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𝜏𝑓 = 𝑐 + 𝜎 𝑡𝑎𝑛𝜙
4.17
Substituting 𝜏𝑓 into Equation 4.16:
𝐹=
𝑁
∑ (𝑐 + 𝜎 𝑡𝑎𝑛𝜙) 𝐿
∑ 𝑊 𝑠𝑖𝑛𝛼
4.18
Since 𝜎 = 𝐿 , the equation for factor of safety in terms of total stress is:
𝐹=
∑ 𝑐 𝐿 + 𝑁 𝑡𝑎𝑛𝜙
∑ 𝑊 𝑠𝑖𝑛𝛼
4.19
In terms of effective stress
The shear strength (𝜏𝑓 ) can be expressed by Mohr-Coulomb’s formula in terms of
effective stress, as shown in Equation 3.4:
𝜏𝑓 = 𝑐′ + 𝜎 ′ 𝑡𝑎𝑛𝜙′
4.20
Substituting 𝜏𝑓 into Equation 4.16:
Since 𝜎 ′ =
𝑁
𝐿
𝐹=
4.21
− 𝑢, the equation for factor of safety in terms of effective stress is:
𝐹=
4.3.1
∑ (𝑐′ + 𝜎 ′ 𝑡𝑎𝑛𝜙′) 𝐿
∑ 𝑊 𝑠𝑖𝑛𝛼
∑(𝑐 ′ 𝐿 + (𝑁 − 𝑢 𝐿) 𝑡𝑎𝑛𝜙 ′ )
∑ 𝑊 𝑠𝑖𝑛𝛼
4.22
Fellenius’ method 1936
The Fellenius method, also known as the Swedish or Ordinary method of Slices, is the first
and most simple method of slices recorded in literature (Sivakugan & Das, 2009). The method
assumes that the interslice forces are ignored and satisfies moment equilibrium only. Figure
4.13 shows the forces on an individual slice with the forces shown in red assumed negligible.
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