The following 3 characteristic (limit) modes of soil actions (pressures) on a retaining structure can be distinguished:
The pressure is directly related to the displacement of a retaining structure. The displacement is determined using the rotation of element ρ, which is assumed to approximately equal the ratio f/H (wall top displacement / element height).
Pa <- ρ ≤ ρa
Po <- ρ = 0
Pp <- ρ ≥ ρp
Where ρa and ρp are the limit pressures for the corresponding modes
It is assumed that there is a linear relation between the following pressures:
Ka * P < Ko * P < Kp * P,
Where P is a certain pressure, which in the simplest case, is equivalent to hydrostatic pressure. Intermediate pressures are contained between the limit pressures.
Where ξ from the interval <-1,1> corresponds to the linearly standardized variable from the interval <ρa, ρp>.
Soil pressures depend on the soil unit weight γ, natural slope angle ϕ, inclination of a retaining element β, and the backfill inclination α. The effect of the wall-soil friction angle δ is disregarded.
It is assumed, that the pressure resulting from loads applied to soil is obtained by multiplying P'(z) pressure by the appropriate K coefficient (Ko, Ka, Kp or their combination), analogously as for soil pressure.
Depending on the code selected, the following methods and factors of load distribution are used:
PN-83/B-03010: α=Φ, β=45+Φ/2 as well as P1= 0 and P2 =K q
PN-85/S-10030: α=Φ, β=45+Φ/2 as well as P1=K q and P2 =K q
SETRA (France): α=Φ, β=45+Φ/2 as well as P1= K q and P2 =K q
RD 31.31.27-81 (Russia): No algorithm
PN-83/B-03010: α=Φ, β=45+Φ/2 as well as P3= K Q and P4 =0
PN-85/S-10030: α=Φ, β=45+Φ/2 as well as P3= K Q and P4 =K Q
SETRA (France): α=Φ, β=45+Φ/2 as well as P3= K Q and P4 =K Q
RD 31.31.27-81 (Russia): α=45+Φ/2, β=45+Φ/2 as well as P3= K Q and P4 =K Q
PN-83/B-03010: α=γ=Φ, β=δ=45+Φ/2 as well as P1=P4=0 and P2=P3=K q
PN-85/S-10030: α=Φ, β=45+Φ/2 as well as P1=P4= P2=P3=K q
SETRA (France): α=Φ, β=45+Φ/2 as well as P1=P4= P2=P3=K q
RD 31.31.27-81 (Russia): α=45+Φ/2, β=45+Φ/2 as well as P1=P4= P2=P3=K q
Forces of soil cohesion are ignored when calculating soil pressure. The cohesion is not always taken into account in calculations, because it has a favorable effect on structures. It is a force which causes an excavation to be preserved even without a retaining element. The cohesion acts in the direction opposite to the displacement of a retaining element, thus reducing the action of the soil on a wall. A value of pressure due to cohesion is constant for a given soil and equals:
Where c denotes soil cohesion and coefficient Kc equals:
Cohesion is considered only for cohesive soils.