Das Foundation Engineering Ch4b
Bearing Capacity of Shallow Foundations
Modifications for Water Table
- Groundwater complicates geotechnical engineering by reducing effective shear stress in soil.
- Three cases will be discussed to adjust Tasaki's theory for bearing capacity calculations.
Case 1: Groundwater Above Foundation
- No adjustment needed for the cohesion group (c group).
- For the q group, calculate original effective stress considering dry soil above groundwater level.
- The gamma group requires using buoyant unit weight instead of total unit weight.
Case 2: Groundwater Below Foundation
- Adjust gamma using effective unit weight plus depth over width of foundation.
- No changes are needed for c and q terms; only gamma needs adjustment.
Case 3: Deep Groundwater Table
- If groundwater is very deep, it has no effect on bearing capacity calculations.
Foundation Design and Bearing Capacity Calculation
- Discussed the impact on bearing capacity using Sagi's formula for calculations.
- Introduced Example 2, similar to textbook Example 4.4, focusing on differences.
- Provided parameters: unit weight of 105 pcf, saturated weight of 118 pcf, friction angle of 34°, and foundation depth of 4 feet.
Calculating Foundation Size
- Explained the need to determine foundation size (b x b) before construction.
- Emphasized backward analysis in real-world practice for foundation design.
- Noted that friction angle is crucial; referred to Table 4.1 for necessary factors.
Effective Stress and Adjustments
- Identified case one for water table modifications affecting effective stress calculation.
- Calculated original effective stress at depth d1 as 321.2 psf.
- Adjusted gamma term using total unit weight minus water weight to find buoyant unit weight.
Ultimate Bearing Capacity Calculation
- Calculated ultimate bearing capacity (q_u = allowable load × factor).
- Noted cohesion is zero; calculated q from previous steps and referenced Table data.
- Solved for unknown b in the formula, resulting in a dimension of 3.87 feet.
Introduction to Mierov Theory
- Transitioned to Mierov theory which addresses rectangular foundations' bearing capacity.
- Explained shearing resistance above the foundation contributes to overall stability.
- Compared Mierov theory with Tazaki theory; noted Mierov is less conservative due to additional considerations.
Understanding Load on Foundations
- The load on the foundation must be vertical and pass through its center of gravity according to Tazaki theory.
- Inclined loads can be decomposed into horizontal and vertical components, affecting bending.
- Eccentricity in loading is discussed; the formula for Meirhoff theory is more complex but manageable.
Factors Affecting Bearing Capacity
- Cohesion-related factors include shape (cs), depth (d), and inclination (i).
- Different theories require different tables; Table 4.2 is essential for Meirhoff theory.
- Friction angles impact factors q and gamma, with variations up to 50 degrees.
Adjustments Based on Experience
- Geotechnical engineering has evolved from practical experiences since the 1960s.
- Practitioners may need to adjust theories based on real-world applications.
Calculating Factors for Foundation Design
- Shape factor calculations involve width (b) and length (l); reference Table 4.2 for values.
- Depth factor considerations depend on ratios of d/b; specific instructions apply based on conditions.
Inclination Factor Definition
- The inclination factor (i) relates to the angle beta between the load direction and vertical.
Example Calculation of Foundation Size
- Example involves a square foundation with specified dimensions and unit weight parameters.
- Gross allowable load is defined, impacting stress calculations significantly.
Stress Calculations in Foundations
- Small q represents stress derived from force divided by area; foundational concepts are revisited.
- Ultimate bearing stress calculations utilize factors from Meirhoff theory, emphasizing accuracy.
Foundation Calculations
- Discusses the need to find the shape factor fqs of qd before calculations.
- Explains using Table 4.3 for formulas, including friction angle and dimensions of a square foundation.
- Introduces calculating effective stress at the bottom of the foundation, referencing example two.
Preparation for Calculation
- Compares preparation work in cooking to preparing data for calculations.
- Emphasizes readiness before starting calculations, similar to preparing ingredients for cooking.
Calculating Allowable Bearing Capacity
- Describes how to calculate allowable bearing capacity using capital Q .
- Highlights challenges in solving equations due to multiple variables and fractions involved.
Methods for Solving Equations
- Suggests trial and error or using a calculator's root finder function as methods to solve complex equations.
Challenges in Example Comparisons
- Notes that this example presents more challenges compared to previous examples due to different factors used.