10.2 Bearing capacity theories (Terzaghi, Meyerhof, Vesic)
4 min read•august 16, 2024
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
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- Bearing capacity defines maximum load per unit area soil supports without failure or excessive settlement
- represents theoretical maximum pressure applied to soil before shear failure occurs
- calculated by dividing ultimate bearing capacity by (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)
- (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 above foundation level
- Introduces three bearing capacity factors
- (cohesion)
- (surcharge)
- (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 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
- 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
- (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
- (c = 0)
- Omit cohesion term from equation
- Focus on friction and unit weight terms
- Example: clean sand or gravel
- (φ = 0)
- Neglect friction and unit weight terms
- Emphasize cohesion term
- Example: saturated clay
-
- 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
-
- 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
Key Terms to Review (27)
Allowable bearing capacity: Allowable bearing capacity is the maximum load per unit area that a foundation can safely support without risking failure or excessive settlement. It is a crucial factor in geotechnical engineering, determining how much weight structures can place on the ground while ensuring stability and safety.
Bearing capacity equation: The bearing capacity equation is a formula used to determine the maximum load that soil can support without experiencing shear failure. It is essential for ensuring the stability of structures and involves various parameters such as soil properties, depth of the foundation, and load characteristics. The equation provides critical insights into how different theories, including those proposed by Terzaghi, Meyerhof, and Vesic, interpret the interactions between foundation loads and soil behavior.
Cohesionless soils: Cohesionless soils are types of soils that do not exhibit any significant cohesion between their particles, primarily relying on friction to resist shear stress. These soils, such as sand and gravel, are typically granular in nature and behave differently under varying conditions like drainage, load stress, and historical stress paths. Understanding cohesionless soils is essential when analyzing factors affecting shear strength and evaluating the bearing capacity of foundations.
Cohesive soil: Cohesive soil is a type of fine-grained soil that exhibits strong inter-particle attraction, primarily due to its clay content, which allows it to retain shape and resist deformation when subjected to external forces. This soil is significant in various engineering applications due to its unique properties, such as high plasticity and compressibility, influencing factors like drainage, load-bearing capacity, and stability in construction projects.
Depth factors: Depth factors are coefficients used in geotechnical engineering to adjust the ultimate bearing capacity of shallow foundations based on the depth of the foundation below the ground surface. These factors take into account how the soil properties and effective stress change with depth, influencing the load-bearing capacity and overall stability of the foundation. They play a crucial role in various bearing capacity theories, determining how well a foundation can support structures while considering factors such as soil type and depth.
Effective Stress: Effective stress is the stress that contributes to the strength and stability of soil, representing the difference between total stress and pore water pressure within the soil. This concept is crucial in understanding how soil behaves under various conditions, particularly in the context of fluid movement, consolidation, and strength properties of soils.
Factor of Safety: The factor of safety is a measure used in engineering to provide a safety margin in design, ensuring that structures can withstand loads greater than the maximum expected load. It is defined as the ratio of the strength of a material or system to the actual applied load, indicating how much stronger a system is than what it needs to be for safe operation. This concept is crucial in various engineering fields, including geotechnical engineering, where it plays a vital role in assessing the stability of structures and soil conditions.
Field Tests: Field tests are on-site evaluations conducted to determine the physical and mechanical properties of soil and other materials in their natural state. These tests are crucial for understanding how soil behaves under load, which directly relates to determining the bearing capacity of foundations and other structures. By providing real-world data, field tests support theoretical models and bearing capacity theories proposed by researchers, ensuring safe and effective engineering practices.
George Meyerhof: George Meyerhof was a prominent civil engineer known for his contributions to the understanding of bearing capacity in soil mechanics. He advanced the field by refining and expanding upon earlier theories, particularly those introduced by Terzaghi, and provided more comprehensive approaches to calculating the bearing capacity of shallow foundations. His work laid the groundwork for subsequent developments in geotechnical engineering and remains influential in contemporary practices.
Granular soil: Granular soil refers to a type of soil that is composed primarily of larger particles, such as sand and gravel, which have little to no cohesion. This type of soil is essential for various geotechnical applications because of its drainage properties and the ability to compact effectively under load. Its characteristics play a critical role in seepage analysis, foundation design, bearing capacity, and stabilization techniques.
Karl Terzaghi: Karl Terzaghi was an influential civil engineer and the father of soil mechanics, known for his groundbreaking work in understanding the behavior of soils under load and the principles governing geotechnical engineering. His theories laid the foundation for modern practices in soil analysis, including effective stress, consolidation, and bearing capacity, shaping how engineers approach soil-related challenges in construction and design.
Laboratory tests: Laboratory tests are systematic procedures used to analyze soil properties in a controlled environment to understand its behavior under various loading conditions. These tests provide crucial data for determining the engineering characteristics of soil, which are essential for applying bearing capacity theories effectively, such as those proposed by Terzaghi, Meyerhof, and Vesic.
Meyerhof's Theory: Meyerhof's Theory is a method used to determine the ultimate bearing capacity of shallow foundations on soil, developed by Karl Terzaghi and further refined by Meyerhof. This theory incorporates factors such as depth of the foundation, width, and soil properties, providing a more nuanced understanding compared to earlier theories. It highlights the impact of both shear strength and soil settlement on the overall bearing capacity, making it a vital consideration in geotechnical engineering.
Mixed soils: Mixed soils refer to soil that contains a combination of different soil types, including varying proportions of sand, silt, clay, and gravel. This term is important in geotechnical engineering as it influences the engineering properties of the soil, particularly its bearing capacity, which is critical for foundation design and stability.
Nc: In geotechnical engineering, 'nc' represents the cohesion factor used in bearing capacity equations, particularly for shallow foundations. This parameter is critical in determining the strength of soil under vertical loads and is essential for estimating the safe bearing capacity of a foundation based on soil properties.
Nq: In geotechnical engineering, the term 'nq' represents the bearing capacity factor related to the ultimate bearing capacity of shallow foundations. It is used in various bearing capacity theories, which help estimate the load a soil can support before failure occurs. Understanding 'nq' is crucial for determining safe design loads and ensuring structural stability when building on soil.
Nγ: nγ, or the unit weight of the soil multiplied by the depth of the footing, is an important parameter in bearing capacity theories. It represents the contribution of the soil's weight to the overall bearing capacity of a foundation. This term plays a crucial role in calculating the ultimate bearing capacity of shallow foundations based on theories proposed by various engineers.
Punching shear failure: Punching shear failure is a type of structural failure that occurs when a concentrated load on a flat slab causes it to fail around the load's perimeter, often resembling a punch through the material. This failure mechanism is particularly significant in reinforced concrete structures, where the design must account for localized stress concentrations that can lead to sudden and catastrophic failure if not properly managed.
Purely cohesive soils: Purely cohesive soils are types of soils that primarily consist of fine-grained particles, such as clay, which exhibit significant cohesion due to the electrochemical forces between particles. These soils are characterized by their ability to retain water and their low permeability, resulting in unique engineering properties that influence their behavior under loading conditions. Understanding purely cohesive soils is critical for evaluating the bearing capacity and stability of foundations and structures.
Shape Factors: Shape factors are numerical values that represent the influence of the geometry of a foundation on its bearing capacity and performance under load. They adjust the theoretical bearing capacity derived from basic principles to account for the shape and size of the footing, ensuring more accurate predictions of how foundations will behave in different soil conditions.
Shear Strength: Shear strength is the maximum resistance of a soil or rock to shear stress, which is critical in understanding how materials behave under loading conditions. This concept is essential in various aspects of geotechnical engineering, as it influences stability, load-bearing capacity, and the overall performance of structures in contact with soil.
Slope failure: Slope failure is the collapse or sliding of a slope or hillside due to a loss of stability, often caused by factors such as gravity, water infiltration, or human activities. This phenomenon can lead to significant damage and is crucial to understand when assessing the bearing capacity of soils and the potential risks involved in construction projects near slopes.
Soil Stratification: Soil stratification refers to the layering of soil types within the ground, often resulting from natural processes such as sediment deposition, weathering, and biological activity. Understanding soil stratification is crucial in geotechnical engineering as it affects factors like drainage, load-bearing capacity, and overall soil behavior under various conditions, which are key considerations in determining safe foundation designs and predicting settlement behavior.
Ultimate bearing capacity: Ultimate bearing capacity is the maximum load per unit area that a soil can support without undergoing failure. This critical value determines how much weight a foundation can safely support before risking structural failure, which is essential for the design and safety of buildings and other structures.
Vesic's Method: Vesic's Method is a well-known approach in geotechnical engineering used to estimate the bearing capacity of shallow foundations. It builds on the foundational theories established by Terzaghi and Meyerhof, refining their concepts to provide more accurate results for various soil conditions. This method incorporates factors like the shape and depth of the foundation, as well as the soil's cohesion and friction angle, making it highly applicable in real-world scenarios.
Vladimir Vesic: Vladimir Vesic was a prominent geotechnical engineer known for his contributions to the theories of bearing capacity in soil mechanics. His work focused on developing more refined methodologies for calculating the ultimate bearing capacity of shallow and deep foundations, addressing limitations in earlier models and integrating empirical data into theoretical frameworks.
Water table: The water table is the upper surface of groundwater saturation, where the soil or rock is completely saturated with water. It separates the unsaturated zone above, where soil pores contain both air and water, from the saturated zone below, where all pore spaces are filled with water. Understanding the water table is crucial for assessing soil behavior under load, analyzing slope stability, and determining the bearing capacity of foundations.