Das Foundation Engineering Ch4a
Chapter 4: Bearing Capacity of Foundation Design
Introduction to Shallow Foundations
- Overview of chapter focusing on bearing capacity and settlement of shallow foundations.
- Discussion on three failure modes of bearing capacity and introduction to Tazaki's theory.
- Mention of groundwater table effects on bearing capacity calculations.
Types of Foundations
- Explanation of shallow vs. deep foundations; shallow foundation depth is ≤3-4 times its width.
- Definition and examples of shallow foundations, including excavation depth considerations.
- Introduction to various types of footings: isolated, wall/strip, combined, and mat footings.
Spread Footings
- Description of spread footings as enlargements at the bottom to distribute loads over a larger area.
- Importance of spread footing in preventing soil punching under high loads from columns.
- Visual representation and explanation of square and rectangular footings for load distribution.
Wall Footings
- Definition and purpose of wall or strip footings in supporting bearing walls from superstructures.
- Emphasis on continuous footings for spreading loads effectively across the foundation width.
- Importance of foundation width (b), applicable to both isolated and continuous foundations.
Foundation Types and Applications
Ring Footing
- Discusses the concept of combining isolated footings into a rectangular shape to support two columns, saving cost and time.
- Explains how to construct a ring footing by creating a larger circular base with a smaller circle cut out.
- Highlights the application of ring footings in oil reservoirs or similar structures.
Mat Foundation
- Introduces mat foundation as an alternative when loads from superstructures are too large for spread footings.
- Describes mat foundations as large spread footings that cover the entire footprint of a structure.
- Emphasizes the cost-effectiveness of using mat foundations for high-rise buildings.
Soil Failure Types
- Discusses soil strength and shear stress, noting that most foundation failures are geotechnical rather than structural.
- Identifies three types of soil failure: general shear failure, local shear failure, and puncture shear failure.
- Explains settlement as displacement caused by load application on foundations.
General Shear Failure
- Details how increased load leads to settlement until reaching ultimate bearing capacity (qu).
- Defines general shear failure occurring suddenly when soil cannot support additional load.
- Reiterates the importance of understanding ultimate bearing capacity in foundation design.
Understanding Failure Modes in Soil Mechanics
General Overview of Settlement and Load
- Discusses the impact of increased load on ground surface settlement.
- Introduces local shear failure, occurring in medium compacted soil.
- Describes how local shear failure extends gradually from the foundation.
Characteristics of Local Shear Failure
- Explains that considerable movement is needed for ground surface extension.
- Notes that local shear failure allows for increased load with larger settlement.
- Highlights the absence of a peak load in local shear failure.
Punching Shear Failure Explained
- Defines punching shear failure as occurring in loose soils like sand or soft clay.
- Illustrates that the ground surface remains flat without significant extension beyond qu.
- Emphasizes the importance of understanding these failure modes for bearing capacity calculations.
Importance of Bearing Capacity Calculations
- States that general shear failure is primarily used for calculating bearing capacity.
- Mentions that local and punching shear failures are controlled by limiting settlement.
- Outlines the two major parts to learn: bearing capacity and settlement.
Key Theories in Bearing Capacity
- Introduces Kazakh bearing capacity theory as a fundamental concept.
- Discusses Mirhoff Tazaki's contributions to geotechnical engineering regarding strip footings.
- Identifies the bottom of foundations as critical when calculating bearing capacity.
Essential Parameters for Calculating Ultimate Bearing Capacity
- Defines df as the distance between ground surface and foundation bottom crucial for calculations.
- Lists necessary soil properties such as unit weight, cohesion, and friction angle for calculations.
- Describes geostatic pressure at specific locations related to bearing capacity failures.
Understanding Failure Surfaces and Bearing Capacity
- Introduction to failure surfaces under load and the importance of understanding how they fail.
- Explanation of the term q , which represents original pressure at the foundation's bottom.
- Definition of effective stress ( sigma' ) and its significance in relation to groundwater.
Key Parameters for Bearing Capacity
- Overview of parameters: N_c , N_q , and N_gamma related to cohesion, pressure, and unit weight respectively.
- Reference to Table 4.1 for Tazaki bearing capacity factors as a resource for calculations.
- Warning against confusing Tazaki theory with Mirhaf theory when calculating bearing capacity.
Calculating Ultimate Bearing Capacity
- Importance of knowing which table to use for calculations; Table 4.1 is specific for Tazaki theory.
- Discussion on friction angle ( phi ) and its impact on determining factors like N_c , N_q , and N_gamma .
- Example values provided for a 30-degree friction angle: N_c = 37.16, N_q = 22.46, N_gamma = 19.13.
Formulas for Different Footing Types
- Formula 4.8 used for strip footings; introduction to formula differences based on footing type.
- Distinction between strip footing (1, 1.5 factor adjustments) versus square footing (1, 1.31 factor adjustments).
- Clarification that memorization isn't necessary; understanding application is key.
Rectangular Foundations and Circular Footings
- Mention of upcoming discussions on rectangular foundations using Mirhaf theory in future lectures.
- Introduction of circular footings with reference to formula 4.18, highlighting different adjustment factors.
Allowable Bearing Capacity Concepts
- Definition of allowable bearing capacity as a factor of safety applied to ultimate capacity ( q_u / FS).
- Explanation of net allowable bearing capacity calculation by subtracting original pressure from ultimate capacity.
- Inquiry into which type—allowable or net allowable—is more conservative in practice.
Understanding Foundation Calculations
Key Concepts in Foundation Design
- The net allowable should be a smaller number; safety factor must be at least three in all cases.
- For gamma df calculations, use unit weight of concrete and steel as standard values for civil engineers.
- Unit weight of concrete is 150 lb/ft³; steel is approximately 490 lb/ft³.
Load Considerations
- When calculating net allowable load, consider the column load, concrete weight, and soil above.
- Example 4.1 involves a square foundation with specific soil parameters to determine gross load.
- Given parameters include friction angle (25°), cohesion (20 kPa), and unit weight of soil (16.5 kN/m³).
Calculation Steps
- Identify the type of foundation: shallow square foundation (2x2 m).
- Use appropriate formulas based on friction angle to find necessary parameters for calculations.
- Calculate ultimate bearing capacity (qu = 1078 kPa); allowable load per unit area is qu divided by safety factor.
Final Load Determination
- Total allowable gross load calculated as stress or force; ensure clarity between stress and force definitions.
- Allowable gross load results in a force of 1438 kN; consider implications if asked for net load instead.
Advanced Example Discussion
- Consideration for calculating net allowable load requires subtracting additional loads from total capacity.
- Next example focuses on a more complex scenario involving groundwater effects on bearing capacity.
Additional Parameters and Solutions
- New example features a square footing with dimensions affected by groundwater depth not impacting calculations.
- Ultimate bearing capacity needs to account for both column loads and concrete weight together affecting failure conditions.
Understanding Effective Stress Calculation
Key Points
- Review Table 4.1 in the textbook for effective stress calculations.
- Identify and correct a typo in the example provided.
- Calculate original effective stress at depth (df): sigma' = gamma_d cdot d - u .
Calculation Steps
- Use values: cohesion c = 242 , unit weight gamma = 131 , and depth b = 3.25 .
- Ultimate bearing capacity calculated as 15,900 psf; this is crucial for foundation design.
- Consider concrete weight: volume of foundation times unit weight gives total self-weight.
Foundation Load Considerations
- Understand that soil fails under general shear failure when pressure reaches a specific threshold.
- Two contributors to pressure: column load and concrete dead weight must be considered together.
- Final pressure calculation yields 165,000 pounds; conservative approach recommended for safety.
Safety Factors and Homework
- Discuss the importance of being conservative in engineering calculations regarding foundation loads.
- Factor of safety not applied here to reach true failure conditions; important for accurate assessments.
- Homework assigned: complete problem 4.1a with reference to example 4.8 for guidance.