Foundation Engineering theory :bearing capacity of shallow foundation :Terzaghi , Meyerhof

Foundation Engineering Theory: Bearing Capacity of Shallow Foundation
Terzaghi's Theory
Karl Terzaghi, known as the father of soil mechanics, developed the first significant theory for the bearing capacity of shallow foundations. His equations have been widely accepted and used due to their simplicity and practicality. Terzaghi's bearing capacity equation for shallow foundations is given as:

𝑞
𝑢
𝑙
𝑡
=
𝑐
𝑁
𝑐
+
𝑞
𝑁
𝑞
+
1
2
𝛾
𝐵
𝑁
𝛾
Where:

𝑞
𝑢
𝑙
𝑡
= Ultimate bearing capacity

𝑐
= Cohesion of the soil

𝑞
= Overburden pressure at the foundation base

𝛾
= Unit weight of the soil

𝐵
= Width of the foundation

𝑁
𝑐
,
𝑁
𝑞
,
𝑁
𝛾
= Bearing capacity factors, which depend on the angle of internal friction (
𝜙
)

Key Factors in Terzaghi's Theory:
Depth Factor: For shallow foundations, the depth of embedment is not considered significant.

Shape Factor: Terzaghi's equation is straightforward, with no additional shape factors initially included.

Load Inclination: The theory assumes a vertical load without any inclination.

Meyerhof's Theory
George G. Meyerhof extended Terzaghi's theory by introducing more comprehensive factors that consider different shapes, load inclinations, and depths. Meyerhof's equation adjusts the bearing capacity factors to provide a more accurate prediction, especially for cases where the foundation may not be perfectly vertical or uniformly loaded. Meyerhof's bearing capacity equation is:

𝑞
𝑢
𝑙
𝑡
=
𝑐
𝑁
𝑐
𝑆
𝑐
𝑑
𝑐
𝑖
𝑐
+
𝑞
𝑁
𝑞
𝑆
𝑞
𝑑
𝑞
𝑖
𝑞
+
1
2
𝛾
𝐵
𝑁
𝛾
𝑆
𝛾
𝑑
𝛾
𝑖
𝛾
Where:

𝑆
𝑐
,
𝑆
𝑞
,
𝑆
𝛾
= Shape factors

𝑑
𝑐
,
𝑑
𝑞
,
𝑑
𝛾
= Depth factors

𝑖
𝑐
,
𝑖
𝑞
,
𝑖
𝛾
= Inclination factors

Key Enhancements in Meyerhof's Theory:
Shape Factors: These account for the geometric shape of the foundation (strip, circular, or square).

Depth Factors: These factors adjust for the depth of the foundation, providing more accuracy for shallow and deep foundations.

Inclination Factors: These factors consider the effects of inclined loads, making the theory applicable to a wider range of practical scenarios.

Comparison and Application
Terzaghi's Theory: Best suited for quick and straightforward calculations, often used for preliminary design and when the foundation conditions align closely with the assumptions of the theory.

Meyerhof's Theory: Provides greater accuracy and flexibility, especially when dealing with more complex scenarios such as inclined loads and varied foundation shapes.

Conclusion
Both Terzaghi's and Meyerhof's theories have significantly contributed to the field of foundation engineering, providing essential tools for designing safe and efficient shallow foundations. While Terzaghi's theory is favored for its simplicity, Meyerhof's enhancements offer a more nuanced approach, accommodating a broader range of conditions and ensuring more reliable results.