Mechanical Behavior of Plastic PiPe Reinforced by Cross-Winding Steel Wire Subject to Foundation Settlement

Li Xiang（李翔）1*，Shi Jianfeng（施建峰）2，Li Jun（李军）3，He Xingjian（何兴建）3

1.China Special Equipment Inspection and Research Institude，Beijing 100029，P.R.China；

2.Institute of Pressure Equipment，Zhejiang University，Hang Zhou 310027，P.R.China；

3.Institute of Chemical Engineering，China University of Petroleum（Beijing），Beijing 102249，P.R.China

Mechanical Behavior of Plastic PiPe Reinforced by Cross-Winding Steel Wire Subject to Foundation Settlement

Li Xiang（李翔）1*，Shi Jianfeng（施建峰）2，Li Jun（李军）3，He Xingjian（何兴建）3

1.China Special Equipment Inspection and Research Institude，Beijing 100029，P.R.China；

2.Institute of Pressure Equipment，Zhejiang University，Hang Zhou 310027，P.R.China；

3.Institute of Chemical Engineering，China University of Petroleum（Beijing），Beijing 102249，P.R.China

Plastic pipe reinforced by cross helically wound steel wires（PSP）is a new plastic-matrix steel composite pipe developed in China.To investigate the stress of PSP under foundation settlement，a finite element model（EEM）is proposed.The stresses and strains of PSP are obtained by the EEM analysis.The mechanic behavior of PSP subject to a foundation settlement is analyzed.Einally，the influence factor analysis of settlement deformation，such as settlement depth，overlying soil depth，diameter of PSP and inner pressure of PSP，are discussed.

composite pipe；finite element model（EEM）；internal pressure；high density polyethylene；foundation settlement

0 Introduction

A new type of metal-plastics composite pipe is first developed in China，consisting of a plastic pipe reinforced by cross helically wound steel wires（PSP），as shown in Eig.1.Combining the advantages of both plastic and metal，PSPs have good material properties，like strong load-carrying capacity，good corrosion resistance and wearresistance［1］.Now，PSP has been widely used in many fields including petroleum and natural gas supply，power engineering，chemical industry，water supply and sewerage，etc.［2］

Eig.1 PSP structure

Since the earthquakes often take place in Alaska，U.S.A，Niigata and Japan，some engineering experts there have focused on the destruction of landside and foundation settlement.Damage records of earthquakes in history shows buried pipe systems are always destroyed heavily. The distortion of the ground base，especially nonuniformly foundation settlement，plays a significant role in the failure of the buried pipe systems［3］.Earthquake settlement is an important damage，since it may lead to a fracture，leaking，fire or explosion of pipelines.Recently，many scholars have focused on the damage of buried pipe systems caused by foundation problem.Shiro Takada investigated the mechanic behavior of PE pipeline by sinking soil box experiments［4］and in 1998，he found out the distortion of PE pipeline via non-uniformly sink test.Considering a large geometric distortion，Gao Huiying［3］used an elastic basis beam model to simulate a pipe as a cubic curve in the theoretical research.The mechanical equilibrium formulas of pipe and recursion formulas of inner forces were obtained.Atlast the results of inner forces and distortion level for buried pipeline subject to the base settlement were acquired.Zhang Tuqiao et al.［5］analyzed the mechanical behavior in the length direction of pipeline subject to the non-uniform settlement. Considering the different kinds of earthquake settlement，Limura［6］used an analytical method based on Winkler foundation model and developed the formulas.Rao Pengqiang［7］conducted some two-dimension analysis of the buried water pipeline subject to a ground side movement using ANSYS.The distributions of shearing stress and axis stress of pipelines were obtained and some precautions were suggested.Hiroshi Yatabe et al.［8］considered a pipeline as a shell and the soil as springs to analyze different variable section pipes. Yun Wook Lira et al.［9］researched on the relationship between the parameters of pipes and distortion.Calvetti et al.［10］combined numerical simulation and experiments to investigate the basic theory of pipelines when landside occurred. The mechanical behaviors of PSP subject to internal pressure，external pressure，torsion，bending have been performed in recent 10 years［11-15］.Although most PSP are buried in the ground，research on the mechanic behavior of PSP subject to foundation settlement is inadequate.

Since the structure of PSP is complicated，the finite element method（EEM）can give a direct view of stress and distortion of pipeline. Thus，a three-dimension finite element analysis（EEA）pipe-soil interaction model is established. Then，nonlinear analysis about pipe-soil interacting system is conducted.Eurthermore，the mechanic behavior of PSP subject to a foundation settlement is analyzed.Einally，the influences of settlement depth，overlying soil depth，diameter of the PSP and inner pressure of PSP on PSP mechanical behavior are discussed.

1 Finite Element Model

1.1 Problem descriPtion

The dimension of a 3D solid model was introduced Ref.［16］，in which the foundation was 25 m×3 m×3 m.Similarly，PSP in this paper is also established as a 3D solid model with a 25 m length，and a 1.5 m embedded depth.The length and the depth of settlement area are 15 m and 1 m，respectively.

1.2 Basic assumPtion

In order to highlight the main factors and shorten calculating time，the assumptions below are proposed for establishing EEM：

（1）The influence of weld joints between pipelines is ignored.

（2）The mechanical property of foundation/ soil is assumed to be elastoplasticity，while the mechanical property of pipeline is assumed to be elasticity.

（3）The interaction between pipeline and soil is simplified，and the interaction is divided into tangential and normal.Eor tangential component，considering the role of the friction between soil and the pipe，it is assumed that no slide between the pipe and soil.Eor normal component，considering the deformation of the pipe，the separation of pipe and soil is allowed after their contact.

1.3 Geometry Parameters and material ProPerties

The diameter of the gas pipeline is 250 mm，and the length of each pipe is 12 m.More basic parameters of PSP are displayed in Table 1.The cross-section of the PSP is laid out in Eig.2.The adhesive resin of both inner layer and outer layer of high density polyethylene（HDPE）consist of modified HDPE.Steel wire is used as reinforcement material.Material properties of PSP are shown in Table 2.The elastic parameter of the two composite layers in the middle of PSP layerscan be obtained through the application of the material property calculation method in Ref.［17］. The results are displayed in Table 3.Mechanical property of different kinds of soil varies largely. The property parameters of clay soil are illustrated in Table 4.

Eig.2 Cross-sectional diagrammatic sketch of PSP

Table 1 Parameters of PSP

Table 2 ProPerties of material

Table 3 ProPerties of comPosite layer

Table 4 ProPerties of soil

1.4 Element and real constant

Considering orthotropic composite material and geometric nonlinearity，SHELL91 element is chosen.SHELL91 element is used for layered structural shells of PSP［12］.Solid45 is used for the 3D modeling of soil.TARGE170 is used as the target element in the contact of pipe and soil. CONTA173 is chosen as the contact element. PSP is divided into 60 pieces in the axial direction and 16 pieces in the hoop direction，and there are totally 12 800 elements in the four-layer structure.The element model is shown in Eig.3.

1.5 Boundary conditions

The pipeline boundary conditions are as follows：a fixed constraint is imposed on an end surface of non-sink region and symmetry constraint is imposed on another end surface of sink region. The soil boundary conditions are as follows：the fixed constrain is applied on an end surface of the sink region and symmetry constraint is applied on the sink region.A fixed constraint is applied on the bottom surface of the non-sink region and a settlement displacement is loaded on the bottom surface in the sink region.

Eig.3 Global structural graph of EEM

2 Analysis Method of FEM

The investigation object consists of buried pipeline and the soil around it［18］.In the analysis of mechanical behavior，many influence factors need to be considered，such as ground load，foundation load，interaction between pipe and soil，etc.

Settlement displacement soil can be applied to the nodes of the EEA model on settlement area.Considering the complexity of soil constitutive relation，Drucker-Prager model is adopted，which is appropriate to simulate soil materials.In EEA，the control of the soil model depends on adjusting three parameters：cohesion，internal friction angle，and expansion angle.Constitutive model of PSP has been shown in Ref.［19］.

The key of EEA model is how to figure out the interaction between the pipe and soil.Because of contact nonlinear characteristics，there is notension between the pipe and soil.Under the compression state，if the shear stress of pipe and soil exceeds the maximal friction，the dislocation will occur in the contact surface.Thus，the relationship of shear stress and normal stress is in accordance with Mohr-Coulomb law.Three kinds of nonlinear analysis are likely to occur simultaneously in the contact analysis，including material nonlinearity，geometry nonlinearity caused by large deformation，and state nonlinearity of contact interface.Thus，in the process of contact interaction，it is necessary to consider the parameters definition of pipe-soil contact interface［18］. The face to face contact element is established to represent the pipe-soil contact.Eriction coefficient of pipe-soil model is chosen as 0.5，considering considerable coefficient measured data between 0.4 and 0.7.The penalty function method was used to solve the problem of contact between soil and pipe.The external surface of PSP is considered as a rigid target surface with TARG 170 element.The interface of soil between soil and pipe is regarded as contact surface，and CONT173 element is used.The interaction between PSP and soil is simulated by flexible and flexible contact pair.

Augmented Lagrangian contact algorithm is used to solve the non-linear problem.In order to find the Lagrange multipliers，correction of the penalty function can be carried out iteratively. The pre-condition CG iterative method and a memory-saving model are used.

3 Results and Discussions

3.1 Effectiveness of method

In order to verify the model，the models in Refs.［16，20］are chosen.At the same time，the parameters corresponding to PSP are replaced as steel pipe parameters and contact type of soil and pipe is defined as steel soft touch.The settlement values of steel pipe calculated with the proposed EEA method are shown in Eig.4，where y means the foundation settlement value.The maximum settlement values are 20.564，20.972，40.969，61.399，81.845 mm.Compared with the values in Ref.［16］，the errors are within 5%.The maximum value of vertical displacement is 23.157 mm，as shown in Eig.5.Compared with the maximum value of vertical displacement in Ref.［20］，the difference is only 3.38%.Additionally，the EEM of PSP has been verified in Ref.［21］.Thus，the model can be used to calculate the mechanical behavior of PSPs subject to the foundation settlement.

Eig.4 Changes of settlement value of steel pipes with length change of pipes

Eig.5 Vertical displacement contour plot of steel pipe

3.2 Stress distribution of PSP

Von-Mises equivalent stress distributions along the pipelines are shown in Eigs.6，7.Erom Eig.7 we can observe that the positions of 12 and16 m are the dangerous region owing to the larger axial stresses.

Eig.6 Von-Mises stress distribution of the PSP

Eig.7 Von-Mises stress along PSP

3.3 Influence factor analysis of settlement deformation

To analyze the main influence factors of foundation settlement around PSP，the researches on soil parameters，internal pressure and PSP geometric parameters are carried out.

In the case of ground settlement，the different ground displacements are applied on the soil model.The ground displacement makes PSP compressive and tensile.When the stress exceeds the yield stress，there is an unrecoverable plastic strain.When the stress exceeds the ultimate stress，pipeline will be fractured or pulled off.

3.3.1 Settlement depth

Eig.8 shows the impact of different sink depth on axial stresses of PSP.The maximum settlement displacement is at the point of 12 m of the pipe，which causes the maximum axial stress. The constraint of even settlement area on the settlement pipe causes a larger inverses axial stress at the point of 15 m of the pipe.As the sink depth increases，the axial stress of PSPincreases. The sink depth has an obvious impact on the axial stress of PSP.

Eig.8 Influence of settlement depth on axial stresses of PSP

3.3.2 Overlying soil depth

The Eig.9 shows the impact of different depths of overlying soil on the axial stresses of PSP with 0.6 m settlement，where B means the depth of overlying soil.As the overlying depth increases，the axial stresses of PSP decreases. Thus，the burying depth can help to prevent the disaster caused by foundation settlement.

Eig.9 Influence of overlying depth on axial stresses of PSP

3.3.3 Diameter of PSP

Only considering the diameter changes with 0.6 m soil settlement，the axial stresses of PSP with the diameters of 140，250，400，500，and 630 mm are shown in Eig.10，where D means the diamenter of PSP.With the increase of pipeline diameter，the axial stresses of PSP increase gradually.Thus，the diameter of pipeline has a larger influence on PSP failure.

Eig.10 Influence of diameter of PSP on axial stresses of PSP

3.3.4 Inner pressure of PSP

Since the settlement always applied on pipe-lines under the working condition，the influence of inner pressure should be considered.With 0.6 m settlement，the curves of axial stress of PSP with different inner pressures are shown in Eig. 11.We can see that inner pressure plays a significant role in pipe failure with base settlement，and with the increase of inner pressure，the axial stress of pipelines will increase as well.Thus，in further research，real working condition should be taken into account.

Eig.11 Influence of internal pressure in PSP on axial stresses of PSP

4 Conclusions

（1）Considering the interaction of pipeline and soil，and the nonlinear characteristics of materials，geometry and contact，an appropriate PSP-soil interact model is proposed.A corresponding ANSYS parametric design language is presented，which is convenient to analyze the mechanical behavior of PSP subject to ground settlement.

（2）When settlement takes place，the most dangerous part of PSP is at the junction of settlement area and non-settlement area.The buried PSP subject to the foundation settlement has higher risk near this junction.Hence，joint of PSP should be avoided at this area.

（3）By analyzing the influence factors of PSP under base settlement，we find that the sink depth has an obvious impact on the axial stress of PSP.As the sink depth increases，the axial stress of PSP increases.The burying depth can help to prevent the disaster caused by foundation settlement.As the overlying depth increases，the axial stresses of PSP decrease.Small diameter and thick wall pipeline can enhance the resistance of settlement.Inner pressure plays a significant role in pipeline failure under base settlement，and with the increase of inner pressure，the axial stress of pipelines will increase as well.

Acknowledgement

This work was supported by the National Natural Science Eoundation of China（No.51203188）.

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（Executive editor：Zhang Bei）

TQ320.72 Document code：A Article ID：1005-1120（2015）03-0348-07

*CorresPonding author：Li Xiang，Senior Engineer，E-mail：lixiang@csei.org.cn.

How to cite this article：Li Xiang，Shi Jianfeng，Li Jun，et al.Mechanical behavior of plastic pipe reinforced by cross-winding steel wire subject to foundation settlement［J］.Trans.Nanjing U.Aero.Astro.，2015，32（3）：348-345.

http：//dx.doi.org/10.16356/j.1005-1120.2015.03.348

（Received 29 January 2015；revised 2 April 2015；accepted 30 April 2015）