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Passive Earth Pressure - The Rankine and Mazindrani Theory

Passive earth pressure follows from the following formula:

where:

σz

-

vertical geostatic stress

Kp

-

coefficient of passive earth pressure due to Rankine

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 Rankine theory. The coefficient of passive earth pressure is then provided by:

where:

φ

-

angle of internal friction of soil

Passive earth pressure σp by Rankine for cohesionless soils is given:

where:

γ

-

unit weight of soil

z

-

assumed depth

Kp

-

coefficient of passive earth pressure due to Rankine

Literature:

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.