8.2 Rankine's and Coulomb's earth pressure theories
4 min read•august 16, 2024
Earth pressure theories are crucial for understanding how soil pushes against structures. assumes a frictionless wall and , while accounts for wall friction and complex geometries.
These theories help engineers design safe retaining walls and other structures. Rankine's theory is simpler but limited, while Coulomb's theory is more versatile for real-world applications. Both are essential tools in geotechnical engineering.
Rankine's Earth Pressure Theory
Fundamental Principles
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Frontiers | Review of the Deformation Mechanism and Earth Pressure Research on the Double-Row ... View original
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Earth Pressure of Retaining Structure Induced by Subgrade under Rainfall View original
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Frontiers | Review of the Deformation Mechanism and Earth Pressure Research on the Double-Row ... View original
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Based on concept of plastic equilibrium in soils where soil mass verges on failure
Assumes frictionless, vertical wall and planar failure surface within soil mass
Considers two extreme states
(minimum lateral pressure)
(maximum lateral pressure)
Coefficient of lateral earth pressure (K) relates vertical to horizontal effective stress
Principal stresses rotate 45° + φ/2 for active condition and 45° - φ/2 for passive condition (φ = soil's )
Applicable to cohesionless and cohesive soils with slight calculation differences
Earth pressure distribution assumed linear with depth, increasing from zero at surface
Calculations for Cohesionless Soils
Active earth pressure coefficient (Ka) calculated as Ka=tan2(45°−φ/2)
Passive earth pressure coefficient (Kp) determined by Kp=tan2(45°+φ/2)
Lateral earth pressure at depth (z) calculated using σh=K∗γ∗z (γ = unit weight of soil)
Total active thrust (Pa) computed by integrating active pressure distribution over wall height
Pa=0.5∗Ka∗γ∗H2 (H = wall height)
Total passive resistance (Pp) calculated similarly
Pp=0.5∗Kp∗γ∗H2
Point of application for active thrust and passive resistance located at H/3 from wall base
Modified equations used for sloping backfills to account for soil surface inclination angle
Active vs Passive Earth Pressures
Comparison of Active and Passive States
Active state occurs when wall moves away from soil mass
Soil expands horizontally
Vertical stress remains constant while horizontal stress decreases
Passive state occurs when wall moves towards soil mass
Soil compresses horizontally
Vertical stress remains constant while horizontal stress increases
Active pressure always less than passive pressure for same soil conditions
At-rest pressure represents intermediate state between active and passive
Practical Applications
Active pressure used in design of retaining walls and sheet pile walls
Determines minimum wall thickness and reinforcement requirements
Passive pressure utilized in design of anchor blocks and sheet pile toe stability
Provides resistance against sliding and overturning
At-rest pressure considered for rigid structures (basement walls, bridge abutments)
Selection of appropriate pressure state crucial for safe and economical design
Overestimation leads to conservative but costly designs
Underestimation results in unsafe structures
Coulomb's Earth Pressure Theory
Assumptions and Limitations
Assumes planar failure surface and considers equilibrium of entire soil wedge behind wall
Accounts for wall friction and non-vertical back face of retaining wall
Assumes soil isotropic, homogeneous, and obeys Mohr-Coulomb failure criteria