Bearing capacity theories are crucial for designing shallow foundations. They help engineers figure out how much weight soil can support before failing. Terzaghi, Meyerhof, and Vesic each developed methods to calculate this, considering factors like soil type and foundation shape.

These theories have evolved over time, becoming more accurate and versatile. They help engineers design safe, cost-effective foundations for buildings and structures. Understanding their differences and when to apply each one is key for successful geotechnical projects.

Bearing Capacity and Shallow Foundations

Fundamental Concepts and Significance

• Bearing capacity defines maximum load per unit area soil supports without failure or excessive settlement
• Ultimate bearing capacity represents theoretical maximum pressure applied to soil before shear failure occurs
• Allowable bearing capacity calculated by dividing ultimate bearing capacity by factor of safety (typically 2 to 3 for shallow foundations)
• Crucial for determining size and depth of shallow foundations to ensure structural stability and prevent excessive settlement
• Factors influencing bearing capacity include
  • Soil type (clay, sand, silt)
  • Foundation size and shape (strip, square, circular)
  • Depth of embedment
  • Groundwater conditions (saturated or unsaturated)
  • Loading conditions (static or dynamic)
• Inadequate bearing capacity leads to foundation failure modes
  • General shear failure (sudden collapse)
  • Local shear failure (partial collapse)
  • Punching shear failure (vertical displacement)
• Bearing capacity analysis optimizes foundation design, ensures safety, and minimizes construction costs in geotechnical engineering projects (bridges, buildings, retaining walls)

Terzaghi, Meyerhof, and Vesic Theories

Terzaghi's Theory (1943)

• Pioneering work in bearing capacity analysis
• Assumes rigid-plastic soil behavior
• Neglects shear strength above foundation level
• Introduces three bearing capacity factors
  • Nc (cohesion)
  • Nq (surcharge)
  • Nγ (soil unit weight)
• Limited to centrally loaded, strip foundations on homogeneous soil
• Provides conservative estimates for bearing capacity

Meyerhof's Theory (1963)

• Extends Terzaghi's work by considering shear strength above foundation level
• Introduces shape and depth factors to account for various foundation geometries
• Incorporates inclination factors for inclined loads on foundation
• Applicable to various foundation shapes (strip, square, circular)
• Accounts for eccentric loading conditions
• Generally predicts higher bearing capacities than Terzaghi's theory

Vesic's Theory (1973)

• Refines bearing capacity analysis by incorporating effects of soil compressibility and foundation roughness
• Introduces compressibility factors to account for soil deformation
• Considers influence of foundation shape on all bearing capacity factors
• Particularly useful for analyzing foundations on compressible soils or rock
• Provides more accurate results for foundations on softer materials

Calculating Ultimate Bearing Capacity

General Equation and Components

• Ultimate bearing capacity equation $q_u = cN_cs_cd_c + qN_qs_qd_q + 0.5γBN_γs_γd_γ$
  • c: cohesion
  • q: surcharge
  • γ: soil unit weight
  • B: foundation width
• Bearing capacity factors (Nc, Nq, Nγ)
  • Functions of soil friction angle
  • Vary among different theories
  • Calculated using specific equations or charts
• Shape factors (sc, sq, sγ)
  • Account for foundation shape (strip, rectangular, circular)
  • Included in Meyerhof's and Vesic's theories
  • Modify bearing capacity based on foundation geometry
• Depth factors (dc, dq, dγ)
  • Consider effect of foundation embedment depth
  • Incorporated in Meyerhof's and Vesic's theories
  • Increase bearing capacity for deeper foundations

Application to Different Soil Types

• Cohesionless soils (c = 0)
  • Omit cohesion term from equation
  • Focus on friction and unit weight terms
  • Example: clean sand or gravel
• Purely cohesive soils (φ = 0)
  • Neglect friction and unit weight terms
  • Emphasize cohesion term
  • Example: saturated clay
• Mixed soils
  • Use full equation considering all terms
  • Example: silty clay or clayey sand
• Divide calculated ultimate bearing capacity by factor of safety (2-3) to determine allowable bearing capacity for design

Bearing Capacity Theories: Differences and Applicability

Comparison of Theory Predictions

• Terzaghi's theory
  • More conservative estimates
  • Generally applicable to strip foundations on homogeneous soils with central vertical loading
  • Suitable for preliminary design calculations
• Meyerhof's theory
  • More accurate for shallow foundations with various shapes
  • Accounts for inclined and eccentric loading conditions
  • Predicts higher bearing capacities than Terzaghi's theory
• Vesic's theory
  • Useful for foundations on compressible soils or rock
  • Considers soil compressibility and foundation roughness effects
  • Provides refined results for softer materials

Variations in Bearing Capacity Factors

• Theories differ in prediction of bearing capacity factors, especially Nγ
• Significant variations in calculated bearing capacities for granular soils
  • Example: for φ = 30°, Nγ values range from 15.1 (Terzaghi) to 22.4 (Meyerhof)
• Cohesive soils (φ = 0) show less pronounced differences
  • Nc factor relatively consistent across all theories (≈ 5.14)

Practical Considerations and Limitations

• Engineers compare results from multiple theories for comprehensive analysis
• Use engineering judgment to select appropriate values for design
• Consider site-specific conditions and local experience
• Limitations of theories in certain soil conditions
  • Layered soils (alternating sand and clay layers)
  • Partially saturated soils
  • Soils exhibiting strain-softening behavior
• Supplementary methods for complex situations
  • Numerical modeling (finite element analysis)
  • In-situ testing (plate load tests)
  • Empirical correlations based on field observations