CELE Geotechnical Engineering — Consolidation and SettlementConcept Map

Concept

Primary Consolidation Settlement

Sub Concepts

• Normally Consolidated (NC) Clay
• Overconsolidated (OC) Clay
• Compression Index (Cc)
• Recompression Index (Cr)
• Void Ratio (e)
• Effective Stress (σ')
• Settlement Equation

Relationship To Central

Core mechanism of soil compression under load

Concept

Time Rate of Consolidation

Sub Concepts

• Degree of Consolidation (U)
• Time Factor (Tv)
• Coefficient of Consolidation (cv)
• Drainage Path (Hdr)
• Double vs Single Drainage
• U-Tv Relationships
• Time Calculations

Relationship To Central

Governs how fast settlement occurs

Concept

Soil Properties & Classification

Sub Concepts

• Initial Void Ratio (e₀)
• Preconsolidation Stress (σ'c)
• Initial Effective Stress (σ'₀)
• Stress Increase (Δσ)
• Saturation Conditions
• Clay Type & Plasticity

Relationship To Central

Determines settlement behavior and rates

Concept

Drainage Conditions

Sub Concepts

• Double Drainage (Both Surfaces)
• Single Drainage (One Surface)
• Drainage Path Length
• Hydraulic Conductivity
• Permeability Effects

Relationship To Central

Controls water expulsion rate and settlement timing

Concept

Settlement Prediction & Analysis

Sub Concepts

• Magnitude of Settlement
• Rate of Settlement
• Time to Specific Consolidation
• Differential Settlement
• Long-Term Settlement Behavior

Relationship To Central

Practical application for design and assessment

Concept

Mathematical Formulations

Sub Concepts

• Terzaghi's Consolidation Theory
• e-log σ' Relationships
• Tv-U Conversion Functions
• Settlement Formula Variants
• Logarithmic Functions

Relationship To Central

Tools to quantify and predict consolidation

To

Compression Index (Cc)

From

Primary Consolidation Settlement

Strength

strong

Relationship

Cc directly determines magnitude of settlement through the settlement equation

To

Void Ratio (e)

From

Primary Consolidation Settlement

Strength

strong

Relationship

Initial void ratio e₀ appears in denominator of settlement formula; higher e₀ means more compressible soil

To

Coefficient of Consolidation (cv)

From

Time Rate of Consolidation

Strength

strong

Relationship

cv directly determines speed of water expulsion and consolidation time; appears in Tv formula

To

Degree of Consolidation (U)

From

Time Factor (Tv)

Strength

strong

Relationship

Tv and U are interdependent; U increases as Tv increases through non-linear logarithmic relationship

To

Time Factor (Tv)

From

Drainage Path (Hdr)

Strength

strong

Relationship

Hdr appears as square term in Tv; doubles in Hdr increases time by factor of 4

To

Compression Index (Cc)

From

Normally Consolidated (NC) Clay

Strength

strong

Relationship

NC clay uses Cc for entire loading history; slope of virgin e-log σ' curve

To

Recompression Index (Cr)

From

Overconsolidated (OC) Clay

Strength

strong

Relationship

OC clay uses smaller Cr when reloading within preconsolidation stress range

To

Overconsolidated (OC) Clay

From

Preconsolidation Stress (σ'c)

Strength

strong

Relationship

σ'c defines the boundary between Cr and Cc regions; critical threshold for settlement calculation

To

Drainage Path (Hdr)

From

Double Drainage

Strength

strong

Relationship

Double drainage reduces effective drainage path to H/2, accelerating consolidation by factor of 4

To

Drainage Path (Hdr)

From

Single Drainage

Strength

strong

Relationship

Single drainage uses full thickness H as drainage path, extending consolidation time

To

Primary Consolidation Settlement

From

Settlement Magnitude

Strength

strong

Relationship

Primary settlement is dominant component in saturated clay layers under sustained loading

To

Time Rate of Consolidation

From

Settlement Prediction & Analysis

Strength

moderate

Relationship

Cannot predict differential settlement without understanding rate; timing affects building tolerance

To

Primary Consolidation Settlement

From

Initial Effective Stress (σ'₀)

Strength

strong

Relationship

σ'₀ determines initial position on e-log σ' curve; final stress = σ'₀ + Δσ

To

Primary Consolidation Settlement

From

Stress Increase (Δσ)

Strength

strong

Relationship

Δσ represents load increment; larger Δσ increases vertical distance on logarithmic scale, increasing settlement

To

Time Factor (Tv)

From

U ≤ 60% Formula

Strength

strong

Relationship

Parabolic approximation Tv = π/4 × U² valid for early-stage consolidation

To

Time Factor (Tv)

From

U > 60% Formula

Strength

strong

Relationship

Logarithmic formula Tv = 1.781 - 0.933 × log(100-U) used for later-stage consolidation

To

Time Factor (Tv)

From

Terzaghi's Consolidation Theory

Strength

strong

Relationship

Terzaghi developed the mathematical framework relating Tv, U, and consolidation behavior

To

Drainage Path (Hdr)

From

Layer Thickness (H)

Strength

strong

Relationship

H is fundamental input; Hdr = H/2 (double) or H (single) determines actual drainage distance

To

Coefficient of Consolidation (cv)

From

Hydraulic Conductivity

Strength

moderate

Relationship

cv depends on both permeability (k) and compressibility; higher k allows faster consolidation

To

Primary Consolidation Settlement

From

Saturation Conditions

Strength

strong

Relationship

Consolidation theory applies to saturated soils; unsaturated soils exhibit different behavior