Test: Earth Pressure at Rest - Civil Engineering (CE) MCQ

Coefficient of Earth pressure:
It is the ratio of horizontal effective stress σh and vertical effective vertical stress σv
Earth pressure at rest:

• It is the ratio of horizontal and vertical effective vertical stress when the retaining wall does not move at all.
• Sometimes it is also referred to as neural lateral earth pressure or lateral earth pressure
• K_o = 1−sin⁡ϕ

The coefficient of earth pressure at rest (K₀) is given by,

σ_h – Effective horizontal stress
σ_v –  Effective vertical stress
Active earth pressure:

• It is the ratio of horizontal to vertical stress when the retaining wall moves away from the retained soil.
• 

​​Passive earth pressure:

• It is defined as the ratio of horizontal to vertical stress when the retaining wall moves towards the retaining wall.
• 

Active earth pressure

• Soil exerts a push against the retaining wall by virtue of its tendency to slip laterally and seek its natural slope or angle of repose. Thus making the wall move slightly away from the backfilled soil mass. This kind of pressure is known as "active earth pressure".
• The portion of the backfill which moves along with the wall is termed a failure wedge.
• The movement of the wedge is being resisted by the shear strength of the soil which develops over the rupture surface upward direction that causes the decrease of pressure acting on the wall.
• This decreases in pressure with the movement of the wall takes place up to an extent when the entire shear strength of the soil is being mobilized and the pressure acting on the wall becomes minimum and is referred to as active pressure.
• For active state strain (ΔH/H) is 0.2% for dense soils & 0.5% for loose soils.

Earth pressure theory:
When the soil is retained behind the retaining structures it will exert lateral pressure on the structure called earth pressure.
1. Passive earth pressure Cohesion less soil

Since P_p is acting on a major principle plane,
Passive earth pressure, 
Passive earth pressure coefficient, 
Where, μ = Poisson ratio, σ_z = vertical stress, C = cohesion of soil, ϕ = Angle of internal friction,
σ₁ = Major stress and σ₂ = Minor stress
In passive state, the minor principal stress denoted by σ₂ is in vertical direction, while the major principal stress σ₁ is in horizontal direction.

Assumptions given by Rankine are:
1. The soil is homogeneous and isotropic, which means c, φ and γ have the same values everywhere, and they have the same values in all directions at every point.
2. The most critical shear surface is a plane.
3. The ground surface is a plane that may be horizontal or inclined.
4. The wall is infinitely long so that the problem may be analyzed in only two dimensions.
5. The wall moves sufficiently to develop the active or passive condition.
6. The wall surface at the back is vertical and smooth.
7. The retaining wall yields about the base and thus deformation condition satisfies plastic equilibrium.

Active Earth Pressure on Retaining wall: 

• When retaining wall, retain dry backfill and if wall rotates about its toe, thus moving away from backfill, the soil mass expands resulting in a decrease of the earth pressure.at this stage entire shear resistance has been mobilized and the force acting on the wall at this stage is called active earth pressure.
• Considering a vertical retaining wall with dry cohesionless backfill having an unloaded horizontal surface and the back of the wall is assumed to be smooth from Rankine's theory active earth pressure at the base of wall is given as:
•  p_A=K_AγH, Where γ = bulk unit weight of soil above water table , K_A = Active earth pressure coefficient , H = Total height of retaining wall
• The force per unit length of the wall due to the active pressure distribution is the total active thrust or total active pressure (P_A) and is given by the area of the active pressure distribution diagram and acts through the centre of the area.
•   acting at a distance H/3 above the base of the wall.
  

Hence ,Total active pressure due to dry backfill acting at h/3 above the base is directly proportional to H².