Passive earth pressure - the Sokolovski theory

Passive earth pressure follows from the following formula:

where:	Kpg	-	passive earth pressure coefficient for cohesionless soils
	Kpc	-	passive earth pressure coefficient due to cohesion
	Kpp	-	passive earth pressure coefficient due to  surcharge
	σz	-	vertical normal total stress

Individual expressions for determining the magnitude of passive earth pressure and slip surface are introduced in the sequel; the meaning of individual variables is evident from Fig.:

Passive eart pressure slip surface after Sokolovski

Angles describing the slip surface:

,   

where:	φ	-	angle of internal friction of soil
	δp	-	angle of friction structure - soil
	β	-	slope inclination

Slip surface radius vector:

Provided that ω < 0 the both straight edges of the zone r₁ and r₂ numerically overlap and resulting in the plane slip surface developed in the overlapping region. The coefficients of passive earth pressure K_pg, K_pp, K_pc then follow from:

where:	φ	-	angle of internal friction of soil
	δp	-	angle of friction structure - soil
	α	-	back face inclination of the structure

Auxiliary variables: i_pg, i_pp, i_pc, g_pg, g_pp, g_pc, t_pg, t_pp, t_pc

for:

where:

For soils with zero value for the angle of internal friction the following expressions are employed to determine the coefficients of passive earth pressure:

where:

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Literature:

Sokolovski, V.V., 1960. Statics of Soil Media,Butterworth, London.