Rankine's theory assumes that there is no wall friction (δ = 0), the ground and failure surfaces are straight planes, and that the resultant force acts parallel to the backfill slope.
In the case of retaining structures, the earth retained may be filled up the earth or natural soil. These backfill materials may exert certain lateral pressure on the wall. If the wall is rigid and does not move with the pressure exerted on the wall, the soil behind the wall will be in a state of elastic equilibrium. Consider the prismatic element E in the backfill at depth, z, as shown in Fig.
The element E is subjected to the following pressures:
Vertical pressure = σ = yz
Lateral pressure = σ_{k}_{,} where g is the effective unit weight of the soil.
If we consider the backfill is homogenous, then both σ_{v} and σ_{k} increases rapidly with depth z. In that case, the ratio of vertical and lateral pressures remain constant with respect to depth, that is σ_{k} / σ_{v} = σ_{k} / yz = constant = K_{ϕ}, where K_{ϕ} is the coefficient of earth pressure for atrest condition.
The atrest earth pressure coefficient (K_{ϕ}) is applicable for determining the active pressure in clays for strutted systems. Because of the cohesive property of clay, there will be no lateral pressure exerted in the atrest condition up to some height when the excavation is made. However, with time, creep and swelling of the clay will occur, and lateral pressure will develop. This coefficient takes the characteristics of clay into account and will always give a positive lateral pressure.
The lateral earth pressure acting on the wall of height H may be expressed as σ_{k} = K_{ϕ}yH.
The total pressure for the soil at rest condition, P_{ϕ} = 0.5K_{ϕyH}^{2}.
The value of K_{ϕ} depends on the relative density of sand and the process by which the deposit was formed. If this process does not involve artificial tamping, the value of K_{ϕ} ranges from 0.4 for loose sand to 0.6 for dense sand. Tamping of the layers may increase it upto 0.8.
From elastic theory, K_{ϕ} = μ/(1  μ), where μ is the Poisson's ratio.
According to Jaky (1994), a good approximation of K_{ϕ} is given by, K_{ϕ} = 1  sinϕ.
Coulomb (1776) developed a method for determining the earth pressure, in which he considered the equilibrium of the sliding wedge, which is formed when the movement of the retaining wall takes place. The sliding wadge is torn off from the rest of the backfill due to the movement of the wall. In the Active Earth pressure case, the siding wedge moves downwards & outwards on a slip surface relative to the intact backfill & in the case of Passive Earth pressure, the sliding wedge moves upward and inwards. The pressure on the wall is, in fact, a force of reaction which it has to exert to keep the sliding wedge in equilibrium. The lateral pressure on the wall is equal and opposite to the reactive force exerted by the wail in order to keep the siding wedge in equilibrium. The analysis is a type of limiting equilibrium method.
The following assumptions are made:
Some Graphical solutions for lateral Earth Pressure are
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1. What is earth pressure in civil engineering? 
2. What are the different types of earth pressure theories in civil engineering? 
3. How does Rankine's theory of earth pressure differ from Coulomb's theory? 
4. What is the Modified Coulomb's theory of earth pressure? 
5. How is earth pressure calculated in civil engineering? 

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