General theory of three-dimensional consolidation

General theory of three-dimensional consolidation

1941 | Maurice A. Biot
The paper by Maurice A. Biot presents a general theory of three-dimensional consolidation, focusing on the settlement of soils under load. The author assumes that the soil is composed of particles bound together by molecular forces, forming an elastic porous medium with water-filled voids. The process of consolidation is described as the gradual adaptation of the soil to the applied load, which involves the squeezing out of water from the voids. Biot derives the mathematical equations that govern the behavior of the soil, including the stress, strain, and water content. The number of physical constants necessary to describe these properties is determined, and the equations are simplified for practical applications. The theory is extended to three-dimensional problems and arbitrary load variables, building upon the one-dimensional work by K. Terzaghi. The paper also discusses the physical interpretation of the soil constants, such as Young's modulus, shear modulus, Poisson's ratio, and the coefficients of compressibility and permeability. These constants are crucial for understanding the soil's behavior under different conditions. A standard soil test is used to illustrate the application of the theory, showing that the settlement of a column of soil follows a parabolic curve over time. For completely saturated clay, the initial compressibility is negligible compared to the final compressibility, simplifying the equations and providing a more straightforward solution. Finally, the paper introduces the operational calculus as a powerful method for solving consolidation problems, particularly for complex two- and three-dimensional scenarios. This method simplifies the calculations and provides a more efficient way to determine the settlement without detailed stress or water pressure distributions.The paper by Maurice A. Biot presents a general theory of three-dimensional consolidation, focusing on the settlement of soils under load. The author assumes that the soil is composed of particles bound together by molecular forces, forming an elastic porous medium with water-filled voids. The process of consolidation is described as the gradual adaptation of the soil to the applied load, which involves the squeezing out of water from the voids. Biot derives the mathematical equations that govern the behavior of the soil, including the stress, strain, and water content. The number of physical constants necessary to describe these properties is determined, and the equations are simplified for practical applications. The theory is extended to three-dimensional problems and arbitrary load variables, building upon the one-dimensional work by K. Terzaghi. The paper also discusses the physical interpretation of the soil constants, such as Young's modulus, shear modulus, Poisson's ratio, and the coefficients of compressibility and permeability. These constants are crucial for understanding the soil's behavior under different conditions. A standard soil test is used to illustrate the application of the theory, showing that the settlement of a column of soil follows a parabolic curve over time. For completely saturated clay, the initial compressibility is negligible compared to the final compressibility, simplifying the equations and providing a more straightforward solution. Finally, the paper introduces the operational calculus as a powerful method for solving consolidation problems, particularly for complex two- and three-dimensional scenarios. This method simplifies the calculations and provides a more efficient way to determine the settlement without detailed stress or water pressure distributions.
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Understanding General Theory of Three%E2%80%90Dimensional Consolidation