The sandy soil axial resistance on a buried section of a pipeline may be calculated using the following equation [1, 2].
Where,
Far is the soil axial resistance including effect of backfill effect
D is the pipeline outside diameter
?r is the friction coefficient between exposed pipeline and sand
Where,
?' is the submerged unit weight of the backfill soil,
Ka is Rankin's active pressure coefficient. It is calculated using the following equation:
H is the cover height to top of the pipeline,
W is the operational submerged weight of the pipeline,
? is the sand friction angle
In order to use the calculated axial resistance of the soil of the buried section of the pipe in global buckling analysis, an equivalent friction coefficient is defined using the following equation:
The total soil resistance against upheaval buckling of the buried section of the pipeline is calculated using the following formula [2]:
Where,
Hc is the depth from the soil surface to the center of the pipe
?' is the submerged unit weight of soil
f is the uplift resistance factor, which equals to 
for loose sand
D is the pipe diameter
w is the pipe unit weight
References:
- The Axial Resistance of Buried and Unburied Pipelines, Oliphant, J., et. al, Proceeding of 6th international offshore site investigation and geotechnics conference, 2007.
- Soil Response for Pipeline Upheaval Buckling Analyses: Full Scale Laboratory Test and Modelling, OTC 6486, 1990
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