The details of an embankment made of cohesive soil with pu-0 and Cu-20 kPa are s

Question

The details of an embankment made of cohesive soil with pu-0 and Cu-20 kPa are shown in Figure 1. The unit weight of the soil is 19 kN/m3. The weight of the sliding sector is 346 kN acting at an eccentricity of 5 m from the centre of rotation. It is assumed that no tension cracks developed. For the trial circle shown, determine the factor of safety against sliding for the following conditions: (i) The full embankment. (ii) The shaded portion of the embankment is removed 70° R=9m e=5m 3 m 1.5 m 1.1 3 m Figure 1

Explanation / Answer

Given,

Weight of sector=346Kn

cu= 20 Kpa

Unit weight of soil = 19kN/m3

Radius r= 9m

Eccentricity e = 5

1. Factor of safety for the full embackment:

Disturbing moment= Wight of sector x Eccentricity

= 346 x 5

= 1730 kNm

Restraining moment= cur2

= 20 x 92 x 70/180 x 3.14

= 1980 kNm

Factor of safety = Restraining moment/ Disturbing moment

= 1980/1730

= 1.14

2. Factor of safety for shaded portion of the slope is removed

Area of portion removed = 1.5 x 3 = 4.5 m2

Weight removed = 4.5 x 19 = 85.5 kN

Eccentricity from O = 3.3+ (3.3+1.5)/2 = 5.7 m

Relief from disturbing moment = 5.7 x 85.5 = 490 kNm

Factor of safety = 1980/(1730-490)

= 1.6

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