Performance of Buried HDPE Pipes
at Elevated Temperatures

 

Hussain Abdullah Alawaji

Associate Professor of Geotechnical Engineering,
King Saud University, Riyadh 11421, Saudi Arabia
E-mail: halawaji@yahoo.com

 

ABSTRACT

This paper presents the effect of temperature on the deformation characteristics and performance of buried High-Density Polyethylene (HDPE) pipes. The testing program consisted of line loading of ring pipe samples submerged in water heated to prescribed temperatures of 30, 40, 50, 60, and 70oC. Nonlinear finite element program (Z-Soil) is used to back calculate the secant deformation moduli and yield strengths for HDPE pipes at various temperatures. Simple elastoplastic constitutive model which captures measured load-deformation response up to 6% vertical deflection is employed. Experimental results reflect deformation modulus, yield strength, and unrecoverable strain decrease with increasing temperature. The calibrated numerical tool is used to predict performance of buried HDPE pipes at various temperatures. Two Installation and two operation procedures are investigated. Medium dense and dense sands are considered for modeling staged pipe backfill and cover with incrementally increasing surface and internal pressures. It is shown that, pipe horizontal deformation slightly increases with temperature and slightly decreases with internal pressure. Buried HDPE pipes perform well under considered surface pressure, internal pressure, and installation conditions even at elevated temperature in the range 30 to 70o C.

Keywords: High-Density Polyethylene Pipes, Temperature, Buried pipes, Backfill, Cover, Deformation.

INTRODUCTION

In arid lands; the pipelines operating temperature can be high especially for desalination planets, water transmission and distribution systems and others hydrocarbons explorations applications. Widespread corrosion and increasing cost of installation and maintenance of traditional pipes in desert environment suggests polyethylene pipe alternative. Through understanding of performance of buried polyethylene pipe at elevated temperature is essential for infrastructure sustainable developments in arid lands.

Corrosion and harsh environmental conditions caused failure and degradation of buried pipes in aggressive soils. Corrosion caused failure of the reinforcing wire on over 10 km of Prestressed Concrete Pipe (PCP) used for the central Arizona project [1]. This PCP pipe had been in service less than 15 years which is significantly shorter than its expected design life. Hassett et al. [2] reported several leaks and breaks over several years in 76 cm cast iron pipelines for Houston treated water transmission system. Talesnick and Baker [3] documented failure of a large diameter concrete-lined steel sewage pipe, buried in a clay soil profile. The project consisted of a 3.5 km long gravity pipe which failed before being taken into service. Failure of the pipe system was attributed to incompatibility between the mechanical behaviour of the pipe and the methodology employed in its design. The studies illustrate the effects of a basic design flaw resulting from lack of adherence to well accepted standard engineering practices. Generally, published investigations of pipes failures illustrate the effectiveness of a simple field test as a diagnostic tool to evaluate site conditions and overall installation procedure quality. Unfortunately, despite the huge leakage and severe failure of buried pipes in under developing countries, there are no documented case studies in arid lands.

Several investigators cited temperature effects on the mechanical, physical, and chemical properties of polyethylene material. Seibi [4] presents the effect of heated crude oil on adsorption and mechanical properties of High-Density Polyethylene (HDPE) samples. Hydrocarbon cause swelling and influence the mechanical properties at elevated temperatures as the cross links become weaker causing the chains to flow easily. It was reported that, the permeability of HDPE is low even at high temperatures implying that HDPE is strongly resistance to aggressive environment. Miyajima et al. [5] demonstrated the polyethylene exhibited excellent mechanical, physical, and chemical properties at elevated temperature of 80oC.

Buried flexible pipes derived their stability from surrounding soil. Moore [6] reported a finite element parametric study to determine how stresses on profiled polyethylene pipe are affected by burial depth and backfill quality. He emphasized the deficiency of design practice that relays on ring compression theory which asserts that the full overburden load acts on the pipe based on very conservative assumption. It is shown by Moore that substantial positive arching and only a fraction of the overburden load reaches the HDPE pipe. Spangler equation or "Iowa" formula [7] ignores the substantial positive arching associated with circumferential shortening and use a soil subgrade modulus, E', which is generally not adjusted to account for the real stiffness of the backfill surrounding the pipe. Faragher et al. [8] experimentally evaluated Spangler's moduli of soil reaction (E') from laboratory testing of buried plastic pipes. They found that values of E' are significantly higher than those currently used in practice and suggest a general underestimation of the support offered to a buried flexible structure by the soil that surrounds it. Zhang and Moore [9] used nonlinear time-dependant finite element model to predict structural performance of HDPE pipe under parallel plate loading and hoop compression tests. Simple plasticity (Von Mises J2 theory) was successfully used in modeling the nonlinear and rate-dependant behavior of HDPE pipe except where there is strain reversal as stated by Zhang and Moore [10]. Further numerical and in-situ studies are needed to examine pipe burial under field conditions and the implications of HDPE pipe limit states for pipe design. Temperature effects on the performance of buried HDPE pipe require further investigations.

In this paper the temperature effect on deformation characteristics of HDPE pipe is evaluated. Line load was applied on HDPE pipe submerged in hot water under prescribed temperature. Measured load-response curves are used to calibrate simple nonlinear finite element model. The calibrated tool is employed in modeling and analysis of buried HDPE pipes under various temperatures. Several installation methods are considered including embankment and trench installation in both strong and weak soils. It is shown that HDPE pipe performs adequately under elevated temperature up to 70oC.

EXPERIMENTAL STUDY

In this study, the experimental investigation is intended to study the nonlinear behaviour of HDPE pipes and the potential effects of temperature on their mechanical properties. To study the effect of temperature on the deformation characteristics and mechanical properties of HDPE pipes, a proper design of the testing fixture must be established. Tests were conducted in steel tank of 0.7 m length, 0.5 m width, and 0.7 m height and supported by a relatively rigid steel framework. Rigid steel plate and I-beams assembly were placed under the pipe at the bottom of the tank such that pipe crown is around 5 cm from the container's rim. With proper adjustment, such arrangements permit testing of various pipe sizes. Two heaters with control regulators were fixed at the bottom of the tank to obtain desired accurate water temperature. During setting and before loading, isolated wood cover was used with vents to allow vapor to ventilate from the water bath as well as to measure the water temperature using thermometers. Initially, weight and geometrical measurements of the pipe ring sample was performed before soaking in the water bath of prescribed constant temperature. Monitoring and adjusting the temperature controller were continued for 24 hours in order to achieve the desired constant temperature of the water bath and submerged pipe. The identical polyethylene pipe samples used in this study were supplied by Amiantit Co., Saudi Arabia. Physical and mechanical properties and other quality control routine tests were conducted at the manufactory according to relevant ASTM standards. Laboratory load tests were conducted on polyethylene pipes of 355 mm diameter (D), 300 mm length (L), 34 mm thickness. Vertical line load was applied to the pipe by means of 10 tone compression test machine (Wykeham Farrance England). It is displacement controlled machine with rate capability in the range 0.0001 to 59.99 mm/min. It is emphasized here that 6 mm steel bar welded to rectangular hollow square steel beam was used to transfer vertical line load and minimize boundary effects. Commonly used flat plate may cause increasing contact area with pipe deformation and mixed boundary conditions. The applied load was measured using a load cell (Tokyo Sokki) of 100 KN capacity placed at the bottom of the machine top reaction beam. Displacement was measured by LVDT (Tokyo Sokki) placed vertically along a diagonal through the center of the pipe. This LVDT had a 50 mm range with 0.001 mm sensitivity. Strain gauges were fixed along central circumferential lines inside and out side the pipe to measure the strain in the pipe wall. Data acquisition system (Tokyo Sokki) and Sony laptop computer were used during the test to scan, monitor and store hoop strain, deflection and load. Figure 1 shows assembled temperature controlled pipe load test. It is emphasized here that the pipe invert was fixed between two thin steel plates (Figure 2) to resist buoyant up lift force and to facilitate pipe alignment inside the test container. This constraint has no effects on the experimental results since it gets remove after slight pipe vertical deformation. Elliptical deformation was observed throughout the entire loading history. Typical load-deformation response curves for the tested polyethylene pipes at various temperatures are presented in Figure 3. Further details of experimental description and test results including internal and external hoop strains along the pipe circumferential line is recently presented by Alawaji [11]. It is emphasized here that nonlinearity is observed from the beginning of the load-deformation response curve. Relatively large unrecoverable deformation which decreases with increasing temperature was observed upon unloading. Reloading response was also nonlinear even within the previous loading locus, i.e. below maximum previous load level. These experimental results are compiled with physical and mechanical properties of polyethylene pipes to calibrate and validate finite elements models as given in the following section.

FEM ANALYSIS OF HDPE POLYETHYLENE PIPES

The finite-element program used in this study, Z-Soil 3D Version 6.13, has been developed by ZACE Co. [12]. Figure 4 shows 3D mesh of single layer four nodes 3D shell elements used to model polyethylene pipe load test. Only a quarter of the pipe is modeled utilizing the dual symmetry of the problem. Simple elastic and Huber-Mises constitutive models is employed. As might be expected, the initial linear elastic model predicts the response successfully only for very small deflection (up to 1.2%). Therefore, nonlinear model which consists of secant elastic deformation modulus (at 2.7% deformation) and Huber-Mises criteria was considered. Figures 5 (a-e) present finite elements fit to the experimental results for the tested HDPE pipes at various temperatures (30, 40, 50, 60, and 70oC). Table 1 presents the calibrated HDPE pipe material parameters at various temperatures in the range of 30 to 70oC. Constant Poisson's ratio, n = 0.4, was assumed for the HDPE pipes [6]. Results indicate that deformation modulus decreases linearly with increasing temperature as shown in Figure 6. Due to temperature increase from 30 to 70oC, the HDPE pipe deformation modulus decreased by 62%. Yield strength decreases while strain at yielding increases with increasing temperature. Where, yield strength of the tested HDPE pipes decreased by 59% due to temperature increase from 30 to 70oC.

 



Figure 1. Pipe load test setup under elevated temperature.

 



Figure 2. Pipe alignment and buoyant force resistance plates.

 



Figure 3. Typical load-deformation response curves for polyethylene pipes at various temperatures.

 



Figure 4. Mesh of single layer four nodes 3D shell elements used to model polyethylene pipe load tests.

 



Figure 6. Variations of secant deformation modulus (at 2.7% deformation)
with temperature for tested DPE pipes.

 

Table 1. HDPE polyethylene pipe material parameters at various temperatures
Temperature
ToC
Deformation modulus
Es – kN/m2
Poisson ratio
n
Tensile & compressive strength
ft & fc – kN/m2
301,630,609 0.4 15,000
401,300,000 0.4 13,000
501,159,129 0.4 11,000
60841,335 0.4 8,829
70614,889 0.4 6,200

 

Typical predicted deformed configuration at 4.71% vertical deflection and 70oC is illustrated in Figure 7. It is clear that this mode of deformation is more general than simple elliptical and uniform deformation assumptions. From the measured and predicted response curves (Figures 5 a-e), it is clear that the used nonlinear model can predict pipe response successfully up to 6% deflection. This deflection level is rarely attained in practice without joint leaks or triggering maintenance and repair remarks. Therefore, model prediction is considered adequate for buried pipe applications. However, failure load was underestimated. Therefore, the overall analysis of buried polyethylene pipes using this model is accurate for working conditions but conservative for ultimate failure prediction. Zhang and Moore [9] showed that, for high-density polyethylene (HDPE) pipes under parallel plate loading, geometrical nonlinearity effect becomes significant beyond 5 percent vertical diameter decrease for there tested pipes. Since design and operation are limited to small deformation, geometrical nonlinearity will not be considered in the following buried polyethylene pipes analyses.

 



Figure 7. Predicted deformed configuration (4.71% vertical deflection) for tested HDPE pipe (PE 4-5) at 70oC.

POLYEHTELINE PIPES BURIED IN DUNE SAND EMBANKMENTS

Numerical Models

In this study, plane strain nonlinear finite element analysis was used to model polyethylene pipes buried in dune sand embankments. Typical polyethylene pipe of 355 mm diameter and 34 mm thickness was simulated. Four nodes Quadlateral and beam elements were used and only a one half of the system was modeled due to symmetry of the problem around X = 0 axis. The finite-element program used in this study, Z-Soil 3D Version 6.13, was developed by ZACE Co. [12]. Mohr-Coulomb and Huber-Mises constitutive models were employed for soil and pipe, respectively. The mesh extends horizontally 3 m from pipe center. Complete fixity was enforced at the lower edge of the mesh. Roller support was used at both vertical sides of the mesh. The mesh configurations are shown in Figures 8(a-e). Figure 8(a) shows mesh used for embankment and surface pressure at final stage. Elements refinement and transition zones shown in Figure 8(b) were used near the pipe to enhance nonlinear solution convergent and prediction accuracy. Figure 8(c) shows mesh used for embankment and internal pressure at final stage. Figure 8(d) shows near pipe view and internal pressure. Contact elements were employed at pipe-soil interface as shown in Figure 8(e). Soil cover layers, soil overburden pressure, and pipe internal pressure were activated in consequent stages to simulate embankment construction and pipe operation conditions as presented in the following sections.

Soils Parameters

Thomamah sand (Sand Th) from sand dunes north eastern Riyadh city, Saudi Arabia, was used to represent sand dunes material in arid lands. Geotechnical properties and characteristics of Thomamah sand was given in details by Alawaji [13]. It can be described as wind blown predominantly fine to medium sand which is classified as poorly graded sand (SP) according to the unified classification system (USCS). The sand has a specific gravity (Gs) of 2.67, and an effective size (D10) of 0.11 mm. The maximum and minimum dry densities were 18.48 kN/m3 and 15.81 kN/m3 in accordance to ASTM D-4253 and D-4254, respectively. The coefficient of uniformity (Cu) and the coefficient of curvature (Cc) were 2.88 and 1.1, respectively. Shear strength for Thomamah sand at 70% relative density (17.57 kN/m3) was determined from conventional consolidated drained triaxial tests. It was found that, for confining pressure in the range of 25 to 150 kPa, the friction angle was found to be 40 degrees at 70% relative density Alawaji [13].

For coarse grained soils, the coefficient of earth pressure at rest, K0, can be estimated by the empirical relationship of Jaky [14],

(1)

where f is the soil drained friction angle. Furthermore, for coarse grained soils, the dilation angle, ?, can be obtained from the empirical expression of Bolton [15],

(2)

where fcv is the friction angle at critical state. For the present purpose, fcv has been taken as 32o.

Solutions were sought for medium dense and loose sand states designated DS1 and DS2, respectively. Moher-Coulomb (M-W) criteria were used for the sand material with Drucker-Prager plastic flow and initial ko state. Table 2 presents the sand material parameters for medium dense and loose sand states. These two material states represent good and poor embankment construction procedures in dune sand at arid lands. Talesnick and Baker [3] measured wide variations in the in-situ stiffness of dune sand backfill along buried pipeline with sand backfill material. Gravel backfill material commonly used in pipe zone consists of crushed stone. The main advantage of gravel backfill near pipe zone is that, gravel is self compaction material which insures adequate compaction at pipe hunches and shoulders. Alawaji (2004) emphasized the low confining pressure effects near haunches and shoulders of flexible pipes even with uniform compacted backfill material for both trenches [16] as well as embankments [17] construction procedures.

Frictional contact elements were used between pipe beam elements and soil quadrilateral continuum elements. Mohr-Coulomb contact material parameters are given in Table 2. Augmented Lagrangian Contact algorithm was activated in the nonlinear equations solver with Maximum number of augmentations of 5, stop augmentation if maximum over penetration is less than 1e-006, increase penalty stiffness with multiplier of 2 at each augmentation, and maximum penalty stiffness multiplier of 100. Detailed description of contact elements and contact algorithm are given in the Z_Soil code user manual [12].

Staged Analysis

Staged construction of buried HDPE polyethylene pipes in dune sand embankment were simulated using nonlinear Z-Soil FEM program. The first stage activates initial ko stress state in five steps (Time = 0.2 to 1 and Increment of 0.2). In this stage, soil layer representing under base material of 0.75 m thickness was activated alone. The second stage consists of successive backfilling of ten soil layers in ten analysis steps (Time = 0 to 11 and Increment of 1). The first step introduced pipe and soil layer of 0.8 m thickness. The pipe was activated simultaneously in the middle of this layer. Then, soil cover layers of 0.25 m thickness were activated in the remaining ten steps. The total soil cover over pipe crown is 2.723 m. The third stage applies uniform vertical pressure of 155 kPa in forty steps (Time = 11 to 51 and Increment of 1). This overburden pressure is equivalent to adding forty successive soil layers of 0.25 m thickness. The complete FEM mesh at final stage for embankment and surface pressure case is shown in Figure 8(a). It is emphasized here that solution iterations were employed at each analysis step. Compacted material parameters were used without surface pressure over backfill lefts. Sharp et al. [18] indicated that pressure application on compacted layers does not improve the results in simulating soil box tests. However, a more objectives layered compaction simulation would require evolution of soil properties such as unit weight, deformation and strength parameters with stress level during compaction of each soil layer.

 

Table 2. Summary of material parameters used in FEM analyses
Material Model Parameter Value
DS1Mohr-Coulomb Deformation modulus, E (MPa) 30
Poisson's ratio, n 0.3
Unit weight, g (kN/m3) 17
Friction angle, qo 45
Dilatancy angle, yo 15
Cohesion, C (kPa) 4
Tension cut-off, I1t (kPa) 0
Ko(x), ko(z), Inclination angle 0.6, 0.6, 0
DS2Mohr-Coulomb Deformation modulus, E (MPa) 10
Poisson's ratio, n 0.3
Unit weight, g (kN/m3) 15.5
Friction angles, qo 38
Dilatancy angle, yo 10
Cohesion, C (kPa) 4
Tension cut-off, I1t (kPa) 0
Ko(x), ko(z), Inclination angle 0.4, 0.4, 0
ContactMohr-Coulomb Normal stiffness multiplier, kn 0.1
Tangent to normal stiffness multiplier ratio, kt/kn 0.1
Friction angles, qo 20
Dilatancy angle, yo 5
Cohesion, C (kPa) 0

 

To investigate the effect of internal pressure on HDPE pipes buried in sand embankments at various temperatures, radial surface pressure was applied inside buried polyethylene pipes. The pipes were installed and covered in staged as described above. The first stage activates initial K0 stress state in five steps (Time = 0.2 to 1 and Increment of 0.2). In this stage, soil layer representing under base material of 0.75 m thickness was activated alone. The second stage consists of successive backfilling of six soil layers in six analysis steps (Time = 0 to 7 and Increment of 1). The first step introduced pipe and soil layer of 0.8 m thickness. The pipe was activated simultaneously in the middle of this layer. Then, soil cover layers of 0.25 m thickness were activated in the remaining ten steps. Soil cover over pipe crown of 1.723 m was maintained without surface pressure. Soil consists of medium dense and loose sand states designated DS1 and DS2, respectively. Third stage applies incremental radial internal pressure. In this analysis stage, internal pressure of 700 kPa was applied in 10 kPa increments. Seventy analysis steps (Time = 7 to 77 and Increment of 1) were used with numerical iterations in each step. The complete FEM mesh at final stage for embankment and internal pressure case is shown in Figure 8(c).

Numerical results obtained in this study show pipe bending moment, shear and normal stresses; pipe-soil contact stresses; soil deformation, plastic zones, stress and strain maps for each analysis step. Typical pipe-soil interaction characteristics for buried polyethylene pipes in dune sand embankments at various temperatures are presented in the following results and discussion section.

RESULTS AND DISCUSSION

The calibrated numerical tool and the refined material parameters are used for modeling and analysis of staged backfilling of buried polyethylene pipes in dune sand embankments at various temperatures. Figure 9 shows typical Normal force (N), shear force (T), and bending moment (M) diagrams in HDPE pipe buried under 2.72 m soil cover and 155 kPa overburden pressure in DS1 sand embankment at 30oC. Figure 10 shows typical normal and shear contact stress diagrams on HDPE pipe under 2.72 m soil cover and 155 kPa overburden pressure in DS1 sand embankment at 30oC. Figures 11 (a) and (b) present typical variation of vertical and horizontal stresses in backfill soil near HDPE pipe buried under 2.723 m soil cover and 155 kPa overburden pressure in DS1 sand embankment at 30oC. Low values of vertical stress were predicted near the pipe springline, and high vales were predicted near the pipe shoulder as shown in Figure 11 (a). Low values of horizontal stress were predicted near the pipe hunch and shoulder, and high vales were predicted near the pipe springline as presented in Figure 11 (b). Plastic zone initiated in the soil near the pipe haunch when the soil cover height reached 1.22 m at Time =5, as shown in Figure 12. The sand material was homogenous, but arching and pipe-soil interaction causes low horizontal stress (low confining pressure) and high stress level at these locations as depicted in Figure 13. In practice, reinforcing the soil

 



Figure 9. Normal (N), shear (T), and bending moment (M) diagrams in buried HDPE pipe.

 



Figure 10. Typical normal (Sn) and shear (Tau) contact stress diagrams on HDPE buried pipe.

 


(a) Vertical stress


(b) Horizontal stress


Figure 11. Typical stress diagrams in backfill soil near HDPE buried pipe.

 



Figure 12. Plastic zone initiated in backfill soil (DS1) near buried HDPE pipe

 



Figure 13. Typical stress levels in backfill soil near HDPE buried pipe.

or placing stiffer material such as cemented crushed sand or gravel near the pipe haunches and shoulders may improve buried flexible pipes performance.

Installation procedure and temperature effects on polyethylene pipes buried in sand embankments were also investigated. Two models for installation procedures were considered. These installation procedures include backfilling and cover with dense sand (DS1) and medium dense sand (DS2) soils (Table 2). Finite element analyses were executed under 30, 40, 50, 60, and 70oC. The used HDPE pipe material parameters at various temperatures were given in Table 1. Table 3 shows predicted horizontal displacement (Ux) and horizontal deflection (dx = 2*Ux/D) at pipe springline, where D is pipe diameter, for buried HDPE pipes under 2.723 m DS1 and DS2 sands covers and 155 kPa surface pressure. It is emphasized here that deflection slightly increases with temperature, but performance remains acceptable and deflection still fare below permissible limit of 3-5%. Due to temperature increase from 30 to 70oC, springline horizontal displacement increased by 3% and 43% for HDPE pipes buried in DS1 and DS2 sand embankments under 155 kPa surface pressures, respectively. Also it is been noticed that, the rate of deflection increase slightly decreases at high temperature (T = 70oC), where mode of pipe deformation probably changes from elliptical to rectangular, especially when dense soil (DS1) is employed for embankments. Where, in case of rectangular mode of deformation, more vertical crown displacement takes place without further increase in springline horizontal displacement. Furthermore, in the investigated temperature range of 30 to 70oC, deflection increases as soil density decreases but pipe performance still remains within acceptable limit of 3-5%. In practice, this may allow for little uncontrollable variations in the in-situ density along the pipeline during field installation.

 

Table 3. Horizontal displacement and deflection at springline of buried HDPE pipes under 155 kPa surface pressure at various temperatures

(a) Dense dune sand (DS2)
ToC 30 40 50 60 70
Ux (mm)0.69726 0.71959 0.72707 0.73334 0.71786
dx (%)0.393 0.405 0.4096 0.413 0.404

(b) Medium dense dune sand (DS2)
ToC 30 40 50 60 70
Ux (mm)0.0014 0.0016 0.0017 0.0019 0.002
dx (%)0.7887 0.9014 0.9577 1.0704 1.1268

 

The effects of backfill and cover materials parameters (types) on cover height which induced prescribed crown vertical deflections were recently studied by Alawaji (2004) [11, 16, 17]. It was found that stiff backfill near pipe zone and stiff embankment cover reduces pipe deflection and allows larger cover height. However, gain from gravel backfill near pipe zone is relatively small. For example; at cover height which induced 3% pipe deflection, cover gain obtained from placing gravel backfill near pipe zone ranges from 17% for medium dense sand to 13% for dense sand cover.

Internal pressure effects on polyethylene pipes buried in embankments were also numerically investigated in this study. Pipe installation procedures include backfilling and cover with dense sand (DS1) and medium dense sand (DS2) soils (Table 2). Operation procedures include application of increasing vertical surface pressure and application of increasing internal radial pressure inside the buried pipes. Finite element analyses of buried HDPE pipes were executed under 30, 40, 50, 60, and 70oC. The used Pipe material parameters at various temperatures were given in Table 1. Figures 14 (a-h) present variations of normal force, shear force, and bending moment diagrams with internal pressure (0-700 kPa) for HDPE pipes buried in 1.723 m DS1 sand cover at 30oC. It is found that normal force changes from compressive to tensile when 100 kPa internal pressure is applied; then it increases as internal pressure increased up to 700 kPa. Maximum value of bending moment decreases as internal pressure increases up to 700 kPa. Figures 15(a-e) present variations of normal force, shear force, and bending moment diagrams with temperature (30-70oC) for HDPE pipes buried under 1.723 m DS1 sand cover with 700 kPa internal pressures. It is found that maximum values for normal force, shear force, and bending moment decreases with increased temperature. Table 4 shows pipes horizontal pipe springline displacement (Ux) and deflection (dx) for buried HDPE pipes under 1.723 m DS1 and DS2 sand covers and 700 kPa internal radial pressures at various temperatures. It is emphasized here that for both density states deflection slightly increases with temperature, but performance still remains acceptable and deflection is fare below permissible limit of 3-5%. Due to temperature increase from 30 to 70oC, springline horizontal displacement increased by 112% and 106% for HDPE pipes buried in DS1 and DS2 sand embankments under 700 kPa internal pressures, respectively. Furthermore, over the investigated temperature range of 30 to 70oC, deflection increases as soil density decreases but pipe performance still remains within acceptable limit of 3-5%. As expected, it is found that internal pressure reduces pipe vertical crown displacement and increases vertical invert displacement. In general, acceptable small deformations are predicted under simulated operational and environmental conditions pertinent to arid lands.

 

Table 4. Horizontal displacement and deflection at springline of buried HDPE pipes under 700 kPa internal pressure and at various temperatures

(a) Dense dune sand (DS2)
ToC 30 40 50 60 70
Ux (mm)0.47143 0.55968 0.61075 0.78133 0.99709
dx (%)0.266 0.315 0.3441 0.4402 0.5617

 

(b) Medium dense dune sand (DS2)
ToC 30 40 50 60 70
Ux (mm)0.58355 0.69768 0.76283 0.97578 1.2
dx (%)0.3288 0.3931 0.4298 0.5497 0.6761

 

CONCLUSIONS

From the staged construction simulation of buried polyethylene pipes in dune sand embankments, the following conclusions can be drawn:

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