Rankine Earth Pressure in Cohesive Soil for Passive Case

Engineeering Projects

In this article we will discuss about Rankine Earth Pressure for passive case. Figure 1 shows the Mohr’s circle in which point B indicates the vertical stress and point E represents the passive pressure. The wall carries a uniform surcharge q. The circle is tangent to the failure envelope. For this case the relation between Pa and \sigma_v is given by:

P_p = K_p\sigma_v + 2c\sqrt{K_p} + qK_p  ———-(1)

Where, K_p = \sqrt{1 + sin\phi}{1-sin\phi} = tan^2(45^0 + \dfrac{\phi}{2})

Mohe Circle in Passive Case in Cohesive Soil

Pressure Distribution of passive case in cohesive soil

Figure 2 given below shows the pressure distribution behind a wall retaining a cohesive backfill. The total resultant passive earth pressure Pp is obtained by integrating Equation 1. Thus:

P_P = \dfrac{1}{2} \gamma H^2 + 2cH + qH            ………..(2)

For, \phi = 0, the equation (2) reduces to:

P_P = \dfrac{1}{2} \gamma H^2 K_P + 2ch \sqrt{K_P} + qHK_P        ………(3)

For soils below the Water table, the submerged unit weight is to be used.

Pressure Diagram of Passive Case in Cohesive Soil

Leave a Comment