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Analytical Investigation of Load Over Pipe Covered with Geosynthetic-Reinforced Sandy Soil

  • Yan KouEmail author
  • Sanjay Kumar Shukla
Technical Note

Abstract

A geosynthetic reinforcement layer can be placed above the pipe in a ditch within the sandy soil cover to reduce the load on the crown of the pipe. The vertical load (V) on the crown of the rigid pipe without the geosynthetic layer is given as \(V={C_{\text{d}}}\gamma {B^2}\), where \(\gamma\) is the total unit weight of sandy soil, B is the ditch width and \({C_{\text{d}}}\) is the load coefficient. The analytical formulation for load on the crown of the pipe covered with a single layer of geosynthetic-reinforced sandy soil has been developed earlier. In this paper, an attempt is made to derive an analytical formulation to investigate the load coefficient for pipe covered with sandy soil reinforced with two layers of geosynthetic reinforcement. It is observed that the two layers of geosynthetic reinforcement provide more benefits than a single-layer reinforcement in terms of the load reduction on the pipe. It is also noted that the stiffness of geosynthetic, buried depth, layer spacing and rut depth affect the load on the crown of the pipe. An illustrative example is presented in order to explain how the engineers can determine the load on the pipe using the analytical expression presented in this paper.

Keywords

Pipe Analytical expression Crown of the pipe Geosynthetic reinforcement Sandy soil 

List of Symbols

\(B\)

Ditch width (m)

\({B_{\text{p}}}\)

Pipe outside diameter (m)

\({C_{\text{d}}}\)

Load coefficient for vertical load at any depth for the unreinforced soil cover case (dimensionless)

\({C_{{\text{d-GL}}}}\)

Load coefficient for vertical load at the initial horizontal level of the geosynthetic layer for the reinforced soil cover case (dimensionless)

\({C_{{\text{dR}}}}\)

Load coefficient for the vertical load at the top of the pipe for the reinforced soil cover case (dimensionless)

\(E\)

Modulus of elasticity of the geosynthetic (N/m)

\({E^ * }\)

Nondimensional modulus of elasticity of the geosynthetic \((=E{\text{/}}(\gamma {B^2})\) (dimensionless)

\(H\)

Depth of the crown of the pipe below the trench surface (m)

\({H^ * }\)

Nondimensional depth of the crown of the pipe below the trench surface \((=H{\text{/}}B)\) (dimensionless)

\(h\)

Depth of the geosynthetic layer above the crown of the pipe (m)

\({h^ * }\)

Nondimensional depth of the geosynthetic layer above the crown of the pipe \((=h{\text{/}}B)\) (dimensionless)

\(K\)

Coefficient of earth pressure (dimensionless)

\(r\)

Maximum vertical deflection or rut depth (m)

\({r^ * }\)

Nondimensional maximum vertical deflection or rut depth \((=r{\text{/}}B)\) (dimensionless)

\(T\)

Tension in the geosynthetic layer (N/m)

\(V\)

Force per unit length acting vertically downward on the top of the soil element (N/m)

\({V^{'}}\)

Force per unit length acting vertically downward at the horizontal level of the geosynthetic layer (N/m)

\({V^{''}}\)

Force per unit length acting vertically upward at the bottom of the geosynthetic layer (N/m)

\({W_{{\text{Fp-R}}}}\)

Vertical load on the flexible pipe for the reinforced case (N/m)

\({W_{{\text{Fp-U}}}}\)

Vertical load on the flexible pipe for the unreinforced case (N/m)

\({W_{{\text{Rp-R}}}}\)

Vertical load on the rigid pipe for the reinforced case (N/m)

\({W_{{\text{Rp-U}}}}\)

Vertical load on the rigid pipe for the unreinforced case (N/m)

\(\varepsilon\)

Tensile strain of the geosynthetic layer (dimensionless)

\(\gamma\)

Total unit weight of sandy soil (N/m3)

\(\mu\)

Coefficient of friction for the sandy soil (dimensionless)

\(\theta\)

Geosynthetic layer inclination to the initial level (°)

Notes

References

  1. 1.
    Moser AP, Folkman S (2008) Buried pipe design. McGraw-Hill Global Education Holdings, LLC, New YorkGoogle Scholar
  2. 2.
    Carleo J, McKenzie K, Weinstein R, Romano J (2012) Handbook of PVC pipe design and construction. Industrial Press, New YorkGoogle Scholar
  3. 3.
    Won MS, Ling HI, Kim YS (2004) A study of the deformation of flexible pipe buried under model reinforced sand. J Civil Eng 8(4):377–385Google Scholar
  4. 4.
    Tahmasebipoor A, Noorzad R, Shooshpasha E, Barari A (2012) A parametric study of stability of geotextile-reinforced soil above an underground cavity. Arab J Geosci 5:449–456CrossRefGoogle Scholar
  5. 5.
    Shukla SK, Sivakugan N (2013) Load coefficient for ditch conduits covered with geosynthetic reinforced granular backfill. Int J Geomech 13(1):76–82CrossRefGoogle Scholar
  6. 6.
    Ahmed MR, Tran VDH, Meguid MA (2015) On the role of geogrid reinforcement in reducing earth pressure on the buried pipes: experiment and numerical investigations. Soil Found 55(3):588–599CrossRefGoogle Scholar
  7. 7.
    Pires ACG, Palmeira EM (2017) Geosynthetic protection for buried pipes subjected to surface surcharge loads. Int J Geosynth Ground Eng 3:30CrossRefGoogle Scholar
  8. 8.
    Kou Y, Shukla SK, Mohyeddin A (2018) Experimental investigation for pressure distribution on flexible pipe covered with sandy soil reinforced with geotextile reinforcement of varying widths. Tunn Undergr Space Technol 80:151–163CrossRefGoogle Scholar
  9. 9.
    Kou Y, Shukla SK, Mohyeddin A (2018) Effect of width of geosynthetic reinforcement within the granular cover on the load distribution over the tunnel lining. Enhanc Appl Geomech Min Excav Simul Anal Sustain Civil Infrastruct 1(6):52–59Google Scholar
  10. 10.
    Das BM, Shukla SK (2013) Earth anchors, 2nd edn. J. Ross Publishing, Inc, Plantation, p 344. ISBN: 978-1-60427-077-8Google Scholar
  11. 11.
    Giroud JP (1995) Determination of geosynthetic strain due to deflection. Geosynth Int 2(3):635–641CrossRefGoogle Scholar
  12. 12.
    Shukla SK, Sivakugan N (2009) Analytical expression for geosynthetic strain due to deflection. Geosynth Int 16(5):402–407CrossRefGoogle Scholar
  13. 13.
    Terzaghi K (1943) Theoretical soil mechanics. Willey, New YorkCrossRefGoogle Scholar
  14. 14.
    Corey R, Han J, Khatri DK, Parsons RL (2014) Laboratory study on geosynthetic protection of buried steel-reinforced HDPE conduits from static loading. J Geotech Geoenviron Eng 140(6):1–10CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Discipline of Civil and Environmental Engineering, School of EngineeringEdith Cowan UniversityPerthAustralia

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