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

## 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/m

^{3})- \(\mu\)
Coefficient of friction for the sandy soil (dimensionless)

- \(\theta\)
Geosynthetic layer inclination to the initial level (°)

## Notes

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