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the weight of each slice (area of slice multiplied by the specified unit weight multiplied by an
assumed 1 m thick slice normal to the plane of analysis). The sum of the weights of each slice
is in the numerator and denominator in Bishop’s simplified method and so the effects cancel
out. This means that the factor of safety is independent of the bulk unit weight for drained
conditions. Figure 6.8 shows the factors of safety for unit weights (γ) from 14 – 22 kN/m3 and
when varying the drained angle of shearing resistance (ϕ′) from 25 – 45°.
Effect of varying γ and ϕ′
2.5
Factor of safety
2
1.5
φ′ = 45
φ′ = 40
1
φ′ = 35
φ′ = 30
φ′ = 25
0.5
0
14
15
16
17
18
Unit weight γ
19
20
21
22
(kN/m3)
Figure 6.8: Effect of varying bulk unit weight and angle of shearing resistance in drained conditions
6.4
Effect of varying bulk unit weight (γ)
6.4.1
Undrained conditions
Figure 6.9 shows the factors of safety for different total weights in undrained conditions. An
increase in the bulk unit weight increases the weight of each slice and hence the normal force
at the base of the slice is also increased which leads to a greater shear resistance (𝜏𝑚𝑜𝑏 ), This
results in a lower factor of safety, evident in Figure 6.9 and Equation 6.2.
𝐹=
𝜏𝑓
𝜏𝑚𝑜𝑏
6.2
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