Retaining walls- Stability Analysis
Earth pressure
P𝑎 = qHK𝑎
1
P𝑎 = 𝛾!"#$ H ! K𝑎
2
1 − sin ∅
𝐾𝑎 =
1 + sin∅
𝐾𝑎 = cos𝛽 ×
!"#!! !"# ! !!!"# ! ∅
!"#!! !"# ! !!!"# ! ∅
Sloping surface P𝑝 = qHK𝑝
1
P𝑝 = 𝛾!"#$ H ! K𝑝
2
1 − sin ∅
𝐾𝑝 =
1 + sin∅
𝐾𝑝 = cos𝛽 ×
!"#!! !"# ! !!!"# ! ∅
!"#!! !"# ! !!!"# ! ∅
𝑊 = 𝑎𝑟𝑒𝑎 × 𝛾!"#!. 𝑃! = 𝑃! sin 𝛽
𝑃! = 𝑃! cos 𝛽
Sloping surface Overturning moments
FOS =
!"# !" !!! !"!#$%& !!!" !"#$#% !"#$%&$'(')
!"# !" !"#$%&$'(') !"!#$%&
𝑀!
≥2
𝑀!
Factor of safety against Sliding
FOS =
!!
!!
≥ 1.5
𝐹! = 𝐶! 𝐵 + 𝑅! tan 𝛿 + 𝑃!
𝑅! = 𝑊! + 𝑃!
𝑅! = total vertical force
𝛿 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑤𝑎𝑙𝑙 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛
𝐶! = 𝑢𝑛𝑖𝑡 𝑜𝑓 𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛
=
!!
!"
Factor of safety against base pressure
X = = ∑𝑀! − ∑𝑀!
𝑃!" + ∑𝑊!
𝑒 = 𝑒 < !
!
- X
𝐵
6
𝑞!
𝑞!
𝑞! ≤ = 𝐹!
3
𝑅!
6𝑒
6𝑒
𝑞! = 1+
= 𝑞! 1 +
𝐵
𝐵
𝐵
𝑞! = 𝑞!
6𝑒
1−
𝐵
𝑅!
𝑞! = = 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
𝐵
𝑞! = 𝑢𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦