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For flexible pipelines, the influence of backfill compaction on the deformation of the pipe has always been the focus of researchers. Through the finite element software, a three-dimensional soil model matching the exterior wall corrugation of the high-density polyethylene pipe was skillfully established, and the “real” finite element model of pipe-soil interaction verified the accuracy through field test. Based on the model, the strain distribution at any position of the buried HDPE pipe can be obtained. Changing the location and extent of the loose backfill, the strain and radial displacement distributions of the interior and exterior walls of the HDPE pipe under different backfill conditions when external load applied to the foundation were analyzed, and the dangerous parts of the pipe where local buckling and fracture may occur were identified. It is pointed out that when the backfill is loose, near the interface between the backfill loose region and the well-compacted region, the maximum circumferential strain occurs frequently, the exterior wall strain is more likely to increase greatly on the region near crown or invert, the interior wall strains increase in amplitude at springline, and the location of the loose region has a greater influence on the strain of the pipe than the size of the loose area.

High-density polyethylene (HDPE) double-corrugated pipe is widely used in the municipal engineering for significant advantages such as chemical resistance, light weight, and simple construct. The special profile of pipe featured with the smooth interior wall, and the corrugated exterior wall makes the ring stiffness much higher than that of the straight wall pipes of the same diameter and thickness. Figure

Profile of pipes: (a) section through pipes; (b) cross section of pipe walls.

The Chinese specification (Buried plastic drainage pipe construction) uses the normalized deflection by diameter to evaluate the pipe deformation [

There are two directions for the study of the deformation of pipes, one is the influence of accidental factors on the deformation of pipelines, such as ground overload [

Based on the theory of granular limit equilibrium and in view of the influence of the pipe diameter and the trench width, Marston and Anderson derived the formula for calculating the vertical

Faragher et al. explored the axial strains of the plastic pipes in installation when changing the compaction degree of the sand or the gravel backfill material by laboratory testing [

Through the laboratory test and FEM, Dhar et al. recommended the two-dimensional finite element analysis, which could be used effectively to calculate pipe deflections; they also applied FEM to study the effect of a soft haunch region on the strains in profiled thermoplastic pipes [

Vehicular load is the external load that municipal buried pipes must consider. The deformation of pipes had been reported by researchers when the vehicular load was applied to the ground as an external load.

McGrath et al. measured the stress and deformation of a large-diameter shallow-embedded HDPE pipe under the real vehicular load through a full-scale field study [

The distribution of HDPE pipe strains and deflection when the backfill degree of compaction was not according to the specification was reported by test and the two-dimensional finite element model; the three-dimensional finite soil-pipe model was not used to simulate the effect of backfill parameters on the pipe response. Therefore, it is necessary to establish a three-dimensional model of the HDPE pipe and study the effect of the compactness of the backfill on the strain and deformation of the pipe.

The objective of this paper is to set up a real three-dimensional finite element model of HDPE double-wall corrugated pipe and soil and provide a theoretical basis for studying the strain distribution and deformation of pipe when the compactness of the backfill soil changes. The validity of the three-dimensional model is verified by comparing the numerical strain with the measured strain collected through the full-scale test. Based on the numerical model, it is analyzed the effects of the loose backfill of different regions on pipe under the vehicular loads.

The HDPE double-wall corrugate pipe with the length of 6.0 m was investigated in this field-test program, and the nominal diameter is 800 mm. The pipe geometries and material properties are shown in Table

Properties of HDPE pipes’ geometry and material.

Properties | Value |
---|---|

Nominal diameter (mm) | 800 |

Corrugate length (mm) | 100 |

Corrugate height (mm) | 55 |

Minimum lamination wall thickness (mm) | 3.5 |

Minimum interior wall thickness (mm) | 2 |

Cross-sectional region per unit length (mm^{2}) |
8.7 |

Moment of inertia per unit length (mm^{4}) |
5,120 |

Hoop stiffness (kPa) | 8 |

Location of strain gauges and the data acquisition method.

A data acquisition instrument (DH5921 dynamic stress-strain analysis system) was used to record the measured pipe strains for once per second. The system is designed for dynamic structural performance testing in large-scale engineering testing and product development processes and is capable of accurately measuring parameters such as strain, force, and displacement. The instrument design connects the strain gauge to the acquisition system through the wire. The instrument sensitively collects and amplifies the weak voltage signal, then converts the voltage signal into true strain by the associated program calculation, and then transmits the data to the computer through the Ethernet. The strain readings were zeroed after installation; the tensile strains and compressive strains are reported as positive values and negative values, respectively. The pipe wall strains at the instrumented pipe sections were monitored and recorded after 5-minute load application.

As to the field installation of pipe in this test, the 6 m pipe was installed in two different compaction conditions, in which the backfill in the range of 3.0 m was compacted according to the standard outline by CJJ 143-2010 [

Basic properties of the field-test soil.

Properties | Value |
---|---|

In-suit soil | |

Maximum dry density (kg/m^{3}) |
1549 |

Water content (%) | 12 |

Liquid limit (%) | 25.9 |

Plastic limit (%) | 17.3 |

Void ratio | 42.3 |

Backfill sand | |

Maximum dry density (kg/m^{3}) |
1730 |

Coarse sand (0.5∼3 mm) (%) | 35 |

Medium sand (0.35∼0.5 mm) (%) | 57 |

Fine sand (0.25∼0.35 mm) (%) | 8 |

Grade | 120 |

The standard installation process in the 3.0 m region during the field test is plotted as follows. The bottom of the trench had a 200 mm thick bedding layer consisting of the sand with 90% compaction (i.e., Lay 01) overlaying the undisturbed natural soil. The region (i.e., Lay 02) from the bedding to haunch was backfilled with 95% related density to provide strong support for the pipe. From the springline of the pipe to the crown of the pipe, the sand backfill was placed surrounding the pipes in lifts of 100 mm and compacted until 95% compaction before the subsequent lifts were added (i.e., Lay 03). The 0.4 m region of the crown of pipes was divided into two parts (i.e., Lay 04 and Lay 05), and the sand backfill had compactions of 85% and 90%, respectively. In the 1.0 m thick range (i.e., Lay 06) from 0.4 m above the crown of the pipe to the ground, the in-suit soil with 90% compaction was placed. Under the condition of uneven compaction of backfill soil, the soil was not compacted when the left-haunch (i.e., the left side of Lay 02) was backfilled, and the remaining regions were compacted according to the standard requirements. The region of backfill was divided and compacted as shown in Figure

(a) Location of the measuring sections; (b) material and compaction degree of the backfill by specification; (c) field installation.

In this field test, there was no pavement layer overlying the surface of soil, and the strain of the pipe was much greater than the real deformation of the pipe buried under the pavement. Therefore, the measured data are only used to be compared with the simulated data, in order to verify the accuracy of the numerical model; however, it cannot be considered as the pipe deformation under the real vehicular load.

Two inspection wells were provided at both ends of the pipeline, and the vehicular load was applied to a heavy truck. Figure

(a) Location and parameters of wheel loads; (b) field test.

For the flexible buried pipe, estimate of pipe deflection and strain can be calculated using design equations. A simplified procedure which is suitable for hand calculation is being developed based on design equations for solving the deformation and strain of buried flexible pipes [_{f} to represent the peak circumferential bending strain as a function of displacement (equation (_{f} is difficult to generalize the strain distribution of all polyethylene pipes, and for HDPE double-wall corrugated pipes with a special cross-sectional shape, the empirical coefficient _{f} is more limited._{s} = one dimensional soil modulus; _{l} = deflection lag factor;

According to the parameters of the HDPE pipe profile and soil used in the field test, we establish a three-dimensional finite element model. Attributable to the pipe exterior wall is the corrugate corresponding soil model having a complicated shape in the contact region, and the exterior wall meshes have coincided with the soil meshes to ensure the accuracy and comparability of the simulation result.

Therefore, the meshing of the “corrugated” area of the soil model is very difficult. In order to control the quality of the elements and ensure the accuracy of the model, the elements size of the soil corrugated area should be small enough. This inevitably makes the element number of corrugated soil much larger than the element number of normal straight wall pipes, the size of the model and the computational efficiency are unbearable for ordinary computers. In this paper, the professional meshing software HYPERMESH is used to mesh the corrugated soil model, and under the condition of ensuring the calculation accuracy, the number of elements is subtly reduced, so the number of soil model elements used in this article is only 630,000. In HYPERMESH, the plotted refined numbered elements and the exterior wall shell elements are generated based on the corresponding pipe-soil interface mesh, and the elements of the contact positions between the interior wall and the exterior wall must also coincide. The independent elements of pipe and soil are exported from HYPERMSH and are inducted into ABAQUS for analysis (Figure

(a) Mesh generation scheme using HYPEMESH; (b) elements of soil and pipes’ exterior walls.

The soil model is 3.0 m long, 4.0 m wide, and 3.6 m deep (Figure

Three-dimensional calculation mode.

Properties of soil used for numerical simulation.

Properties | Lay 01 | Lay 02 | Lay 03 | Lay 04 | Lay 05 | Lay 06 | In-suit soil |
---|---|---|---|---|---|---|---|

Dry density (kg/m^{3}) |
2020 | 1670 | 1670 | 2020 | 2000 | 1800 | 1850 |

Related density (%) | 90 | 95 | 95 | 90 | 85 | 90 | |

Elastic modulus (MPa) | 10 | 15 | 15 | 7 | 9 | 9 | 30 |

Poisson’s ratio | 0.30 | 0.26 | 0.26 | 0.23 | 0.30 | 0.32 | 0.35 |

Cohesion (kPa) | 0.50 | 0.25 | 0.25 | 0.30 | 0.35 | 0.40 | 0.40 |

Friction angle (°) | 35 | 31 | 25 | 28 | 30 | 27 | 30 |

According to the Structure Design Code for Pipelines of Water Supply and Waste Engineering (GB 50332-2002), the relationship between soil compaction and elastic modulus is presented; in the next part of numerical model validation, the elastic modulus of loose backfill is designed as 3 MPa. The bottom plane of the soil is fully constrained, and horizontal displacements of the four vertical planes are not allowed.

The elastic model and the eight-node reduced-integration shell element (S8R) are used to simulate the pipe of the initial interior diameter of 0.8 m and the length of 3.0 m (Figure

Elements of double-wall corrugated pipe.

Idealized thickness of pipe walls for numerical simulation.

Properties | HDPE corrugated pipes |
---|---|

Modulus of elasticity (MPa) | 800 |

Density | 950 |

Poisson’s ratio | 0.4 |

Idealized exterior wall thickness (mm) | 3 |

Idealized interior wall thickness (mm) | 2 |

The structure model simulated the foundation and does not consider about the pavement and the subgrade; the vertical load _{z} applied to the foundation is consisted of _{z1} and _{z2}; _{z1} is the vehicular load and _{z2} is caused by the pavement structure and subgrade.

In the 1960s, the fourth power theory was proposed by the American Association of Interstate Highway Workers (AASHO): static axle load is more suitable for simulating traffic load with low speed and light axle load [_{z1} caused by the vehicular load is related to the thickness of subgrade and the expansion angle of subgrade pressure (equation (_{z2} of the foundation surface caused by the pavement structure and subgrade is seen in equation (

Traffic load dispersion and parameters of urban road.

By equations (_{z} of the applied load on the surface foundation soil is 50 kPa. Therefore, the 40 kPa and 3.28 m × 3.08 m static load acting on the foundation soil is employed by simulating the vehicular loads acting on the pipe in this paper.

Corresponding numerical models are established according to the implementation of the full-test; the vehicular load is applied according to the position of the tire in the test and the load size is 0.7 MPa.

It can be seen from Figure

Comparison of measurements and calculation of pipe strains in the well-compacted backfill: (a) liner circumferential strain; (b) valley circumferential strain; (c) crest circumferential strain; (d) valley axial strain.

For pipe with the uniform backfill, the maximum compression value of the pipe can be represented by the circumferential strain on the valley or the interior wall at the springline [

The result of the circumferential strain distribution is slightly different from that reported in the literature; this may be caused by different compaction methods and backfill materials during pipe installation. The detailed report of the measured circumferential strains can be found in the study by Brachman [

Figure

Comparison of measurements and calculation of pipe strains in the poor haunch backfill: (a) liner circumferential strain; (b) valley circumferential strain; (c) crest circumferential strain; (d) valley axial strain.

Based on the three-dimensional finite element model, effect of loose backfill of different regions on the pipe strain and deformation are studied under the vehicular load in the next part. The distribution of circumferential strain discussions is highlighted and considered to be a more sensitive indicator of deformation, and the difference between liner circumferential strain and valley circumferential strain is regarded as an indicator of the possibility of local buckling.

If the compaction of the backfill is asymmetrical, the pipe is eccentrically compressed. Under the long-term load, the eccentric compression of the pipe is more likely to cause the failure of the pipe. Since the specification requires attention to the compaction of backfill under the haunch of the pipe, in this part, the most severe conditions considered may exceed typical design conditions. Some compaction conditions are designed on the left and right regions of the backfill compaction which are asymmetrical; the strain distribution and deformation of the pipe are studied under the vehicular load. The possibility of local buckling is indicated through the difference between circumferential strain of the liner and circumferential strain of the valley. This part uses a static load of 50 kPa and 3.28 m × 3.08 m to act on the foundation soil.

In Figure

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 01 was loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 01 was loose.

The distribution of circumference strain and displacement of pipe when the left base is softer (i.e., the backfill of left Lay 01 was loose) is plotted in Figures

As plotted in Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 02 was loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 02 was loose.

For the pipe buried in soil where the backfill of Lay 03 left region in loose, the distributions of strains are shown in Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 03 was loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 03 was loose.

Distributions of circumferential strain on the pipe when the Lay 01 and Lay 02 left regions are loose are plotted in Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left sides of Lay 01 and Lay 02 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left sides of Lay 01 and Lay 02 were loose.

Although the loose region of the pipe is larger in this case, the circumferential strain increment caused by the loose backfill became smaller; the influence of the loose backfill on the maximum strain of the pipe is not simply positively related to the size of the loose region.

Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left sides of Lay 01 and Lay 03 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left sides of Lay 01 and Lay 03 were loose.

When the backfills on the left sides of the Lay 02 and Lay 03 were loose, the structural field determined the deformation and the strain of the pipe (Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left sides of Lay 02 and Lay 03 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left sides of Lay 02 and Lay 03 were loose.

It is assumed that in extreme cases, the backfill on the left side of the pipe is loose, and the strain and displacement of the pipe are shown in Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left sides of Lay 01, Lay 02 and Lay 03 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left sides of Lay 01, Lay 02, and Lay 03 were loose.

The circumferential strain distribution and deflection are complex when the combined action of the left side of Lay 01 and right side of Lay 02 is loose (Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 01 and the right side of Lay 02 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 01 and the right side of Lay 02 were loose.

As can be seen from Figures

(a) Location of loose backfill; the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 01 and the right side of Lay 03 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 01 and the right side of Lay 03 were loose.

Figures

(a) Location of loose backfill: the circumference strain nephogram of the (b) interior wall and (c) exterior wall when the left side of Lay 02 and the right side of Lay 03 were loose.

Distribution of (a) circumferential strain and (b) radial displacement when the left side of Lay 02 and the right side of Lay 03 were loose.

The response of the crest strain to backfill stiffness is more sensitive and complex. The distribution of the crest strain is completely different from that under standard compaction, and the standard strain is smaller. The strain changed mostly near the crown and the springline, and the maximum appears at the left-haunch and increased by 32%. In the regions supported by the loose backfill, the radial displacement increases greatly and the maximum value appears near the left-haunch.

The failure of the pipeline usually starts from the position of the maximum strain, and the local buckling is most likely to occur in the position of the maximum difference between the liner circumferential strain and the valley circumferential strain. Table

Increments of maximum circumferential strain of the pipe.

Condition | Crest (%) | Valley (%) | Liner (%) | Difference between valley strain and liner strain (%) |
---|---|---|---|---|

L01 | 0 | 0 | 0 | 0 |

L02 | 25 | 28 | 34 | 27 |

L03 | 18 | 26 | 33 | 27 |

L01-L02 | 5 | 13 | 16 | 12 |

L01-L03 | 20 | 28 | 23 | 20 |

L02-L03 | 15 | 14 | 22 | 13 |

L01-L02-L03 | 15 | 17 | 24 | 14 |

L01-R02 | 30 | 32 | 38 | 30 |

L01-R03 | 19 | 33 | 40 | 42 |

L02-R03 | 32 | 39 | 48 | 36 |

The response of the pipe to the loose backfill is related not only to the size of the region with loose backfill but also to the location of the region, and the location of the region with loose backfill is more critical than the size. It can be found that the pipe had higher requirements on the compaction of the backfill in the surrounding pipe (i.e., Lay 02 and Lay 03), especially the haunch backfill (i.e., Lay 02). In the case of loose local backfill, the maximum value of the liner circumferential strain is more susceptible than the change in the valley circumferential strain. However, for the base of the pipe, proper reduction of the stiffness of backfill can reduce the strain of the pipe. When Lay 02 and the backfill with the adjacent region are loose on the left side of the pipe, although the range of the backfill of low stiffness has expanded, the variation of the pipe strain maximum is reduced. When the loose region of the backfill is distributed on the left and the right, the asymmetry of backfill stiffness is enhanced and the maximum strain increment is greater than that when the left side of single-layer backfill is loose and had more possibilities of local buckling of pipe occurring.

The paper compared the measured value and calculated value of the buried HDPE double-wall corrugated pipes, which showed that the three-dimensional finite element model can be effectively employed to calculate the pipe strain under the structure field. Based on the finite element model, it studied the strain distribution of the pipe under the exterior load. The following conclusions are obtained:

The strain distribution trends of the liner and the valley are very similar, and the maximum strain of the interior wall often appears near the springline, which is the region most likely to be locally buckling.

When the pipe is buried in the well-compacted soil, the most dangerous location of the exterior wall is the springline. Nevertheless, if the backfill is loose around the pipe, the most obvious change of the crest circumferential strain is near the crown or the invert.

When there is a loose region in the backfill around the pipe, near the interface between the backfill loose region and the well-compacted region, the maximum circumferential strain occurs frequently, and the point where the pipe radial displacement changes the most often coincides with the maximum point of the valley circumferential strain.

The response of the pipe to the loose backfill is related not only to the size of the backfill loose region but also to the location of the region, and the location of the region with loose backfill is more critical than the size.

The compaction of backfill under the haunch has the greatest influence on the strain state and deformation of the pipe. Therefore, in the actual construction process, it must be ensured that the compaction degree of the backfill in the region was good enough for specification requirements.

The figure and table data used to support the findings of this study are included within the article. In addition, the finite element models are available from the corresponding author upon request.

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

The authors acknowledge the financial support provided by the National Key Research and Development Program of China (No. 2016YFC0802400), the National Natural Science Foundation of China (No. 51978630, 51678536), the Program for Science and Technology Innovation Talents in Universities of Henan Province (Grant no. 19HASTIT043), the Outstanding Young Talent Research Fund of Zhengzhou University (1621323001), and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (18IRTSTHN007).