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20
Soil Retention Elements
3.2.3. Calculation of the ‘at rest’ pressure
p h = γ ⋅ z ⋅ λh ; pv = γ ⋅ z ⋅ λ v
The ‘at rest’ pressure is resolved by applying Jaky’s theory.
It is calculated as:
where:
λ h=
sin2 ( α + ϕ )

sin ( ϕ + δ ) · sin ( ϕ − β ) 

sin2α · 1 +
sin (α − δ ) · sin (α + β ) 



2
prest = γ ⋅ z ⋅ Krest
=
where:
Krest = 1− sin ϕ
z: depth
γ: unit weight of the soil
ϕ: internal friction angle of the soil
λ v = λh ⋅ cot g (α − δ)
z: depth
α: angle of the wall face with the horizontal
In the case where there is a slope or embankment, the
complementary formulation of the Corps of Engineers,
1961, is used.
γ: unit weight of the soil
δ: wall-soil friction angle
ϕ: internal friction angle of the soil
β: angle of the slope
3.2.4. Pressure from loads situated on the
ground
When the cohesion of the soil is considered:
ph = γ ⋅ z ⋅ λh − 2 ⋅ c ⋅ λ h ⋅ cos δ
3.2.4.1. Pressures produced by a uniformly
distributed load
where:
Coulomb’s method is applied and the horizontal and vertical pressures produced by a uniform surcharge equal:
c = cohesion of the soil
3.2.2. Calculation of the passive pressure
The calculation of the passive pressure is similar to the calculation of the active pressure. But one must change the
sign of the internal friction angle in the previous formulas.
Moreover, when the cohesion of the soil is considered:
ph = γ ⋅ z ⋅ λh + 2 ⋅ c ⋅ λh ⋅ cos δ
where:
c = cohesion of the soil
Fig. 2.1
CYPE