8.1 At-rest, active, and passive earth pressure states

Lateral earth pressures are crucial in designing retaining walls and understanding soil-structure interactions. This topic explores three key pressure states: at-rest, active, and passive. Each state represents different soil conditions and wall movements, affecting the magnitude of horizontal stresses on structures.

Understanding these pressure states helps engineers design safer and more efficient retaining structures. We'll examine factors influencing earth pressures, calculation methods, and their impact on wall stability. This knowledge is essential for tackling real-world geotechnical challenges in construction and earthwork projects.

Earth Pressure States in Soil

Types of Earth Pressure States

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• Earth pressure states represent horizontal stresses exerted by soil on retaining structures
• At-rest earth pressure develops when retaining structure experiences no lateral movement
• Active earth pressure occurs when retaining wall moves away from soil mass
  • Allows soil to expand horizontally
  • Reduces lateral pressure
• Passive earth pressure forms when retaining wall moves towards soil mass
  • Compresses soil
  • Increases lateral pressure
• Magnitude of earth pressure follows order passive > at-rest > active
• Earth pressure coefficients (K) relate vertical effective stress to horizontal effective stress
  • K0 for at-rest state
  • Ka for active state
  • Kp for passive state

Soil Deformation and Stress Redistribution

• Transition from at-rest to active or passive states involves soil deformation
• Stress redistribution within soil mass occurs during state changes
• Soil particles rearrange leading to volume changes (expansion or compression)
• Shear planes may develop in soil mass during active or passive pressure development
• Magnitude of wall movement required for full active or passive pressure development varies
  • Typically 0.1-0.5% of wall height for active state (sandy soils)
  • Approximately 2-4% of wall height for passive state (sandy soils)
• Stress paths differ for each pressure state transition

Factors Influencing Earth Pressure

Soil Properties and Groundwater Conditions

• Soil type impacts earth pressure magnitudes (sand, clay, silt)
• Unit weight of soil affects vertical stress and resulting lateral pressures
• Cohesion in clayey soils reduces active pressures and increases passive resistance
• Internal friction angle influences soil shear strength and pressure coefficients
• Groundwater conditions alter effective stresses in soil mass
  • Saturated soil exerts higher pressures due to buoyancy effects
  • Seepage forces can increase or decrease earth pressures
• Pore water pressures impact effective stress calculations
  • Positive pore pressures reduce effective stress
  • Negative pore pressures (suction) can increase soil strength

Structural Geometry and Loading Conditions

• Retaining structure height directly affects magnitude of earth pressures
• Wall inclination modifies pressure distribution and resultant force direction
• Surcharge loads on retained soil increase earth pressures
  • Uniform loads (distributed pressure)
  • Point loads (concentrated forces)
• Type of wall movement influences pressure state development
  • Rotation about top (active case)
  • Rotation about bottom (passive case)
  • Translation (uniform movement)
• Soil compaction during backfilling can induce residual lateral stresses
• Overconsolidation ratio affects at-rest earth pressure coefficient (K0)
  • Higher OCR leads to increased K0 values

Environmental and Reinforcement Factors

• Temperature changes cause soil volume fluctuations
  • Expansion in hot conditions
  • Contraction in cold conditions
• Freeze-thaw cycles alter soil structure and strength properties
• Moisture content fluctuations impact soil cohesion and effective stress
• Reinforcement elements modify earth pressure distribution
  • Geosynthetics (geotextiles, geogrids) in mechanically stabilized earth walls
  • Soil nails in nailed soil walls
  • Anchors or tiebacks in anchored wall systems
• Vegetation root systems can provide additional soil reinforcement
• Chemical changes in soil (e.g., cementation) may alter pressure characteristics over time

Earth Pressure Calculation

Rankine's and Coulomb's Earth Pressure Theories

• Rankine's theory calculates active and passive earth pressures
  • Assumes cohesionless soils, horizontal backfills, vertical walls
  • Neglects wall friction
  • Active pressure coefficient: $K_a = tan^2(45° - φ/2)$
  • Passive pressure coefficient: $K_p = tan^2(45° + φ/2)$
• Coulomb's theory accounts for wall friction, inclined backfills, cohesive soils
  • More complex equations for pressure coefficients
  • Considers wall-soil interface friction angle (δ)
  • Allows for inclined backfill surface (β)
  • Incorporates wall face inclination (α)
• Both theories assume plane failure surfaces in soil mass
• Graphical solutions (e.g., Culmann's method) available for complex geometries

Pressure Calculations and Force Distributions

• Calculate vertical effective stress at any depth: $σ'_v = γ * z$
• Determine horizontal earth pressure: $σ_h = K * σ'_v + u$
  • K is the appropriate earth pressure coefficient (Ka, K0, or Kp)
  • u is the pore water pressure
• Incorporate surcharge loads in pressure calculations
  • Uniform surcharge: $Δσ_h = K * q$
  • Point loads: Use Boussinesq theory for stress distribution
• Account for cohesion in cohesive soils
  • Reduces active pressure: $σ_a = K_a * σ'_v - 2c * √(K_a)$
  • Increases passive pressure: $σ_p = K_p * σ'_v + 2c * √(K_p)$
• Calculate resultant force magnitude and point of application
  • Triangular distribution: $F = 1/2 * γ * H^2 * K$, acts at H/3 from base
  • Trapezoidal distribution: Use method of moments

Earth Pressure Impact on Retaining Structures

Stability Analysis of Retaining Walls

• Evaluate sliding stability
  • Compare horizontal driving forces to resisting forces
  • Factor of safety against sliding: $FS_{sliding} = \frac{Resisting Force}{Driving Force}$
• Assess overturning stability
  • Compare overturning moments to resisting moments
  • Factor of safety against overturning: $FS_{overturning} = \frac{Resisting Moment}{Overturning Moment}$
• Check bearing capacity
  • Ensure applied pressure does not exceed soil bearing capacity
  • Consider eccentricity of resultant force
• Analyze global stability using slip circle methods (Bishop, Janbu)
• Evaluate internal stability of reinforced soil structures
  • Tensile capacity of reinforcement layers
  • Pullout resistance of reinforcement

Dynamic and Long-term Considerations

• Assess seismic earth pressures
  • Mononobe-Okabe method for pseudo-static analysis
  • Seed-Whitman approach for dynamic earth pressures
• Consider earth pressure redistribution during and after construction
  • Account for soil consolidation and creep effects
• Evaluate potential for progressive failure
  • Analyze cumulative deformations under cyclic loading
  • Assess long-term creep behavior of retained soil
• Analyze composite retaining systems
  • Load transfer between soil and structural elements (anchors, tiebacks)
  • Distribution of earth pressures in multi-tiered walls
• Consider effects of drainage systems on long-term pressure distribution
  • Weep holes, drainage blankets, geocomposite drains