applied sciences Article  
A Numerical Investigation of Induced and Embedded Trench Installations for Large-Diameter Thermoplastic Pipes under High Fill Stresses  
[PERSON],*2, [PERSON] and [PERSON]  
1 Civil Engineering, Yilduz Technical University, Istanbul 34220, Turkey  
2 Civil Engineering, Namuk Kemal University, Tekirdag 59860, Turkey  
*Correspondence: [EMAIL_ADDRESS]  
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buckling. Numerous experimental studies and numerical analyses have been carried out examining the pipe-soil interaction for various types of thermoplastic pipes [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. High embankments impose significant earth stresses on buried infrastructures. Because the stiffness of the buried pipe is generally not the same as that of the backfill, the magnitude of vertical stress on a deeply buried pipe depends on the arching (positive or negative) that develops over the pipe. When high embankments are required for rigid culverts, the installation methods typically used are positive projection or induced trench and embedded trench installations. The induced trench installation (ITI) and embedded trench installation (ETI) models require a compressible soft zone such as EPS Geofoam above or surrounding the pipe (Figure 1). The ITI method for rigid culverts buried under high embankments has been used since the early 1900s. Numerous research studies have been conducted on the soil-structure interaction of EPS Geofoam using laboratory tests and field instrumentation [21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. Numerical analyses were also performed to better understand method uncertainties [10; 22; 24; 25; 27; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45]. The ITI and ETI models reduce vertical stress on the culvert by including a lower-density material (compressible soft zone) to increase positive arching. Compressible material in the ITI and ETI models for the culvert causes differential settlement of the soil column directly above the pipe relative to the adjacent soil. The earth load from the soil column directly above the culvert is partially supported by the shear forces developed on the soil interface with adjacent soil columns, thereby resulting in some of the load being redistributed to the adjacent fill (Figure 1). [PERSON] et al. [26] observed soil stresses on four rigid culverts buried using an ITI model with EPS Geofoam in Norway from 1988 to 1992. At the end of 20 years, the average measured earth pressure above the crown of the pipe ranged from 23 to 25% of the overburden pressure for installations with granular backfill material and about 45% for the ones with cohesive backfill material. The ITI model using Geofoam to reduce earth pressure has also been used on concrete culverts below high fill (see [22; 46; 47]). For circular pipes, [PERSON] et al. [48] studied a condition where the pipe was inserted into a zone of soft material. [PERSON] [49] concluded that, based on many parametric studies, surrounding the pipe with a soft zone was the most effective way of reducing earth pressures [49]. According to the numerical analysis of the embedded trench installation  
Figure 1: (**a**) Embedded trench installation (ETI). (**b**) Induced trench installation (ITI) [PERSON] et al. [43]. (ETI) model, [PERSON] et al. [10] suggested the optimum soft zone geometry for deeply buried PVC pipes. Recent studies claimed that the ITI method [38; 43] does not mitigate the earth pressure at the spring line and the invert of the structures. Therefore, creating a soft zone around the pipe was recommended, known as an ETI model.