolated with near-recorded strain. As the locations were far from the interface, it may not cause a worse error.Figure 8
Time histories of strain of AL pipe under the seismic wave.
(a)(b)(c)(d)(e)(f)Figure 9
Time histories of strain of PVC pipe under seismic wave.
(a)(b)(c)(d)(e)(f)Because the deformation of pipeline caused by earthquake should be calculated based on the strain before and after the earthquake, “before seismic” and “after seismic” were used to calculate the strain amplitude and residual strain of pipeline in the time-strain histories as shown in Figure8(a), also the same with other figures.The centrifugal g-level was raised from 1 g to 40 g before the seismic experiment. After 40 g-level was reached, the soil stress state was real. The strain of pipeline caused by the uneven settlement of Soil-1 and Soil-2 before seismic was defined as “before seismic” in Figure8(a) minus the initial strain and was shown in Figure 10. The simplified numerical model was established and the vertical and axial SPI was represented by nonlinear spring elements. Spring parameters were evaluated according to standard expressions proposed by the ALA [2], with vertical and axial stiffness and separate displacement of SPI of Soil-1 as 3 × 108 N/m2 and 6 × 107 N/m2, and 5 × 10−5 m, Soil-2 as 4.5 × 108 N/m2 and 1 × 108 N/m2, and 3 × 10−5 m. The numerical results were also shown in Figure 10 and compared with the test results. The strain distributions in the two pipelines had the same tendency, except that the results are offset by approximately 2 m in the horizontal direction. This was because the lateral spreading of Soil-2 had happened in the test before seismic, and this could be testified in Figure 6(b) after 0.3 g seismic. But in the numerical model such a phenomenon was not found.Figure 10
Initial strain of pipelines by uneven settlement of soils before seismic.The initial strain of PVC and AL pipe at (2 × 1.6) m in Soil-2 reached 0.02 and 0.01, respectively, exceeding the nominal yield strain but not reaching the tensile limit strain of PVC and AL respectively. The corresponding mechanical model of pipeline caused by uneven settlement was shown in Figure11 and not explained in detail here as it had been studied profoundly such as in Ref. [1, 4]. f0(x) and t0(x) were unit of the friction force and unit of the normal force acting on the surface of the pipe. M and F were bending moment and axial force acting on the cross section of the pipe. The sharp change of the strain on the crown of II0 section could be caused by bending moment MII0 from f02(x) besides t02(x) in Figure 11.Figure 11
Mechanical model of pipeline caused by uneven settlement.


### 3.3. Deformation of Pipe Caused by Seismic

The pipe deformation was caused by PGD and TGD simultaneously, as shown in Figure8(a). The vertical TGD of soils was ignored and the strain of pipes caused by a 0.6 g earthquake at 12 s and 18 s were chosen to show, respectively, after the PGD by the earthquake was in a constant value.The strain of AL pipe caused by PGD was calculated by the strain “after 0.6 g seismic” minus the strain “before seismic” as in Figure8(a) and marked as “AL-PGD” and also the “PVC-PGD” in Figure 12(a). The strain of AL pipe by PGD and TGD at 12 s was calculated by the strain at 12 s minus the strain “before seismic” as in Figure 8(a) and marked as “AL-12 s” and also the “PVC-12 s” in Figure 12(a).Figure 12
Strain of pipe caused by 0.6 g earthquake at 12 s and 18 s. (a) Strain caused by PGD and TGD (b) strain caused by TGD.
(a)(b)It must be noted that the deformation of pipelines caused by PGD of the earthquake in Figure12(a) was different from the initial strain of pipelines by uneven settlement in Figure 10, where the PGD was composed of vertical and axial ground deformation and lateral spreading simultaneously. In order to illustrate the coupled effect and reveal the deformation of pipe by TGD clearly, the strain of pipe caused by TGD was calculated by “AL-12 s” minus “AL-PGD” in Figure 12(a) and noted as “AL-12 s-TGD” shown in Figure 12(b), and others with “−18 s” and so on. The numerical results of the PVC pipeline by TGD during an earthquake at 12 s and 18 s were also shown in Figure 12(b), and it was found that the peak strain was the same with the experiment results. But the strain of the PVC pipeline at (−2 × 1.6) m at 18 s and (−1 × 1.6) m at 12 s were different from the experiment results.The compression and tension of pipelines by TGD during the earthquake were alternating in the loose and dense site shown in Figure12(b). The mechanical models of the pipeline by TGD during an earthquake at 12 s and 18 s were, respectively, shown in Figures 13 and 14, corresponding to Figure 12(b). Here f(x) and t (x) were the unit of friction force and the unit of normal force caused by TGD. N was the external force acting on the pipe and a was the acceleration of soil at the block interface at 12 s. Bending moment MI and axial force FI both resulted from f1(x) on I section in Figure 13. Superscript “′” indicated the related parameters at 18 s.Figure 13
Mechanical model of pipe by TGD during 0.6 g earthquake at 12 s.Figure 14
Mechanical model of pipe by TGD during 0.6 g earthquake at 18 s.The axial strain on the crown ofI and I′ section near the block interface in Soil-1 was caused by bending moment (MI and MI′) and axial force (FI and FI′) in Figures 13 and 14, respectively, while it was no bending deformation in the uniform site during seismic. The tensile strains on the crown of AL pipe at (−2 × 1.6) m and PVC pipe at (−1 × 1.6) m at 12 s in Figure 12(b) were mainly caused by bending moment MI as I section shown in Figure 13, while the compression strain on the crown of AL pipe at (−3 × 1.6) m and PVC pipe at (−2 × 1.6) m at 18 s were mainly caused by bending moment MI′ as I′ section shown in Figure 14. The different location of tension of AL pipe at (−2 × 1.6) m in “AL-12 s-TGD” and compression at (−3 × 1.6) m in “AL-18 s-TGD” indicated that the friction amplitude f1′x was bigger than f1(x), so that bending moment value MI′ > MI at the same location.The strain on the crown of pipelines at (−2 × 1.6) m caused by PGD of 0.6 g earthquake was compressive in Figure12(a), not like the sharp change of tensile strain at (−2 × 1.6) m caused by uneven settlement in Figure 10, which indicated the axial and bending deformation of pipeline’s coupled effect was more obvious than the vertical deformation during 0.6 g earthquake.The compression strain of pipelines at the interface (II section) had a sharp change, which was caused by TGD at 12 s with a different acceleration of “Soil-1” and “Soil-2” (a2 > a1) and FII acting on the II section in Figure 13, while the tension strain of pipe at the interface (II′ section) by a2′>a1′ and FII′ shown in Figure 14.


### 3.4. Strain Amplitude of Pipe Caused by Seismic Wave

Strain amplitude of pipe caused by 0.6 g earthquake was calculated by strain during 0.6 g seismic minus strain “before seismic,” and that caused by 0.3 g earthquake was strain during 0.3 g seismic minus strain “before 0.3 g seismic” as shown in Figure8(a). Strain amplitudes of pipelines by different seismic waves were shown in Figure 15, where the tensile strain amplitude of AL pipe caused by a 0.6 g earthquake was noted as “AL-0.6 g-TEN,” and so on.Figure 15
Strain amplitudes of pipelines by seismic wave.The maximum tensile and compressive strains of pipelines were all in Soil-1 and changed obviously near the block interface and were more affected by bending deformation by PGD. The tensile strain amplitudes of pipelines had a sharp change at the block interface and were more affected by axial deformation by TGD.The tensile strain amplitudes of both pipelines were very small at (−2 × 1.6) m in Soil-1, which was mainly caused by the axial compressionFI on the pipe as I section shown in Figure 13. The compression strain amplitudes of PVC and AL pipe had a sharp change at (−2 × 1.6) m and (−3 × 1.6) m, respectively, in Soil-1 and were larger than that in Soil-2, which was mainly caused by compression on the crown of pipe by bending moment MI′ as I′ section in Figure 14.The pipeline strain caused by the earthquake reached peaks near the block interface in the loose site. The tensile strain amplitude of pipeline in the loose site was larger than that in dense site, while compression strain amplitude of pipeline in the dense site was larger than that in the loose site. Compression strain of the pipeline was more affected by the seismic intensity in the dense site than that in the loose site, while tensile strain was more affected in the loose site.The maximum tensile and compressive strain amplitudes of PVC pipeline caused by 0.6 g seismic wave were all in Soil-1 and not at the interface, reaching 1.7 × 10−3 and −1.7 × 10−3, while the maximum tensile strain amplitude of AL pipeline was at the interface, reached 7.5 × 10−4. The maximum tensile and compressive strain amplitudes of AL and PVC pipelines caused by 0.3 g seismic waves were all at the interface, which indicated that the seismic response of the pipeline was more affected by the PGD of a strong earthquake.


### 3.5. Residual Strain of Pipeline after Earthquake

After the earthquake, the residual strain of the pipeline was calculated by strain “after seismic” minus strain “before seismic” as shown in Figure8(a), and the results were shown in Figure 16, such as “AL-0.6 g” was the residual strain in AL pipe calculated by strain “after 0.6 g seismic” minus strain “before seismic” and “AL-Tot” was the total residual strain in AL pipe calculated by strain “after seismic” minus “before seismic.”Figure 16
Residual strain of pipelines under different conditions.The residual strains of pipelines after the earthquake were mainly due to PGD caused by a strong earthquake. For example, the total residual strains of AL pipe after the earthquake in Soil-1 were tensile strains, except for the compression on the crown caused by bend deformation by PGD of the earthquake at (−2 × 1.6) m and (−3 × 1.6) m. The residual strain of pipe in the dense site was compression strain because of Soil-2 (the dense site) slid down Soil-1 (the loose site) by the lateral spreading of the earthquake shown in Figure6(b).Residual strains of AL pipe by 0.6 g earthquake was extensional-compressive-extensional mode in loose site, while PVC pipe was extensional-compressive-extensional-compressive mode. Residual strains of two pipelines by 0.3 g earthquake were compressive-extensional-compressive mode in the loose site.The peak residual tensile strain of PVC pipeline by 0.6 g seismic was in Soil-1, reached 1.6 × 10−3, while compressive strain was in Soil-2, reached −1.1 × 10−3. The peak residual strains of PVC pipeline by 0.3 g seismic were both in Soil-1. The peak residual tensile strain of AL pipeline by 0.6 g seismic was in Soil-1, reached 4.5 × 10−4, while compressive strain was in Soil-2, reached −4.8 × 10−4.


## 3.1. PGD of Soils Caused by Seismic

The centrifugal g-level was raised from 1 g to 40 g to represent the real soil stress state before the seismic experiment, so the soil settlement would unavoidably happen during the centrifugal acceleration elevated. The surface of the Soil-1 after seismic was shown in Figure6(a) and could not be recorded because of the excessively large displacement. The lateral spreading of Soil-2 after 0.3 g seismic was found, as shown in Figure 6(b).Figure 6
Surface of soils after 0.3 g seismic in the model. (a) Vertical displacement of soil-1. (b) Lateral spreading caused by seismic.
(a)(b)The time histories of vertical displacement of the Soil-2 in the prototype were marked as “before seismic,” “after 0.6 g seismic,” and “after 0.3 g seismic,” respectively, in Figure7 after the centrifugal g-level was 40 g. The displacement value measured by LDM has fluctuated between the true value such as the vertical displacement of Soil-2 before seismic is 5 cm in amplitudes in prototype (0.125 cm in model scale). Here the relative displacement value of PGD caused by 0.6 g seismic and 0.3 g seismic was calculated for comparison. Ground uneven settlement measured was not used in this paper.Figure 7
Time histories of vertical displacement of soil-2 in the prototype.The vertical PGD of the Soil-2 caused by a 0.6 g earthquake was about 16 cm in prototype (4 mm in the model) calculated by the displacement of “after 0.6 g seismic” minus the displacement of “before seismic” and by 0.3 g earthquake was about 5 cm calculated by the displacement of “after 0.3 g seismic” minus the displacement of “after 0.6 g seismic.” The vertical TGD amplitude of the Soil-2 caused by a 0.6 g earthquake was about 5 cm, and by a 0.3 g earthquake was about 4 cm. Compared with a 0.3 g earthquake, the PGD was mainly caused by a 0.6 g earthquake, and the vertical TGD caused by different seismic waves was similar and neglected for simplicity in the following analysis.


## 3.2. Initial Strain of Pipeline before Seismic

The time histories of strains of AL and PVC pipe under seismic waves were shown in Figures8(a)–8(f) and 9(a)–9(f) for some locations, especially near the soil interface. Because of the strain gauges failure, Str-4 and Str-20 were not recorded. The corresponding results were interpolated with near-recorded strain. As the locations were far from the interface, it may not cause a worse error.Figure 8
Time histories of strain of AL pipe under the seismic wave.
(a)(b)(c)(d)(e)(f)Figure 9
Time histories of strain of PVC pipe under seismic wave.
(a)(b)(c)(d)(e)(f)Because the deformation of pipeline caused by earthquake should be calculated based on the strain before and after the earthquake, “before seismic” and “after seismic” were used to calculate the strain amplitude and residual strain of pipeline in the time-strain histories as shown in Figure8(a), also the same with other figures.The centrifugal g-level was raised from 1 g to 40 g before the seismic experiment. After 40 g-level was reached, the soil stress state was real. The strain of pipeline caused by the uneven settlement of Soil-1 and Soil-2 before seismic was defined as “before seismic” in Figure8(a) minus the initial strain and was shown in Figure 10. The simplified numerical model was established and the vertical and axial SPI was represented by nonlinear spring elements. Spring parameters were evaluated according to standard expressions proposed by the ALA [2], with vertical and axial stiffness and separate displacement of SPI of Soil-1 as 3 × 108 N/m2 and 6 × 107 N/m2, and 5 × 10−5 m, Soil-2 as 4.5 × 108 N/m2 and 1 × 108 N/m2, and 3 × 10−5 m. The numerical results were also shown in Figure 10 and compared with the test results. The strain distributions in the two pipelines had the same tendency, except that the results are offset by approximately 2 m in the horizontal direction. This was because the lateral spreading of Soil-2 had happened in the test before seismic, and this could be testified in Figure 6(b) after 0.3 g seismic. But in the numerical model such a phenomenon was not found.Figure 10
Initial strain of pipelines by uneven settlement of soils before seismic.The initial strain of PVC and AL pipe at (2 × 1.6) m in Soil-2 reached 0.02 and 0.01, respectively, exceeding the nominal yield strain but not reaching the tensile limit strain of PVC and AL respectively. The corresponding mechanical model of pipeline caused by uneven settlement was shown in Figure11 and not explained in detail here as it had been studied profoundly such as in Ref. [1, 4]. f0(x) and t0(x) were unit of the friction force and unit of the normal force acting on the surface of the pipe. M and F were bending moment and axial force acting on the cross section of the pipe. The sharp change of the strain on the crown of II0 section could be caused by bending moment MII0 from f02(x) besides t02(x) in Figure 11.Figure 11
Mechanical model of pipeline caused by uneven settlement.


## 3.3. Deformation of Pipe Caused by Seismic

The pipe deformation was caused by PGD and TGD simultaneously, as shown in Figure8(a). The vertical TGD of soils was ignored and the strain of pipes caused by a 0.6 g earthquake at 12 s and 18 s were chosen to show, respectively, after the PGD by the earthquake was in a constant value.The strain of AL pipe caused by PGD was calculated by the strain “after 0.6 g seismic” minus the strain “before seismic” as in Figure8(a) and marked as “AL-PGD” and also the “PVC-PGD” in Figure 12(a). The strain of AL pipe by PGD and TGD at 12 s was calculated by the strain at 12 s minus the strain “before seismic” as in Figure 8(a) and marked as “AL-12 s” and also the “PVC-12 s” in Figure 12(a).Figure 12
Strain of pipe caused by 0.6 g earthquake at 12 s and 18 s. (a) Strain caused by PGD and TGD (b) strain caused by TGD.
(a)(b)It must be noted that the deformation of pipelines caused by PGD of the earthquake in Figure12(a) was different from the initial strain of pipelines by uneven settlement in Figure 10, where the PGD was composed of vertical and axial ground deformation and lateral spreading simultaneously. In order to illustrate the coupled effect and reveal the deformation of pipe by TGD clearly, the strain of pipe caused by TGD was calculated by “AL-12 s” minus “AL-PGD” in Figure 12(a) and noted as “AL-12 s-TGD” shown in Figure 12(b), and others with “−18 s” and so on. The numerical results of the PVC pipeline by TGD during an earthquake at 12 s and 18 s were also shown in Figure 12(b), and it was found that the peak strain was the same with the experiment results. But the strain of the PVC pipeline at (−2 × 1.6) m at 18 s and (−1 × 1.6) m at 12 s were different from the experiment results.The compression and tension of pipelines by TGD during the earthquake were alternating in the loose and dense site shown in Figure12(b). The mechanical models of the pipeline by TGD during an earthquake at 12 s and 18 s were, respectively, shown in Figures 13 and 14, corresponding to Figure 12(b). Here f(x) and t (x) were the unit of friction force and the unit of normal force caused by TGD. N was the external force acting on the pipe and a was the acceleration of soil at the block interface at 12 s. Bending moment MI and axial force FI both resulted from f1(x) on I section in Figure 13. Superscript “′” indicated the related parameters at 18 s.Figure 13
Mechanical model of pipe by TGD during 0.6 g earthquake at 12 s.Figure 14
Mechanical model of pipe by TGD during 0.6 g earthquake at 18 s.The axial strain on the crown ofI and I′ section near the block interface in Soil-1 was caused by bending moment (MI and MI′) and axial force (FI and FI′) in Figures 13 and 14, respectively, while it was no bending deformation in the uniform site during seismic. The tensile strains on the crown of AL pipe at (−2 × 1.6) m and PVC pipe at (−1 × 1.6) m at 12 s in Figure 12(b) were mainly caused by bending moment MI as I section shown in Figure 13, while the compression strain on the crown of AL pipe at (−3 × 1.6) m and PVC pipe at (−2 × 1.6) m at 18 s were mainly caused by bending moment MI′ as I′ section shown in Figure 14. The different location of tension of AL pipe at (−2 × 1.6) m in “AL-12 s-TGD” and compression at (−3 × 1.6) m in “AL-18 s-TGD” indicated that the friction amplitude f1′x was bigger than f1(x), so that bending moment value MI′ > MI at the same location.The strain on the crown of pipelines at (−2 × 1.6) m caused by PGD of 0.6 g earthquake was compressive in Figure12(a), not like the sharp change of tensile strain at (−2 × 1.6) m caused by uneven settlement in Figure 10, which indicated the axial and bending deformation of pipeline’s coupled effect was more obvious than the vertical deformation during 0.6 g earthquake.The compression strain of pipelines at the interface (II section) had a sharp change, which was caused by TGD at 12 s with a different acceleration of “Soil-1” and “Soil-2” (a2 > a1) and FII acting on the II section in Figure 13, while the tension strain of pipe at the interface (II′ section) by a2′>a1′ and FII′ shown in Figure 14.


## 3.4. Strain Amplitude of Pipe Caused by Seismic Wave

Strain amplitude of pipe caused by 0.6 g earthquake was calculated by strain during 0.6 g seismic minus strain “before seismic,” and that caused by 0.3 g earthquake was strain during 0.3 g seismic minus strain “before 0.3 g seismic” as shown in Figure8(a). Strain amplitudes of pipelines by different seismic waves were shown in Figure 15, where the tensile strain amplitude of AL pipe caused by a 0.6 g earthquake was noted as “AL-0.6 g-TEN,” and so on.Figure 15
Strain amplitudes of pipelines by seismic wave.The maximum tensile and compressive strains of pipelines were all in Soil-1 and changed obviously near the block interface and were more affected by bending deformation by PGD. The tensile strain amplitudes of pipelines had a sharp change at the block interface and were more affected by axial deformation by TGD.The tensile strain amplitudes of both pipelines were very small at (−2 × 1.6) m in Soil-1, which was mainly caused by the axial compressionFI on the pipe as I section shown in Figure 13. The compression strain amplitudes of PVC and AL pipe had a sharp change at (−2 × 1.6) m and (−3 × 1.6) m, respectively, in Soil-1 and were larger than that in Soil-2, which was mainly caused by compression on the crown of pipe by bending moment MI′ as I′ section in Figure 14.The pipeline strain caused by the earthquake reached peaks near the block interface in the loose site. The tensile strain amplitude of pipeline in the loose site was larger than that in dense site, while compression strain amplitude of pipeline in the dense site was larger than that in the loose site. Compression strain of the pipeline was more affected by the seismic intensity in the dense site than that in the loose site, while tensile strain was more affected in the loose site.The maximum tensile and compressive strain amplitudes of PVC pipeline caused by 0.6 g seismic wave were all in Soil-1 and not at the interface, reaching 1.7 × 10−3 and −1.7 × 10−3, while the maximum tensile strain amplitude of AL pipeline was at the interface, reached 7.5 × 10−4. The maximum tensile and compressive strain amplitudes of AL and PVC pipelines caused by 0.3 g seismic waves were all at the interface, which indicated that the seismic response of the pipeline was more affected by the PGD of a strong earthquake.


## 3.5. Residual Strain of Pipeline after Earthquake

After the earthquake, the residual strain of the pipeline was calculated by strain “after seismic” minus strain “before seismic” as shown in Figure8(a), and the results were shown in Figure 16, such as “AL-0.6 g” was the residual strain in AL pipe calculated by strain “after 0.6 g seismic” minus strain “before seismic” and “AL-Tot” was the total residual strain in AL pipe calculated by strain “after seismic” minus “before seismic.”Figure 16
Residual strain of pipelines under different conditions.The residual strains of pipelines after the earthquake were mainly due to PGD caused by a strong earthquake. For example, the total residual strains of AL pipe after the earthquake in Soil-1 were tensile strains, except for the compression on the crown caused by bend deformation by PGD of the earthquake at (−2 × 1.6) m and (−3 × 1.6) m. The residual strain of pipe in the dense site was compression strain because of Soil-2 (the dense site) slid down Soil-1 (the loose site) by the lateral spreading of the earthquake shown in Figure6(b).Residual strains of AL pipe by 0.6 g earthquake was extensional-compressive-extensional mode in loose site, while PVC pipe was extensional-compressive-extensional-compressive mode. Residual strains of two pipelines by 0.3 g earthquake were compressive-extensional-compressive mode in the loose site.The peak residual tensile strain of PVC pipeline by 0.6 g seismic was in Soil-1, reached 1.6 × 10−3, while compressive strain was in Soil-2, reached −1.1 × 10−3. The peak residual strains of PVC pipeline by 0.3 g seismic were both in Soil-1. The peak residual tensile strain of AL pipeline by 0.6 g seismic was in Soil-1, reached 4.5 × 10−4, while compressive strain was in Soil-2, reached −4.8 × 10−4.


## 4. Conclusion

This article carried out a centrifugal dynamic experiment to simulate the seismic response of a buried pipeline in nonuniform sites and the pipeline’s response to earthquakes after ground settlement deformation. The numerical model corresponding with the experiment was established and the results were compared. The mechanical character of buried pipelines crossing nonuniform sites with the PGD and TGD coupled effect caused by seismic simultaneously was studied. Some conclusions were obtained.(1)
The compression of the strain of pipelines caused by PGD before seismic were fitted well between numerical and experimental results, while the strain of pipelines by TGD was different, especially in the loose site. This indicated that the PGD and TGD coupled effect must be considered for the dynamic response of pipelines during seismic.(2)
The initial peak strain of PVC and AL pipe caused by PGD reached 0.02 and 0.01, respectively, exceeding the nominal yield strain. The maximum tensile and compressive strain amplitudes of PVC pipeline caused by 0.6 g seismic wave were all in Soil-1 and not at the interface, reaching 1.7 × 10–3 and −1.7 × 10–3, while the maximum tensile strain amplitude of AL pipeline was at the interface, reaching 7.5 × 10–4. The peak residual tensile strain of PVC pipeline by 0.6 g seismic was in Soil-1, reaching 1.6 × 10–3, while compressive strain was in Soil-2, reaching −1.1 × 10–3. The peak residual tensile strain of AL pipeline by 0.6 g seismic was in Soil-1, reaching 4.5 × 10–4, while compressive strain was in Soil-2, reaching −4.8 × 10–4.(3)
The total strain of pipeline in nonuniform sites by a strong earthquake was caused by bend deformation by vertical PGD and axial deformation by TGD and reached peaks near the block interface in the loose site. The strain of pipeline by TGD was compressive-extensional alternating mode between the loose and dense site and had a sharp change at the block interface, and in loose site, it was compressive-extensional alternating mode because of PGD by a strong earthquake.(4)
The tensile strain amplitude of the pipeline in the loose site was larger than that in dense site, while compression strain amplitude in the dense site was larger than that in the loose site. The compression strain of pipeline was more affected by the seismic intensity in the dense site than that in the loose site.(5)
Residual strain of AL pipe by a strong earthquake was extensional-compressive-extensional mode in loose site, while PVC pipe was extensional-compressive-extensional-compressive mode. The residual strain of pipe in the dense site was compression strain.(6)
The vertical ground settlement and lateral spreading by the strong earthquake had great effects on the pipeline deformation in nonuniform sites.



---

*Source: 1133036-2022-04-20.xml*