This may be illustrated by application of the Rankine equations to a vertical retaining wall supporting a cohesive soil with a surcharge acting on the backfill.

 As the wall rotates away from the soil, a gap or tension crack forms between the wall and the soil.  The soil stands without support to the depth of the crack.

In undrained conditions, a tension crack may develop at the top of the slope and hence no shear strength can occur over that length.

Consider a slip circle, water in the crack will supply an

additional hydrostatic force, acting to reduce the factor of safety. This can be incorporated into the analysis by treating it as an additional disturbing moment, = Fw zw.

WHERE, W = vertical load of the slipping mass θ = angle subtended by the slip circle C = cohesion in terms of total stress R = radius of the slip circle hc = depth of tension crack

ϒ= unit weight of soil

Fw = resultant force for water pressure in tension crack acting at ²/3 depth of water

zw = moment arm of resultant force Fw  x = moment arm of the slipping mass

Consider the vertical cut of height H. Assume that the soil is undrained and the strength can be represented by: t = C.

H = (4C/ϒ) - h If there is no tension crack, i.e. h = 0, then, H = (4C/ϒ) The theoretical value of h is (2C/ϒ) and then H = (2C/ϒ)

ϒ= unit weight of soil C = undrained strength of soil

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