CELE Geotechnical Engineering — Bearing Capacity of SoilsConcept Map

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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)

Concept

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

Concept

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

Concept

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

Concept

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

To

Ultimate Bearing Capacity

From

Terzaghi's Bearing Capacity Equation

Strength

strong

Relationship

The equation is the mathematical tool that calculates ultimate bearing capacity (qu) directly from soil parameters and footing geometry

To

Allowable Bearing Capacity

From

Ultimate Bearing Capacity

Strength

strong

Relationship

Allowable bearing (qa) is derived by dividing ultimate bearing capacity by a factor of safety

To

Soil Friction Angle (φ)

From

Bearing-Capacity Factors (Nc, Nq, Nγ)

Strength

strong

Relationship

All three N-factors are functions of φ alone; they are obtained from tabulated values or formulas based on the soil's friction angle

To

Terzaghi's Bearing Capacity Equation

From

Shape Factors

Strength

strong

Relationship

Shape factors modify the coefficients in the Terzaghi equation to account for non-strip footing geometries (square, circular, rectangular)

To

Width Component Term

From

Footing Width (B) and Geometry

Strength

strong

Relationship

Footing width B directly appears in the ½γBNγ term; larger footings develop larger bearing capacity from this component

To

Surcharge Component (q·Nq)

From

Depth of Foundation (Df)

Strength

strong

Relationship

Surcharge pressure q is calculated as q = γ·Df; deeper footings have higher surcharge and thus higher bearing capacity from this term

To

Soil Unit Weight (γ and γ')

From

Water-Table Correction

Strength

strong

Relationship

When the water table is present, the effective unit weight changes from γ to γ' (submerged), which reduces the bearing capacity calculation

To

Bearing Capacity Factors

From

Failure Modes and Shear Types

Strength

moderate

Relationship

Local/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

To

Allowable Bearing Capacity

From

Settlement Analysis

Strength

moderate

Relationship

In many soils (especially clays), settlement governs the design allowable bearing more than the ultimate shear capacity; serviceability limits control

To

Allowable Bearing Capacity

From

Factor of Safety (FS)

Strength

strong

Relationship

The factor of safety (2.5–3.0 per NSCP 2015) is the divisor applied to ultimate bearing capacity to obtain the safe design allowance

To

Bearing Capacity Factors

From

Soil Cohesion (c) and Friction Angle (φ)

Strength

strong

Relationship

These fundamental soil strength parameters determine which N-factors to use and control the magnitude of bearing capacity through the equation

To

Bearing Capacity Factors

From

Special Cases (φ=0 Clay)

Strength

strong

Relationship

For undrained clay with φ=0, the N-factors simplify to Nc=5.7, Nq=1, Nγ=0, allowing rapid calculation without consulting tables

To

Shape Factors

From

Footing Geometry

Strength

strong

Relationship

Different footing shapes (strip, square, circular, rectangular) require different shape factors to modify the bearing capacity equation

To

Allowable Bearing Capacity

From

Column Load Capacity

Strength

strong

Relationship

The maximum safe column load is calculated as the product of allowable bearing pressure and footing area: Q_allowed = q_a × Area

To

Bearing-Capacity Factors

From

Soil Characterization

Strength

strong

Relationship

Accurate determination of c, φ, and γ through field investigation and laboratory testing is essential for selecting correct N-factors and equation terms

To

Factor of Safety

From

NSCP 2015 Requirements

Strength

moderate

Relationship

Philippine building code specifies minimum factors of safety for shallow foundations; typically 2.5–3.0 on ultimate bearing capacity