Bearing Capacity of Soils - Concept Map
Bearing Capacity of Soils
Related concepts
Ultimate Bearing Capacity (qu)
Sub concepts
- Terzaghi's Equation (strip footing)
- Shape Factor Modifications (square, circular, rectangular)
- Bearing-Capacity Factors (Nc, Nq, Nγ)
- General Shear vs Local Shear Failure
Relationship to central
Core calculation — determines soil's maximum load-carrying ability before shear failure
Terzaghi's Bearing Capacity Equation
Sub concepts
- Cohesion Component (c·Nc)
- Surcharge Component (q·Nq)
- Width Component (½γ·B·Nγ)
- Three soil-strength contributions
Relationship to central
Fundamental formula governing ultimate bearing capacity calculation
Bearing-Capacity Factors (Nc, Nq, Nγ)
Sub concepts
- Function of soil friction angle φ
- Tabulated values from soil mechanics references
- For φ=0 clay: Nc=5.7, Nq=1, Nγ=0
- Increase nonlinearly with increasing φ
Relationship to central
Dimensionless coefficients that depend on friction angle φ
Shape Factors
Sub concepts
- Strip footing: Nc coefficient = 1.0, Nγ coefficient = 0.5
- Square footing: Nc coefficient = 1.3, Nγ coefficient = 0.4
- Circular footing: Nc coefficient = 1.3, Nγ coefficient = 0.3
- Rectangular: interpolated between strip and square
Relationship to central
Modify equation for non-strip geometries; affect cohesion and width terms
Depth of Foundation (Df)
Sub concepts
- Shallow footing definition (Df/B < 3)
- Surcharge pressure calculation
- Water-table depth relative to Df
- Confinement effect on bearing capacity
Relationship to central
Controls overburden surcharge q = γ·Df; deeper foundations have higher capacity
Footing Width (B) and Geometry
Sub concepts
- Strip footing (infinite length, finite B)
- Square footing (B = L)
- Circular footing (diameter = B)
- Rectangular footing (L and B distinct)
Relationship to central
Directly affects the width-dependent term ½γ·B·Nγ in bearing-capacity equation
Soil Unit Weight (γ and γ')
Sub concepts
- Dry unit weight γd (above water table)
- Saturated unit weight γsat (below water table)
- Submerged unit weight γ' = γsat - γw
- Water-table location affects which unit weight to use
Relationship to central
Material property appearing in surcharge and width terms; changes with water saturation
Soil Cohesion (c) and Friction Angle (φ)
Sub concepts
- Cohesion c (kPa) — undrained shear strength
- Effective stress friction angle φ' — angle of repose behavior
- Undrained strength cu for saturated clay
- c-φ soil classification (mixed-strength soils)
Relationship to central
Fundamental soil parameters determining strength and bearing-capacity factors
Water-Table Correction
Sub concepts
- Water table at or above footing base → use γ' in width term
- Water table within depth B below footing → interpolate unit weight
- Water table well below footing → no correction (use γ or γsat)
- Buoyancy reduces effective weight contribution
Relationship to central
Adjusts unit weight in bearing-capacity calculation when water is present near footing
Failure Modes and Shear Types
Sub concepts
- General shear failure (dense soil, high φ)
- Local/punching shear failure (loose soil, low relative density)
- Reduce c and tan(φ) to 2/3 for local shear calculation
- Settlement-controlled vs bearing-capacity-controlled design
Relationship to central
Determines which bearing-capacity equation form to apply (general vs local/punching shear)
Allowable Bearing Capacity (qa)
Sub concepts
- qa = qu / FS (gross allowable bearing)
- qa,net = (qu - γ·Df) / FS (net allowable bearing)
- Factor of safety FS = 2.5 to 3.0 (typical range)
- Governs footing design and column load capacity
Relationship to central
Safe design stress obtained by dividing ultimate capacity by factor of safety
Factor of Safety (FS)
Sub concepts
- Minimum FS = 2.5 for well-characterized soils
- FS = 3.0 for typical projects (standard practice)
- FS = 3.5+ for highly variable or uncertain soils
- Related to NSCP 2015 foundation design requirements
Relationship to central
Safety margin applied to ultimate bearing capacity to obtain design allowance
Settlement Analysis
Sub concepts
- Immediate settlement (elastic deformation)
- Primary consolidation (clay compression)
- Secondary compression (long-term creep)
- Allowable settlement limits from NSCP 2015
Relationship to central
Often controls footing design more than bearing-capacity shear; governs serviceability
Special Cases and Modifications
Sub concepts
- φ = 0 undrained clay: Nc=5.7, Nq=1, Nγ=0
- Sloping ground or inclined loads (inclination factors)
- Eccentric or inclined footing bases
- Nonhomogeneous or layered soil profiles
Relationship to central
Extends basic theory to account for ground conditions and geometric variations
Concept connections
- Terzaghi's Bearing Capacity EquationUltimate Bearing CapacityThe equation is the mathematical tool that calculates ultimate bearing capacity (qu) directly from soil parameters and footing geometry
- Ultimate Bearing CapacityAllowable Bearing CapacityAllowable bearing (qa) is derived by dividing ultimate bearing capacity by a factor of safety
- Bearing-Capacity Factors (Nc, Nq, Nγ)Soil Friction Angle (φ)All three N-factors are functions of φ alone; they are obtained from tabulated values or formulas based on the soil's friction angle
- Shape FactorsTerzaghi's Bearing Capacity EquationShape factors modify the coefficients in the Terzaghi equation to account for non-strip footing geometries (square, circular, rectangular)
- Footing Width (B) and GeometryWidth Component TermFooting width B directly appears in the ½γBNγ term; larger footings develop larger bearing capacity from this component
- Depth of Foundation (Df)Surcharge Component (q·Nq)Surcharge pressure q is calculated as q = γ·Df; deeper footings have higher surcharge and thus higher bearing capacity from this term
- Water-Table CorrectionSoil Unit Weight (γ and γ')When the water table is present, the effective unit weight changes from γ to γ' (submerged), which reduces the bearing capacity calculation
- Failure Modes and Shear TypesBearing Capacity FactorsLocal/punching shear failure in loose soils requires reduction of c and tan(φ) to ⅔ of their values, which reduces the N-factors used in calculation
- Settlement AnalysisAllowable Bearing CapacityIn many soils (especially clays), settlement governs the design allowable bearing more than the ultimate shear capacity; serviceability limits control
- Factor of Safety (FS)Allowable Bearing CapacityThe factor of safety (2.5–3.0 per NSCP 2015) is the divisor applied to ultimate bearing capacity to obtain the safe design allowance
- Soil Cohesion (c) and Friction Angle (φ)Bearing Capacity FactorsThese fundamental soil strength parameters determine which N-factors to use and control the magnitude of bearing capacity through the equation
- Special Cases (φ=0 Clay)Bearing Capacity FactorsFor undrained clay with φ=0, the N-factors simplify to Nc=5.7, Nq=1, Nγ=0, allowing rapid calculation without consulting tables
- Footing GeometryShape FactorsDifferent footing shapes (strip, square, circular, rectangular) require different shape factors to modify the bearing capacity equation
- Column Load CapacityAllowable Bearing CapacityThe maximum safe column load is calculated as the product of allowable bearing pressure and footing area: Q_allowed = q_a × Area
- Soil CharacterizationBearing-Capacity FactorsAccurate determination of c, φ, and γ through field investigation and laboratory testing is essential for selecting correct N-factors and equation terms
- NSCP 2015 RequirementsFactor of SafetyPhilippine building code specifies minimum factors of safety for shallow foundations; typically 2.5–3.0 on ultimate bearing capacity
Diagrams
Bearing Capacity of Soils — Complete Concept Hierarchy
Master concept map showing all key topics in bearing capacity of soils, organized hierarchically. The central concept branches into ultimate bearing capacity, bearing-capacity factors, soil parameters, footing geometry, water-table effects, allowable bearing, and design considerations. Each branch contains specific sub-concepts and formulas critical for PRC licensure examination.
Bearing Capacity Calculation Procedure — Step-by-Step Workflow
Flowchart showing the complete procedure for calculating bearing capacity and allowable footing load. Covers soil type identification, N-factor selection, water-table correction, shape-factor application, ultimate capacity calculation, failure-mode check, and allowable load determination. This is the standard problem-solving sequence for PRC board exams.
Terzaghi Bearing Capacity Equation — Component Breakdown
Detailed breakdown of the three components in Terzaghi's bearing-capacity equation. Shows that each term (cohesion, surcharge, width) is independent and depends on distinct soil and geometry parameters. Demonstrates how N-factors are functions of friction angle alone, enabling use of standardized tables for rapid calculation.
Water-Table Correction Logic — Unit Weight Selection
Decision tree for water-table correction in bearing-capacity calculations. Guides engineers through the logic of when and how to apply submerged unit weight (γ') versus saturated or dry unit weight. Critical for accurate footing design in tropical regions like the Philippines where high water tables are common.
Shape Factor Application — Footing Geometry Influence
Flowchart showing how footing geometry (shape and size) affects bearing-capacity calculations through shape factors. Demonstrates that square and circular footings have higher capacity per unit width than strip footings, and that shape factors modify both cohesion and width-dependent terms in Terzaghi's equation.
Bearing Capacity Components — Typical Contribution Percentages for c-φ Soil
Pie chart showing the relative contributions of the three terms in Terzaghi's bearing-capacity equation for a typical c-φ soil (e.g., φ=25°, moderate c). In practice, all three terms contribute significantly, so neglecting any term leads to serious underestimation of capacity. The distribution varies with soil strength and footing depth/width geometry.
Footing Design State Transitions — From Investigation to Final Design
State diagram showing the iterative process of footing design from site investigation through final approval. Highlights the feedback loops when initial dimensions prove inadequate (either bearing capacity or settlement), and demonstrates that both shear failure and serviceability must be verified before design is complete.