## Abbreviations and Notation  
* D: Diameter \(\mathrm{d}_{i}\): initial displacement or deflection \(\mathrm{d}_{\ell}\): Final displacement or deflection \(\mathrm{d}_{\ell}\): Deformation ratio \(\mathrm{e}_{\ell}\): Axial stiffness \(\mathrm{e}_{\ell}\): Bending stiffness \(\mathrm{e}_{\ell}\): Soil elasticity modulus \(\mathrm{e}_{\ell}\): Pipe elasticity modulus \(\mathrm{e}_{\ell}\): EPS: Expanded Polystyrene \(\mathrm{e}_{\ell}\): Finite element \(\mathrm{e}_{\ell}\): Fv: The frictional force in vertical planes \(\mathrm{h}\): Burial depth \(\mathrm{e}_{\ell}\): HDE: High Density Polyethylene \(\mathrm{e}_{\ell}\): H.S: Hardening soil \(\mathrm{e}_{\ell}\): Lateral earth pressure coefficient \(\mathrm{e}_{\ell}\): Ra: Rankine's active lateral earth pressure coefficient \(\mathrm{e}_{\ell}\): Lateral earth pressure coefficient \(\mathrm{e}_{\ell}\): Lateral earth pressure coefficient \(\mathrm{e}_{\ell}\): Ra  
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