Stresses in Soil Mass - Concept Map
Effective Stress Principle and Stress Distribution in Soil
Related concepts
Effective Stress (σ')
Sub concepts
- Terzaghi's Effective-Stress Equation
- Total Stress Component
- Pore Pressure Component
- Strength and Settlement Control
Relationship to central
Foundation principle governing soil behavior
Total Stress (σ)
Sub concepts
- Geostatic Stress
- Layer-by-Layer Summation
- Unit Weight Application
- Saturated vs. Unsaturated Conditions
Relationship to central
First component of effective stress calculation
Pore Pressure (u)
Sub concepts
- Hydrostatic Pore Pressure
- Seepage-Induced Pressure
- Water Table Position
- Quick Condition (u approaching σ)
Relationship to central
Second component of effective stress; critical below water table
Stress Increase from Surface Loads (Δσ)
Sub concepts
- Boussinesq Point Load Theory
- 2:1 Approximation Method
- Influence Factors
- Newmark's Chart
Relationship to central
Application of effective-stress principle to foundation design
Boussinesq Point Load
Sub concepts
- Vertical Stress Directly Below Load
- Stress at Horizontal Offset (r)
- Depth Dependency (z)
- Decay Function with Distance
Relationship to central
Theoretical model for concentrated load stress distribution
2:1 Spread Method (Approximate)
Sub concepts
- Footing Dimensions (B, L)
- Load Spreading at Depth
- Quick Field Calculations
- Depth and Area Relationships
Relationship to central
Practical footing design method based on 2:1 slope assumption
Water Table Effects
Sub concepts
- Submerged vs. Above Water Table
- Saturated Unit Weight (γsat)
- Buoyancy Effects
- Capillary Rise Complications
Relationship to central
Controls pore pressure and effective stress profile
Seepage and Flow Conditions
Sub concepts
- Upward Seepage Pressure
- Downward Seepage Pressure
- Hydraulic Gradient
- Critical Gradient (Quick Condition)
Relationship to central
Alters pore pressure beyond hydrostatic; affects effective stress
Board-Exam Common Errors
Sub concepts
- Forgetting Pore Pressure Below Water Table
- Using Wrong Unit Weight
- Misapplying 2:1 Spread Formula
- Ignoring Seepage Pressure
Relationship to central
Practical knowledge for PRC licensure exam success
Concept connections
- Effective Stress PrincipleTotal StressEffective stress is calculated as: σ' = σ - u; total stress is the first component
- Effective Stress PrinciplePore PressurePore pressure is subtracted from total stress in the effective-stress equation; both are equally critical
- Total StressUnit Weight SelectionTotal stress is computed by summing γ × z for each layer; correct unit weight is essential
- Pore PressureWater Table EffectsPore pressure develops only below the water table; water table position is the primary control
- Pore PressureSeepage and Flow ConditionsSeepage pressure adds to or subtracts from hydrostatic pore pressure depending on flow direction
- Effective Stress PrincipleStrength and Settlement ControlEffective stress (not total stress) governs shear resistance, compressibility, and bearing capacity
- Stress Increase from Surface LoadsBoussinesq Point LoadBoussinesq theory is one method to calculate stress increase beneath a point load
- Stress Increase from Surface Loads2:1 Approximation Method2:1 method is an approximate alternative to rigorous solutions, suitable for quick footing estimates
- Boussinesq Point LoadDepth DependencyBoussinesq stress increase is inversely proportional to z²; deeper points experience lower stress
- 2:1 Approximation MethodFoundation Design2:1 method is widely used in foundation design for quick settlement and bearing-capacity estimates
- Water Table EffectsSaturated Unit WeightBelow water table, γsat (not γ_moist) must be used for total stress calculation
- Quick ConditionSeepage and Flow ConditionsQuick condition (u ≈ σ, σ' ≈ 0) occurs when critical hydraulic gradient ic is reached; upward seepage is the common cause
- Board-Exam Common ErrorsPore Pressure Below Water TableMost frequent exam error: forgetting that u is nonzero and reduces σ' below the water table
- Board-Exam Common Errors2:1 Formula MisapplicationCommon error: using B×L instead of (B+z)(L+z) in the denominator
- Effective Stress PrincipleFoundation Bearing CapacityBearing capacity equations (e.g., Terzaghi, Meyerhof) use effective stresses and effective stress parameters
- Stress Increase from Surface LoadsSettlement CalculationStress increase Δσ is input to settlement formulas; accurate Δσ is essential for reliable settlement estimates
- Influence FactorsNewmark ChartNewmark's chart is a graphical tool based on influence factors for non-rectangular loaded areas
- Seepage PressureHydraulic GradientSeepage pressure is proportional to hydraulic gradient i; when i ≥ ic, quick condition is reached
- Capillary RiseWater Table EffectsCapillary rise extends above the true water table; pore pressure in capillary zone is negative (tension)
- Total StressGeostatic StressGeostatic stress is the in-situ total stress before any external load is applied; foundation stress increases add to it
Diagrams
Stresses in Soil Mass — Complete Concept Hierarchy
Hierarchical mind map showing the complete structure of stress concepts in soil mass, from fundamental principles (effective stress) through calculation methods (Boussinesq, 2:1 method) to practical applications and common examination errors. This map organizes all key topics and their relationships for comprehensive review.
Effective Stress Calculation Procedure
Step-by-step flowchart for calculating effective stress at any soil depth. Guides the user through selecting appropriate unit weights, accounting for the water table, considering seepage conditions, and identifying critical quick conditions. This procedure is essential for all PRC board-exam problems involving soil stress analysis.
Choosing the Correct Stress-Increase Method
Decision tree for selecting the appropriate stress-increase calculation method based on load type and geometry. Helps exam takers quickly identify whether to use Boussinesq point load theory, the 2:1 approximation, influence factors, or Newmark's chart. This saves time and reduces calculation errors on PRC exams.
Effective Stress Profile Construction (Layered Deposit)
Systematic procedure for constructing the effective-stress profile through a layered soil deposit. Shows how total stress increases layer by layer, how pore pressure develops below the water table, and how effective stress is derived at each depth. Essential for understanding soil behavior and performing settlement calculations.
Common Examination Errors — Diagnostic Flowchart
Diagnostic flowchart to identify and correct common mistakes in effective-stress calculations. Guides students through four critical checks: water table inclusion, unit weight selection, 2:1 formula application, and seepage pressure accounting. This is invaluable for exam preparation and quality assurance before submitting answers.
Soil State Transitions Under Varying Pore Pressure
State diagram showing how soil transitions between normal (drained) conditions, suspended (critical) conditions, and quick (unstable) conditions based on pore pressure changes. Illustrates the progressive danger of increasing pore pressure due to upward seepage and the critical role of the effective-stress principle in foundation safety.
Boussinesq Point Load Problem-Solving Flow
Step-by-step problem solver for Boussinesq point load calculations. Distinguishes between the simplified case (load directly above observation point) and the general case (offset load). Includes reasonableness checks to catch common calculation errors. Essential for settling and bearing-capacity problems in PRC exams.
Composition of Total Stress: Above vs. Below Water Table
Pie charts comparing the composition of total stress in unsaturated versus saturated zones. Above the water table, all stress is carried by grain-to-grain contact (100% σ'). Below the water table, the total stress is split between effective stress and pore pressure, illustrating how water reduces the soil skeleton's load-carrying capacity and the critical importance of pore pressure in effective-stress calculations.