🏔️Intro to Geotechnical Science Unit 8 – Lateral Earth Pressures & Retaining Walls

Key Concepts and Definitions

• Lateral earth pressure refers to the horizontal pressure exerted by soil on a vertical or near-vertical structure (retaining walls, basement walls, or sheet piles)
• Active earth pressure occurs when a retaining wall moves away from the soil mass, allowing the soil to expand and mobilize its shear strength
  • Develops a minimum value of lateral earth pressure
• Passive earth pressure occurs when a retaining wall moves towards the soil mass, compressing the soil and causing it to resist the movement
  • Develops a maximum value of lateral earth pressure
• At-rest earth pressure is the lateral pressure that exists in the soil when no wall movement or soil deformation occurs
• Coefficient of lateral earth pressure (K) represents the ratio of horizontal to vertical effective stress in the soil
  • Depends on soil properties, wall movement, and drainage conditions
• Surcharge load is an additional vertical load applied to the soil surface behind the retaining wall (traffic, buildings, or construction equipment)
• Backfill refers to the soil placed behind a retaining wall during construction
  • Properties of the backfill material significantly influence the lateral earth pressures acting on the wall

Types of Earth Pressure

• Active earth pressure develops when a retaining wall moves away from the soil, allowing the soil to relax and mobilize its shear strength
  • Occurs when the wall tilts or rotates sufficiently to mobilize the full shear strength of the soil (typically 0.1% to 0.4% of the wall height)
• Passive earth pressure develops when a retaining wall moves towards the soil, causing the soil to compress and resist the movement
  • Requires larger wall movements (typically 2% to 5% of the wall height) to fully mobilize the passive resistance
• At-rest earth pressure occurs when the retaining wall is restrained from movement, and the soil is in its natural state of stress
  • Represents an intermediate condition between active and passive earth pressures
• Seismic earth pressure is an additional lateral force acting on retaining walls during earthquakes due to the inertial forces generated by ground accelerations
• Hydrostatic pressure is the pressure exerted by groundwater behind the retaining wall
  • Increases linearly with depth and can significantly contribute to the total lateral earth pressure
• Surcharge pressure is the additional lateral earth pressure caused by external loads applied to the soil surface behind the retaining wall (uniform, strip, or point loads)

Lateral Earth Pressure Theories

• Rankine's theory assumes a frictionless wall, a cohesionless soil, and a linear failure surface in the soil mass
  • Provides closed-form solutions for active and passive earth pressure coefficients based on the soil friction angle (K_a = \\tan^2(45^\\circ - \\phi/2) and K_p = \\tan^2(45^\\circ + \\phi/2))
• Coulomb's theory considers wall friction, cohesion, and a planar failure surface in the soil mass
  • Provides more accurate earth pressure coefficients for walls with friction and cohesive soils
  • Requires trial and error or graphical methods to determine the critical failure surface and corresponding earth pressure coefficients
• Log-spiral theory assumes a curved failure surface in the soil mass, which more closely represents the actual failure mechanism in soils
  • Provides more accurate results for passive earth pressure cases and for soils with high friction angles
• Limit equilibrium methods (Method of Slices or Wedge Method) divide the soil mass into slices or wedges and analyze the equilibrium of forces acting on each slice or wedge
  • Suitable for complex soil profiles, groundwater conditions, and external loads
• Finite element analysis is a numerical method that can model complex soil-structure interaction, including wall deformations and soil behavior
  • Requires advanced software and expertise to set up and interpret the results

Factors Affecting Lateral Earth Pressure

• Soil properties significantly influence the lateral earth pressures acting on retaining walls
  • Friction angle ($\\phi$) affects the shear strength and the earth pressure coefficients ($K_a$ and $K_p$)
  • Cohesion ($c$) provides additional shear strength and reduces the lateral earth pressures
• Wall geometry, including the height, inclination, and roughness of the wall face, affects the distribution and magnitude of lateral earth pressures
  • Taller walls experience higher lateral pressures due to the increased soil mass
  • Inclined walls (battered or stepped) can reduce active earth pressures but increase passive earth pressures
• Surcharge loads applied to the soil surface behind the retaining wall increase the lateral earth pressures
  • Uniform surcharge (traffic or construction equipment) increases the lateral pressure linearly with depth
  • Strip or point loads (foundations or concentrated loads) create a non-linear pressure distribution
• Groundwater conditions behind the retaining wall can significantly increase the lateral earth pressures
  • Hydrostatic pressure acts in addition to the earth pressures and increases linearly with depth
  • Seepage forces can reduce the effective stress in the soil and affect the earth pressure coefficients
• Earthquake loading generates additional dynamic lateral earth pressures on retaining walls
  • Pseudo-static methods (Mononobe-Okabe) estimate the seismic earth pressures based on the peak ground acceleration and the soil properties
• Construction sequence and compaction of the backfill can influence the lateral earth pressures
  • Over-compaction near the wall face can increase the lateral pressures and cause excessive wall deformations
  • Proper placement and compaction of the backfill are essential to ensure the desired performance of the retaining wall system

Retaining Wall Types and Design

• Gravity walls rely on their own weight and the weight of the soil above the base to resist the lateral earth pressures
  • Suitable for low to moderate wall heights (up to 3-4 meters) and can be constructed using concrete, masonry, or gabions
• Cantilever walls consist of a vertical stem and a base slab, which resist the lateral earth pressures through the cantilever action
  • Commonly used for wall heights up to 6-8 meters and can be constructed using reinforced concrete or steel sheet piles
• Counterfort walls have vertical ribs (counterforts) that connect the stem to the base slab, providing additional resistance to bending moments
  • Suitable for high walls (up to 12 meters) and can be more economical than cantilever walls for larger heights
• Anchored walls use tie-backs or ground anchors to transfer the lateral forces to a stable soil or rock layer behind the wall
  • Suitable for excavations or situations where limited space is available for wall construction
• Mechanically Stabilized Earth (MSE) walls use reinforcing elements (steel strips, geogrids, or geotextiles) embedded in the backfill to create a composite soil-reinforcement structure
  • Suitable for high walls (up to 30 meters) and can accommodate significant settlements and poor foundation conditions
• Design of retaining walls involves evaluating the external stability (overturning, sliding, and bearing capacity) and internal stability (structural design of wall components)
  • Load and Resistance Factor Design (LRFD) or Allowable Stress Design (ASD) methods are used to ensure adequate safety factors or resistance factors
  • Design codes and guidelines (AASHTO, FHWA, or Eurocode 7) provide recommendations for load combinations, material properties, and design criteria

Stability Analysis of Retaining Walls

• External stability analysis ensures that the retaining wall as a whole is stable against failure modes such as overturning, sliding, and bearing capacity
  • Overturning stability is evaluated by comparing the resisting moments (wall weight and passive pressure) to the overturning moments (active pressure and surcharge loads)
  • Sliding stability is assessed by comparing the available shear resistance (friction and passive pressure) to the horizontal driving forces (active pressure and surcharge loads)
  • Bearing capacity of the foundation soil is checked to ensure that the wall base does not experience excessive settlements or foundation failure
• Internal stability analysis verifies the structural integrity of the wall components (stem, base slab, or reinforcing elements)
  • Bending moments and shear forces in the stem and base slab are calculated using the lateral earth pressure distributions
  • Reinforcement layout and sizing are determined based on the maximum moments and forces, considering the appropriate safety factors or resistance factors
• Global stability analysis examines the overall stability of the retaining wall and the surrounding soil mass, considering potential deep-seated failure surfaces
  • Slope stability methods (Method of Slices or Finite Element Analysis) are used to evaluate the factor of safety against global instability
  • Particular attention is given to walls constructed on slopes or in areas with weak foundation soils
• Seismic stability analysis assesses the performance of retaining walls during earthquake loading
  • Pseudo-static methods (Mononobe-Okabe) are used to estimate the seismic earth pressures and evaluate the external and internal stability under seismic conditions
  • Displacement-based methods (Newmark sliding block analysis) can estimate the permanent wall displacements during earthquakes

Construction and Maintenance Considerations

• Site investigation and soil characterization are essential for the proper design and construction of retaining walls
  • Subsurface exploration (borings or test pits) and laboratory testing provide information on soil stratigraphy, strength, and deformation properties
  • Groundwater conditions and drainage requirements should be carefully evaluated to prevent hydrostatic pressures and seepage issues
• Selection of backfill material and compaction requirements are critical for the performance of retaining walls
  • Well-graded, granular soils with good drainage properties are preferred for backfill to minimize lateral pressures and ensure proper drainage
  • Compaction specifications (relative density or standard Proctor) should be followed to achieve the desired soil properties without inducing excessive lateral pressures
• Drainage systems, such as weep holes, drainage blankets, or geocomposite drains, are essential to prevent the buildup of hydrostatic pressures behind the wall
  • Proper design and construction of drainage systems ensure the long-term performance and stability of retaining walls
• Construction sequence and quality control measures should be carefully planned and implemented
  • Staged excavation and backfilling, temporary support systems, and monitoring of wall movements are important aspects of the construction process
  • Quality control testing (compaction tests, concrete strength tests, or reinforcement inspections) ensures that the materials and workmanship meet the design requirements
• Regular inspection and maintenance of retaining walls are necessary to identify and address potential issues
  • Monitoring wall movements, checking for signs of distress (cracks, tilting, or settlement), and assessing the condition of drainage systems are part of the maintenance program
  • Timely repairs and remedial measures can prevent minor issues from developing into major stability problems

Real-World Applications and Case Studies

• Highway and railway projects often require the construction of retaining walls to accommodate grade separations, embankments, or cut slopes
  • MSE walls and cantilever walls are commonly used in transportation infrastructure projects due to their cost-effectiveness and flexibility
• Residential and commercial developments in hilly or sloping areas rely on retaining walls to create level building sites and stabilize slopes
  • Gravity walls, segmental block walls, and soldier pile walls are popular choices for smaller-scale projects and landscaping applications
• Waterfront structures, such as quay walls, bulkheads, and seawalls, are designed to resist lateral earth pressures and hydrodynamic loads
  • Anchored walls, sheet pile walls, and caisson walls are suitable for waterfront applications, considering the unique challenges posed by the marine environment
• Excavation support systems for deep foundations, basements, or underground facilities require temporary or permanent retaining walls
  • Soldier pile and lagging walls, secant pile walls, and diaphragm walls are commonly used for excavation support, often in combination with ground anchors or bracing systems
• Landslide mitigation and slope stabilization projects employ retaining walls to prevent or control the movement of unstable soil or rock masses
  • Anchored walls, soil nail walls, and MSE walls are effective solutions for stabilizing slopes, particularly when combined with drainage improvements and surface protection measures
• Failure case studies and lessons learned from past projects provide valuable insights into the design, construction, and performance of retaining walls
  • The Malpasset Dam failure (France, 1959) highlighted the importance of considering the geological conditions and the potential for foundation instability
  • The collapse of the Nicoll Highway (Singapore, 2004) emphasized the need for proper design, construction quality control, and monitoring of deep excavations and retaining systems
  • The Pinheiros Station collapse (Brazil, 2007) underscored the significance of accounting for groundwater pressures and the influence of adjacent structures on the stability of retaining walls