# A Numerical Investigation of Induced and Embedded Trench Installations for Large-Diameter Thermoplastic Pipes under High Fill Stresses

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## Abstract

**:**

## 1. Introduction

_{3}nominal densities were selected as the compressible material, and five different pipe compressible inclusion configurations were designed for the laboratory test program. It was reported that the induced trench installation (the single EPS panel above the pipe crown) offered the best solution regarding pipe performance and cost efficiency. Embedded trench installations (one EPS saddle above the pipe crown and one below the pipe invert) significantly reduced the soil stresses around the pipe and improved the pipe behavior [59]. Azizian et al. and Moghaddas Tafreshi et al. [60,61,62] investigated through full-scale laboratory tests the efficacy of using EPS alone or in combination with other geosynthetics (i.e., geogrid or geocell) in protecting the high-density polyethene (HDPE) pipe buried in a shallow trench against repeated surface loads. Moghaddas Tafreshi et al. [61] showed that using EPS with a density of at least 30 kg/m

_{3}, combined with geocell over the HDPE pipe, provided the best solution in terms of both pipe performance and trench surface settlements. However, since design concerns (i.e., burial depths and load types) are different, the optimal configuration proposed by [61] is not deemed suitable for the induced trench installation of the thermoplastic pipe under high embankment fills.

## 2. ORITE Project Field Experiment

## 3. Materials and Method

#### 3.1. Numerical Modeling Method

#### 3.2. Soil and Pipe Parameters

^{ref}= 100 kPa was taken into account [64].

#### 3.3. Interface Parameters

_{inter}) are given in Table 4. Interface strength reduction factors were obtained from the literature review [75,76,77].

#### 3.4. Verification of the Numerical Model

#### 3.5. Use of EPS Geofoam with Thermoplastic Pipes under High Fill Stresses

^{3}(EPS15) using the ITI model and ETI model, respectively. In the analyses, the stresses and vertical and horizontal deflections at the crown of the pipe, in the spring line, and invert were all evaluated.

#### 3.6. EPS Geofoam

^{3}(EPS15). Axial strain–axial stress and axial strain–volumetric strain relationships for EPS15 were determined by performing a uniaxial compression test [52]. The uniaxial monotonic compressive behavior of EPS15 was idealized by three linear segments (Figure 6a). The first segment was the secant line between the origin and 1% axial strain: the slope of the initial tangent modulus [83]. The second segment was the secant line between 2 and 6% axial strains: the slope of the transitional tangent modulus. The third segment was the secant line between 6 and 30% axial strains: the slope of the plastic tangent modulus [55]. The abscissa of the intersection point of the first and the second segments was determined to be 1.45% axial strain for EPS15. For the curve given in Figure 6a, the slopes of the linear segments (i.e., moduli) were determined to be E

_{1}= 3560 kPa, E

_{2}= 470 kPa, and E

_{3}= 170 kPa for EPS15. The Poisson’s ratios for the three linear segments were determined using the axial strain–volumetric strain relationships given in Figure 6b. The Poisson’s ratios were determined to be v

_{1}= 0.189, v

_{2}= 0.007, and v

_{3}= 0.040 for EPS15, respectively.

## 4. Numerical Analyses Result and Discussion

#### 4.1. Pipe Diameter Effect

#### 4.2. Pipe Stiffness Effect

#### 4.3. Pipe Material (HDPE–PVC) Effects

#### 4.4. Horizontal and Vertical Arching

_{e}= total vertical load, W

_{h}= total horizontal load, PL = Prism load, N

_{sp}= soil stress on the pipe in the horizontal axis, N

_{c}= total soil stress on the pipe crown, and N

_{i}= total soil stress at the bottom of the pipe.

#### 4.5. Vertical and Horizontal Deflections

#### 4.6. Effect of Using EPS Together with Thermoplastic Pipe

^{3}. This shows that some positive arching develops due to the vertical deflection of the thermoplastic pipe under the applied stress. However, when EPS Geofoam is used in the ITI and ETI models, the stresses determined at the pipe crown are smaller than the reference. It can be said that the use of EPS Geofoam material together with the pipe increases positive soil arching regardless of pipe deflection and has a positive effect on pipe behavior.

## 5. Conclusions

- In ETI and ITI models in which the EPS material was used with thermoplastic pipe, positive soil arching increased regardless of the vertical pipe deflection. There was a decrease in the stress in the regions where the EPS Geofoam material was placed. Stress was uniformly distributed across the EPS Geofoam in the pipe crown; however, significant increases in stresses occurred from the edge point of the EPS. Creating a compressible zone on the pipe in the ITI model caused greater stress at the pipe spring line and pipe invert than in the ETI model. Thus, the importance of the geometry of the compressible region to be formed around the pipe was highlighted. It was determined that the ETI model reduced the stresses acting on the pipe and caused a more uniform stress distribution around the pipe;
- The effects of diameter in HDPE pipes were investigated, and it was determined that the increase in pipe diameter increased the stresses acting on the pipe. Similar stress increases were determined in the ITI and ETI models. When the HDPE pipe diameter increased by approximately twice in the ETI model, there was an approximately 20%, 15%, and 35% increase in stress calculated at the crown, invert, and spring lines, respectively. The type of backfill soil around the pipe also affected the stresses. High stresses occurred in clay, sand, and crushed stone backfills, respectively;
- The stiffness effect was examined in the PVC pipe, and higher stresses were observed on the pipes with higher rigidity. In the ITI and ETI models, the stress acting on the pipe decreased regardless of pipe stiffness. The stresses calculated in pipes whose stiffnesses differed by a factor of two were very close. Thus, it was determined that it is appropriate to use the lower rigidity pipe with EPS Geofoam (especially in the ETI model) under the higher fill stresses;
- HDPE and PVC pipes were taken into account to examine the effects of pipe material on stress in thermoplastic pipes. It was determined that the stresses affecting the PVC pipe were higher than the HDPE pipe. This is because the stiffness of the HDPE pipe is lower than the PVC pipe. The HDPE pipe deflects more, causing further development of positive arching and resulting in less stress affecting the HDPE pipe;
- The use of EPS in the installation of thermoplastic pipes greatly affected the VAF and HAF values. When the thermoplastic pipe was buried according to the ETI method, active soil wedges at the sides of the pipe were induced, leading to a significant reduction in the horizontal stresses that act on the pipe wall. Reduction in horizontal stress in the pipe spring line was controlled by compression of the EPS zone that covers the side of the pipe;
- The VAF and HAF values were compared. The highest values were determined in clay, sand, and crushed stone backfills when comparing the reference to the ITI and ETI models, respectively. With the increase in the H/D ratio in the ETI model, VAF and HAF values decreased to almost the same values for all three backfill types. This situation shows that clay backfill can be used instead of the sand and crushed stone material used as traditional backfill with the ETI model;
- The induced trench methods significantly affected thermoplastic pipe deflections due to the interaction between the thermoplastic pipe, EPS, and the backfill. The results showed that using EPS meant that arching increased regardless of pipe deflection caused by relative soil settlements compressing the EPS with either the ETI or ITI method for thermoplastic pipe and, consequently, lower pipe deflections;
- In applications subjected to high fill stresses, burying the large-diameter thermoplastic pipes with EPS Geofoam material significantly reduces the stresses affecting the pipe deflections. In this study, reductions in the stresses acting on the pipes were calculated for the ETI model and found to be up to 62% at the pipe crown, 53% at the invert, and 65% at the spring line.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Embedded trench installation (ETI). (

**b**) Induced trench installation (ITI) Santos et al. [43].

**Figure 3.**Numerical model and finite element mesh of B-B’ cross-section. (

**a**) General view of section. (

**b**) A magnified view of the trench geometries (Pipe 17, 14, 11, 8, 5, and 2 from left to right).

**Figure 4.**Field test and numerical analyses. (

**a**) Vertical stress on the pipe crown and horizontal stress on the pipe spring line in Pipe 4. (

**b**) Horizontal and vertical deflection in Pipe 4. (

**c**)Vertical stress on the pipe crown and horizontal stress on the pipe spring line in Pipe 14. (

**d**) Horizontal and vertical deflection in Pipe 14.

**Figure 6.**(

**a**) Axial stress–axial strain. (

**b**) Volumetric strain–axial strain graphs for EPS15 geofoam material.

**Figure 13.**Arching factors for 0.762 m diameter PVC pipe. (

**a**) Vertical arching factor (VAF). (

**b**) Horizontal arching factor (HAF).

**Figure 14.**Arching factors for 1.524 m diameter HDPE pipe. (

**a**) Vertical arching factor (VAF). (

**b**) Horizontal arching factor (HAF).

Pipe No | Pipe Material | Pipe Diameter (mm) | Wall Type ^{(1)} | Ring Stiffness ^{(2)}(kPa) | Backfill | H (m) | Bedding Thickness (mm) | |
---|---|---|---|---|---|---|---|---|

Type | RC (%) | |||||||

2 | PVC | 762 | A | 45.15 | Cr. S. | 96 | 12.2 | 150 |

4 | PVC | 762 | B | 97.45 | Sand | 86 | 6.1 | 150 |

5 | PVC | 762 | B | 97.45 | Cr. S. | 96 | 12.2 | 150 |

8 | HDPE | 762 | C | 73.31 | Sand | 96 | 12.2 | 150 |

14 | HDPE | 1067 | E | 61.69 | Sand | 96 | 12.2 | 80–230 |

17 | HDPE | 1524 | F | 34.42 | Cr. S. | 96 | 12.2 | 80–230 |

^{(1)}[63] for details.

^{(2)}Initial values. Cr. S.—Crushed Stone. RC—Relative compaction.

Soils | γ_{n} (kN/m ^{3}) | ${\mathit{E}}_{50}$ (MPa) | ${\mathit{E}}_{50}^{\mathit{r}\mathit{e}\mathit{f}}$ (MPa) | ${\mathit{E}}_{\mathit{u}\mathit{r}}^{\mathit{r}\mathit{e}\mathit{f}}$ (MPa) | c (kPa) | φ (°) | Ψ (°) |
---|---|---|---|---|---|---|---|

Cr. S. (96% RC) | 22.19–23.81 | 90 | 89.2 | 267.6 | 69 | 45 | 15 |

Sand (86% RC) | 17.70–18.3 | 9.7 | 9.5 | 28.5 | 0 | 37 | 7 |

Sand (96% RC) | 19.35–19.95 | 36 | 35.5 | 106.5 | 0 | 45 | 15 |

Bedding Cr. S. | 18 | - | 32 | 96.0 | 20 | 40 | 10 |

Bedding Sand | 16 | - | 6.3 | 18.9 | 0 | 33 | 3 |

Native Soil Clay | 20.4 | - | 20 | 60.0 | 34.5 | 24 | 0 |

Embankment Fill Clay | 20.4 | - | 5.21 | 15.6 | 34.5 | 15 | 0 |

Pipe Profile Types | A | B | C | E | F |
---|---|---|---|---|---|

Pipe diameter (m) | 0.762 | 0.762 | 0.762 | 1.067 | 1.524 |

Pipe Rigidity (kN/m/m) | 302 | 650 | 490 | 413 | 230 |

Normal Stiffness, EA(kN/m) | 32,620 | 35,550 | 8335 | 11,960 | 18,190 |

Flexural Stiffness, EI (kNm^{2}/m) | 2.490 | 5.390 | 4.050 | 9.360 | 15.220 |

Equivalent Thickness, d (m) | 0.030 | 0.043 | 0.076 | 0.097 | 0.100 |

Poisson’s Ratio, ν | 0.300 | 0.300 | 0.450 | 0.450 | 0.450 |

Parameter | Local Soil-Backfill | Pipe-Backfill | Pipe-EPS | EPS-Backfill |
---|---|---|---|---|

φ_{inter} (°) | 24 | 20 ^{(1)} | 14 ^{(2)} | >30 ^{(3)} |

R_{inter} (-) | 1.00 | 0.67 | 1.00 | 1.00 |

Layer 1 | Layer 2 | Layer 3 | Layer 4 | Layer 5 | Layer 6 | |
---|---|---|---|---|---|---|

Pipe 4 | 1.0 | 0.9 | 1.4 | 1.0 | - | - |

Pipe14 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |

Backfill Parameters | Cr. S | Sand | Clay |
---|---|---|---|

Natural unit volume weight, γ_{n} (kN/m^{3}) | 22 | 17.7 | 20.4 |

$\mathrm{Reference}\text{}\mathrm{mean}\text{}\mathrm{sec}\mathrm{ant}\text{}\mathrm{module},\text{}{E}_{50}^{ref}$ (MPa) | 18 | 9.5 | 5.2 |

$\mathrm{Reference}\text{}\mathrm{unloading}-\mathrm{reloading}\text{}\mathrm{module},\text{}{E}_{ur}^{ref}$ (MPa) | 54 | 28.5 | 15.6 |

Cohesion, c (kN/m^{2}) | - | - | 34.5 |

Shear strength angle, φ (°) | 40 | 37 | 15 |

Dilatancy angle, ψ (°) | 5 | 7 | - |

Exponential power for the stress–level dependency of stiffness, m (-) | 0.5 | 0.5 | 0.8 |

1.524 m (F) (HDPE) | 0.762 m (C) (HDPE) | ||||||
---|---|---|---|---|---|---|---|

Crown | Spring Line | Invert | Crown | Spring Line | Invert | ||

Reference | Cr. S | 267 | 331 | 248 | 267 | 235 | 209 |

Sand | 326 | 348 | 287 | 316 | 254 | 256 | |

Clay | 397 | 366 | 370 | 379 | 297 | 338 | |

ITI model | Cr. S | 195 | 197 | 216 | 156 | 154 | 178 |

Sand | 207 | 224 | 246 | 176 | 185 | 224 | |

Clay | 248 | 280 | 334 | 237 | 257 | 301 | |

ETI model | Cr. S | 163 | 151 | 134 | 138 | 97 | 121 |

Sand | 171 | 167 | 147 | 153 | 113 | 136 | |

Clay | 209 | 222 | 205 | 206 | 193 | 207 |

PS-650 (B) (PVC) | PS-302 (A) (PVC) | ||||||
---|---|---|---|---|---|---|---|

Crown | Spring Line | Invert | Crown | Spring Line | Invert | ||

Reference | Cr. S | 307 | 269 | 247 | 280 | 290 | 252 |

Sand | 341 | 271 | 281 | 314 | 294 | 275 | |

Clay | 392 | 294 | 348 | 350 | 306 | 312 | |

ITI model | Cr. S | 158 | 168 | 197 | 167 | 169 | 187 |

Sand | 178 | 192 | 236 | 184 | 196 | 218 | |

Clay | 235 | 252 | 298 | 225 | 243 | 282 | |

ETI model | Cr. R | 138 | 103 | 122 | 123 | 100 | 118 |

Sand | 152 | 116 | 135 | 133 | 111 | 153 | |

Clay | 194 | 179 | 185 | 184 | 156 | 198 |

HDPE (C Type) | PVC (B Type) | ||||||
---|---|---|---|---|---|---|---|

Crown | Spring Line | Invert | Crown | Spring Line | Invert | ||

Reference | Cr. R | 267 | 235 | 209 | 307 | 269 | 247 |

Sand | 316 | 254 | 256 | 341 | 271 | 281 | |

Clay | 379 | 297 | 338 | 392 | 294 | 348 | |

ITI model | Cr. R | 156 | 154 | 178 | 158 | 168 | 197 |

Sand | 176 | 185 | 224 | 178 | 192 | 236 | |

Clay | 237 | 257 | 301 | 235 | 252 | 298 | |

ETI model | Cr. R | 138 | 97 | 121 | 138 | 103 | 122 |

Sand | 153 | 113 | 136 | 152 | 116 | 135 | |

Clay | 206 | 193 | 207 | 194 | 179 | 185 |

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## Share and Cite

**MDPI and ACS Style**

Kılıç, H.; Biçer, P.; Bozkurt, S.
A Numerical Investigation of Induced and Embedded Trench Installations for Large-Diameter Thermoplastic Pipes under High Fill Stresses. *Appl. Sci.* **2023**, *13*, 3040.
https://doi.org/10.3390/app13053040

**AMA Style**

Kılıç H, Biçer P, Bozkurt S.
A Numerical Investigation of Induced and Embedded Trench Installations for Large-Diameter Thermoplastic Pipes under High Fill Stresses. *Applied Sciences*. 2023; 13(5):3040.
https://doi.org/10.3390/app13053040

**Chicago/Turabian Style**

Kılıç, Havvanur, Perihan Biçer, and Sercan Bozkurt.
2023. "A Numerical Investigation of Induced and Embedded Trench Installations for Large-Diameter Thermoplastic Pipes under High Fill Stresses" *Applied Sciences* 13, no. 5: 3040.
https://doi.org/10.3390/app13053040