Rankine의 수평토압

문서 내 토픽

1. William Rankine

William John Macquorn Rankine (1820~1872, Scotland)는 1857년에 Rankine의 토압 이론(최대 수직응력 이론)을 개발했습니다.
2. Rankine 토압의 가정

Rankine 토압 이론의 주요 가정은 다음과 같습니다: 1) 흙 입자는 입자 간 마찰력에 의해서만 평형을 유지한다. 2) 흙은 비압축성이고 균질한 입자이다. 3) 토압은 지표면에 평행하게 작용한다. 4) 지표면에 작용하는 하중은 등분포하중이다. 5) 지표면은 무한히 넓게 존재한다.
3. 정지토압계수(K0)

정지토압계수(K0)는 수평응력과 수직응력의 비로 정의됩니다. 정상 압밀 토양과 수직 벽체의 경우 K0 = (1 - sin φ) / (1 - sin β)로 계산할 수 있습니다. 여기서 β는 뒤채움 지반의 경사각입니다. 과압밀 토양과 수평 지반, 수직 벽체의 경우 K0 = (1 - sin φ) / (OCR)^(sin φ)로 계산할 수 있습니다. 여기서 OCR은 과압밀비입니다.
4. Rankine 능동 및 수동 토압

Rankine은 수동토압과 능동토압을 다음과 같이 정의했습니다: 1) Rankine 능동토압: 뒤채움 지반이 수평이거나 경사진 경우의 능동토압 공식 2) Rankine 수동토압: 뒤채움 지반이 수평이거나 경사진 경우의 수동토압 공식

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1. William Rankine

William Rankine was a Scottish engineer and physicist who made significant contributions to the field of thermodynamics and soil mechanics in the 19th century. He is best known for his work on the Rankine theory of soil mechanics, which provides a framework for analyzing the behavior of soils under various loading conditions. Rankine's work laid the foundation for modern soil mechanics and has been widely used in geotechnical engineering applications, such as the design of retaining walls, foundations, and slope stability analysis. His contributions to the understanding of soil behavior and the development of analytical tools have had a lasting impact on the field of civil engineering.
2. Rankine 토압의 가정

The Rankine theory of soil mechanics is based on several key assumptions and simplifications. The main assumptions of the Rankine theory include: 1. The soil is homogeneous, isotropic, and linearly elastic. 2. The soil is in a state of plane strain, meaning that the deformation and stress conditions are constant in the direction perpendicular to the plane of analysis. 3. The soil is in a state of limit equilibrium, where the stresses within the soil are at the point of failure. 4. The soil-structure interface is smooth, and there is no friction between the soil and the structure. 5. The soil is dry and cohesionless, with the only resistance to shear being due to the internal friction angle of the soil. These assumptions allow for the development of analytical solutions for the calculation of active and passive earth pressures, which are widely used in the design of retaining structures and other geotechnical applications. However, it is important to note that real-world soil behavior can be more complex, and the Rankine theory may not always accurately capture the full range of soil-structure interactions.
3. 정지토압계수(K0)

The coefficient of at-rest earth pressure, or K0, is an important parameter in soil mechanics that represents the ratio of the horizontal effective stress to the vertical effective stress in a soil mass that is not undergoing any shear deformation. The Rankine theory provides a simplified expression for calculating K0 for cohesionless soils, which is: K0 = 1 - sin(φ) Where φ is the angle of internal friction of the soil. This expression assumes that the soil is in a state of limit equilibrium and that the soil-structure interface is smooth. In reality, the value of K0 can be influenced by various factors, such as the soil's stress history, the method of soil placement, and the presence of cohesion. More advanced soil models and empirical correlations have been developed to better estimate K0 for different soil types and conditions. The accurate determination of K0 is crucial in the design of geotechnical structures, as it affects the distribution of stresses within the soil and the design of retaining walls, foundations, and other earth-retaining structures. While the Rankine expression provides a useful starting point, it is important to consider the limitations of the theory and to use more sophisticated methods when necessary to ensure the safety and reliability of geotechnical designs.
4. Rankine 능동 및 수동 토압

The Rankine theory of soil mechanics provides a framework for calculating the active and passive earth pressures acting on retaining structures, such as retaining walls and slopes. Active earth pressure refers to the pressure exerted by the soil on a retaining structure when the structure is moving away from the soil, causing the soil to reach a state of limit equilibrium. The Rankine active earth pressure coefficient (Ka) is used to calculate the active earth pressure, and it is given by the expression: Ka = tan^2(45° - φ/2) Where φ is the angle of internal friction of the soil. Passive earth pressure, on the other hand, refers to the pressure exerted by the soil on a retaining structure when the structure is moving towards the soil, causing the soil to reach a state of limit equilibrium. The Rankine passive earth pressure coefficient (Kp) is used to calculate the passive earth pressure, and it is given by the expression: Kp = tan^2(45° + φ/2) The Rankine theory provides a simple and widely-used approach for estimating the active and passive earth pressures acting on retaining structures. However, it is important to note that the theory makes several simplifying assumptions, such as the soil being homogeneous, isotropic, and cohesionless, and the soil-structure interface being smooth. In practice, more advanced soil models and numerical methods may be required to accurately capture the complex soil-structure interactions and the effects of factors such as soil cohesion, anisotropy, and the presence of groundwater.

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