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Passive earth pressure - the Rankin and Mazindrani theory
Passive earth pressure follows from the following formula:
| where: | σz | - | vertical geostatic stress |
| Kp | - | coefficient of passive earth pressure due to Rankin | |
| β | - | slope inclination | |
| γ | - | weight of soil | |
| z | - | assumed depth | |
|
- | coefficient of passive earth pressure due to Mazindrani |
The coefficient of passive earth pressure Kp is given by:
| where: | β | - | slope inclination |
| φ | - | angle of internal friction of soil | |
| c | - | cohesion of soil |
If there is no friction (δ = 0) between the structure and cohesionless soils (c = 0), the ground surface is horizontal (β = 0) and the resulting slip surafce is also plane with the slope:
,
the Mazindrani theory then reduces to the Rankin theory. The coefficient of passive earth pressure is then provided by:
| where: | φ | - | angle of internal friction of soil |
Passive earth pressure σp by Rankin for cohesionless soils is given:
| where: | γ | - | unit weight of soil |
| z | - | assumed depth | |
| Kp | - | coefficient of passive earth pressure due to Rankin |
Literature:
Arnold Verruijt: Soil mechanics, Delft University of Technology, 2001, 2006, http://geo.verruijt.net/
Mazindrani, Z.H., and Ganjali, M.H. 1997. Lateral earth pressure problem of cohesive backfill with inclined surface. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(2): 110–112.
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