CELE Geotechnical Engineering — Lateral Earth Pressure and Retaining StructuresConcept Map

Concept

Earth-Pressure States and Coefficients

Sub Concepts

• At-Rest Pressure (K₀)
• Active Pressure (Kₐ)
• Passive Pressure (Kₚ)
• Rankine Theory
• Coulomb Theory

Relationship To Central

Foundation for all pressure calculations; determines the magnitude of force acting on the wall

Concept

Resultant Thrust and Pressure Distribution

Sub Concepts

• Vertical Pressure Distribution
• Horizontal Thrust Calculation
• Point of Application
• Effect of Cohesion
• Effect of Surcharge
• Hydrostatic Pressure

Relationship To Central

Converts coefficients into actual forces and moments for stability analysis

Concept

Retaining-Wall Types and Design

Sub Concepts

• Gravity Walls
• Cantilever Walls
• Sheet Piles
• Anchored Walls
• Soldier Pile Walls

Relationship To Central

Structural forms used to resist lateral earth pressure

Concept

Stability Analysis and Safety Checks

Sub Concepts

• Overturning Check (FS ≥ 1.5–2.0)
• Sliding Check (FS ≥ 1.5)
• Bearing Capacity Check
• Tension in Base
• Middle-Third Rule

Relationship To Central

Methods to verify that a designed wall meets geotechnical and structural safety requirements

Concept

Special Conditions and Modifications

Sub Concepts

• Cohesive Soils
• Water Table and Seepage
• Sloping Backfill
• Wall Friction Angle
• Surcharge Loads

Relationship To Central

Factors that modify basic pressure calculations in practical applications

To

Earth-Pressure Coefficients (K₀, Kₐ, Kₚ)

From

Earth-Pressure States

Strength

strong

Relationship

States determine which coefficient to use; coefficient value depends directly on whether wall moves away (active), toward (passive), or not at all (at-rest)

To

Resultant Thrust Calculation

From

Earth-Pressure Coefficients

Strength

strong

Relationship

Thrust magnitude is calculated using Pa = ½Kγ H² or Pp = ½KpγH²; coefficient is the primary multiplier

To

Point of Application

From

Resultant Thrust Calculation

Strength

strong

Relationship

For dry cohesionless backfill, the resultant acts at H/3 from the base; this distance is crucial for moment calculations in stability checks

To

Overturning Check

From

Resultant Thrust and Pressure

Strength

strong

Relationship

The horizontal component of active thrust (Pa) creates the overturning moment; its point of application determines the magnitude of this moment

To

Resultant Thrust

From

Cohesion Effect

Strength

moderate

Relationship

Cohesion reduces the active pressure by 2c√Kₐ and creates a tension crack near the surface at depth Ht = 2c√Kₐ/γ; reduces overall thrust magnitude

To

Resultant Thrust

From

Water Table and Seepage

Strength

strong

Relationship

Water below the water table adds full hydrostatic pressure γw·hw²/2 independently of soil pressure; increases total thrust significantly and changes point of application

To

Resultant Thrust

From

Surcharge Load

Strength

moderate

Relationship

Surcharge adds uniform pressure Ka·q across the wall height; increases active thrust and acts at H/2 from base, affecting overturning moment

To

Overturning Check

From

Wall Weight

Strength

strong

Relationship

Weight acts at the center of gravity of the wall section; its moment about the toe resists the overturning moment from earth pressure

To

Sliding Check

From

Wall Weight

Strength

strong

Relationship

Weight provides the normal force; friction force = μ × W provides resistance to sliding from horizontal thrust component

To

Stability Analysis

From

Overturning Check

Strength

strong

Relationship

First stability check performed; if FS_OT < 1.5–2.0, wall design is inadequate and must be enlarged

To

Stability Analysis

From

Sliding Check

Strength

strong

Relationship

Second stability check; compares friction resistance to horizontal thrust; if FS_slide < 1.5, base friction is inadequate

To

Stability Analysis

From

Bearing Capacity Check

Strength

strong

Relationship

Third stability check; ensures resultant force falls within middle third of base (e ≤ L/6) to avoid excessive tension and bearing failure

To

Earth-Pressure Coefficients

From

Gravity Wall Type

Strength

moderate

Relationship

Gravity walls rely entirely on mass to resist earth pressure; active pressure coefficients determine the forces the wall must resist

To

Stability Analysis

From

Cantilever Wall Type

Strength

moderate

Relationship

Cantilever walls use reinforced concrete and structural action (heel effect) to reduce base size required; still require all three stability checks

To

Passive Pressure

From

Sheet Pile Type

Strength

moderate

Relationship

Sheet piles in excavations develop passive resistance along the depth of embedment; passive pressure helps anchor the wall

To

Active Pressure Coefficient

From

Rankine Theory

Strength

strong

Relationship

Rankine provides the simplified formula Ka = tan²(45° - φ/2) for smooth vertical walls with horizontal backfill; foundation for all active pressure calculations

To

Earth-Pressure Coefficients

From

Coulomb Theory

Strength

moderate

Relationship

Coulomb generalizes Rankine by including wall friction angle δ and sloping backfill; gives more accurate coefficients for real walls but requires graphical or iterative solution

To

Coulomb Theory

From

Sloping Backfill

Strength

moderate

Relationship

Sloping backfill (angle β) increases earth pressure above the horizontal case; Coulomb method required; vertical and horizontal components must be analyzed separately

To

Passive Pressure

From

Wall Friction Angle

Strength

moderate

Relationship

Wall friction angle δ increases passive resistance significantly; Kp increases when δ > 0, making anchored walls more effective

To

Middle-Third Rule

From

Tension in Base

Strength

strong

Relationship

If resultant eccentricity e > L/6 (outside middle third), tension develops at the toe; concrete walls avoid tension design by using the middle-third rule

To

Allowable Pressure

From

Bearing Capacity

Strength

strong

Relationship

Toe pressure must not exceed soil bearing capacity; if soil is weak, foundation must be enlarged or ground improved

To

Horizontal and Vertical Components

From

Resultant Thrust

Strength

moderate

Relationship

For vertical walls, thrust is horizontal; for inclined walls, thrust acts normal to wall face and must be resolved into horizontal and vertical components

To

Design Pressure

From

Active Pressure

Strength

strong

Relationship

Active pressure (smallest) is used for design of structures resisting earth (retaining walls, basement walls); represents the critical design condition

To

Design Conservatism

From

Passive Pressure

Strength

moderate

Relationship

Passive pressure (largest) is rarely fully mobilized in design; only credited when wall can reliably push soil (e.g., sheet piles); usually neglected for conservative design

To

Stability Analysis

From

Safety Factors

Strength

strong

Relationship

Each of the three checks uses a target FS (overturning 1.5–2.0, sliding 1.5, bearing based on soil); FS ensures adequate safety margin