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Presented by: Civil Engineering Academy
Lateral Earth PressurePresented by: Civil Engineering Academy
Earth pressure is the force per unit area exerted by soil. The
ratio of horizontal to vertical stress (effective stresses) is called
coefficient of lateral earth pressure (K)
K=𝜎ℎ
𝜎𝑣=
𝜎′ℎ
𝜎′𝑣
Earth pressure is at-rest, active, or passive (CERM Ch. 37):
𝜎′ℎ(𝑎𝑐𝑡𝑖𝑣𝑒) or
𝜎′ℎ (𝑝𝑎𝑠𝑠𝑖𝑣𝑒)
𝜎′ℎ(𝑎𝑡−𝑟𝑒𝑠𝑡)
At-rest: Ko = 1-sinΦ
Active: Ka = tan²(45-Φ/2) or 1/ tan²(45+Φ/2)
Passive: Kp = tan²(45+Φ/2)
You have 2 ways of solving for K. Rankine or Coulomb
method. If you have no backfill and the wall is vertical then
use Rankine, it’s the most popular method.
Use the Coulomb equation to calculate K when given the batter
angle and the friction angle between the backfill soil and the
wall surface is given. Use CERM Eq. 37.5 for active earth pressure,
CERM Eq. 37.14 for passive earth pressure, and CERM Eq. 37.21
for at-rest soil pressure.
λ rake angle of retaining wall face
angle of internal friction
angle of external friction
slope of backfill
Equations to remember:
Rankine Active
Ka = tan²(45-Φ/2) or 1/ tan²(45+Φ/2)
𝑃𝑎=Ka𝜎′𝑣-2c(Ka)1/2 (If cohesion isn’t given then that term goes to 0)
Ra=1
2𝑃𝑎H =
1
2𝐾𝑎𝛾H²
Rankine Passive
Kp = tan²(45+Φ/2)𝑃𝑝=Kp𝜎′𝑣 +2c(Kp)1/2 (If cohesion isn’t given then that term goes to 0)
Rp=1
2𝑃𝑝H =
1
2𝐾𝑝 𝛾 H²
Rankine At-Rest
Ko = 1-sinΦ
𝑃𝑜=Ko𝑃𝑣 (If cohesion isn’t given then that term goes to 0)
Ro=1
2𝑃𝑜H =
1
2𝐾𝑜𝛾H²
A basement wall is shown. Plot the distribution of total active earth
pressure acting on the wall. Also, compute the active horizontal
thrust acting on the wall due to the soil.
3 ft
9 ft
C=0, Φ=40°, γ=125
pcf
C=0, Φ=34°, γ=130
pcf
5 ft
Solution:
1) Solve for Ka for each layer.
1) Top 3’: Ka=tan²(45-40/2)= 0.217
2) 3’ to 12’: Ka=tan²(45-34/2)=0.283
2) Solve for vertical stresses as you move from top to
bottom. Be sure to account for the water table.
3) Solve for active pressure acting (𝑝𝑎) on the wall for each layer.
𝑃𝑎=Ka𝜎′𝑣-2c(Ka)1/2
4) Solve for the areas of each distribution (resultant force) and sum them all
up to find the total active horizontal force acting on the wall.
= 0.5(B)(H) or area of triangle
= 0.5(B)(H) + (B)(H) or area of triangle + square
What if you have a surcharge at the top of the wall?
More later earth pressure problems! Yay!
Next Topic: Soil Consolidation